InGaAs/Si avalanche photodiode (APD) employs Si materials with extremely low electron hole ionization coefficients as the multiplication layer, which to some extent solves the problem of high equivalent noise. However, its manufacturing involves ion implantation of Si charge layer and high-temperature annealing activation, which features a complex process, uneven impurities distribution, and high cost. We propose the utilization of etching technology to prepare groove rings in the Si multiplication layer and fill different media in the groove rings to modulate the electric field in the InGaAs layer and Si layer, thus building a charge-free layer InGaAs/Si APD device model. The results indicate that filling the groove ring with air or SiO₂ can achieve high-performance InGaAs/Si APD. Finally, theoretical guidance can be provided for the subsequent development of InGaAs/Si APD with simple processes, stable performance, and low noise.

We propose to adopt etching technology to prepare a groove ring within the Si multiplication layer and fill different media inside the groove ring to modulate the electric field in the InGaAs layer and Si layer, which helps build a charge-free layer InGaAs/Si APD device model. Firstly, the changes in APD optical and dark current with different media are simulated. The changes in recombination rate and carrier concentration are simulated to explore the reasons for the changes in optical current. Secondly, the energy band changes of the APD are simulated to further understand the reasons for electron concentration changes. Thirdly, the changes of charge concentration, impact ionization rate, electric field, and other parameters with different media are simulated. Finally, the gain, bandwidth, and gain-bandwidth product of APD are simulated, and a comparison of different media shows that filling with the air can yield the best device performance.

The overall trend of optical current and dark current decreases with the increasing dielectric constant of the medium (Fig. 2). As the dielectric constant of the medium rises, the recombination rate decreases in the InGaAs absorption layer, Si multiplication layer, and Si substrate, consistent with the trend of optical current variation (Fig. 3). The conduction band of APD has no band order at the bonding interface, while the valence band at the interface has obvious band orders, making it difficult for carriers to transport at the interface and a large number of holes to accumulate at the interface (Fig. 5). The ionization coefficients of electrons and holes in the absorption layer slowly increase, while the ionization coefficients of electrons and holes in the multiplication layer further decrease, which is consistent with the trend of electric field changes (Fig. 7). As the dielectric constant increases, the electric field strength in the multiplication region gradually reduces, which weakens the carrier impact ionization effect and decreases the gain (Fig. 8). When the bias voltage is 35 V, the gain-bandwidth product basically shows a downward trend with the increasing dielectric constant of the medium. Additionally, when the medium inside the groove ring is air and the reverse bias voltage is equal to the avalanche voltage (35.2 V), the gain-bandwidth product reaches 100 GHz (Fig. 11).

We investigate the effect of filling different media in the Si multiplication layer groove ring on the charge-free layer InGaAs/Si APD. The results show that as the dielectric constant of different media increases, both optical current and dark current present a decreasing trend under the same bias voltage. The InGaAs/Si APD with air or SiO₂ as the dielectric materials finally overlaps with the optical current and dark current after reaching the avalanche voltage, exhibiting the best current characteristics. As the dielectric constant of the medium rises, the gain-bandwidth product shows a downward trend under the same bias voltage. After the device avalanche, the gain-bandwidth product exhibits a trend of first increasing and then decreasing. When the medium inside the groove ring is air and the reverse bias voltage is 35.2 V, the gain-bandwidth product reaches 100 GHz. In summary, replacing the charge layer with a groove ring to construct a charge-free layer InGaAs/Si APD does not require ion implantation, and the process is simple. Meanwhile, filling the groove ring with air can yield the best device performance, and this new configuration provides a new idea for designing high-performance InGaAs/Si APD with simple processes.

As an important tool for quantum optical measurement, the balanced homodyne detector (BHD) is highly sensitive to the amplitude and phase of the incident light. It can reliably extract quantum fluctuations, suppress classical common-mode noise, and amplify quantum fluctuations to the macro level. Additionally, it has been widely employed in quantum noise measurement, gravitational wave detection, high-sensitivity interferometric timing measurement, continuous variable quantum key distribution, and quantum random number generator. The common-mode rejection ratio (CMRR), operating bandwidth, and signal-to-noise ratio (SNR) of the detector have been the research focuses. The optical frequency comb contains a large number of equally spaced longitudinal modes, which is a good multi-mode resource. The spectrum width of the optical frequency comb is in the order of nanometers. The quantum optical frequency comb which breaks the limit of shot noise can be generated by nonlinear processes. Quantum optical frequency comb has a great application prospect in quantum precision measurement. Spectrally resolved balanced homodyne detection is an important detection method of quantum optical frequency comb. We analyze the noise source of the balanced homodyne detector theoretically and design the multi-pixel balanced homodyne detector (MBHD) based on photodiode array and multi-channel inductance-capacitance (L-C) coupled transimpedance amplifier (TIA) circuit. These designs enable MBHD to meet multi-channel parallel and high-SNR quantum noise measurements.

The MBHD consists of two highly symmetrical multi-pixel photodetectors (MPDs) and a multi-channel subtracter (Fig. 1). Each MPD includes a photodiode array, a multi-channel L-C coupled structure, AC amplification, and DC amplification. The photocurrent generated by the corresponding pair of pixels in the two MPD flows through their respective AC amplification outputs, and the common-mode signal in the detection result is eliminated by the subtracter to complete the multi-pixel parallel balanced homodyne detection. Multi-channel DC output monitors the optical power of all pixels by a multi-function data acquisition card (DAQ). In the amplification circuit structure of the single pixel in MPD, the generated photocurrent signal is divided into DC signal and AC signal through the L-C coupled circuit. The AC signal is converted into a voltage signal by a TIA and is further adopted to measure the intensity noise power of the incident light. The DC signal is converted into a voltage signal by a load resistor and a isolation amplifier. Additionally, an equivalent noise model is built to analyze the electronic noise. Due to the multi-channel parallel structure of the MBHD, each channel is similar to each other and independent. The electronic noise of the single-pixel channel includes the noise generated by the dark current of the photodiode, the thermal noise generated by the feedback resistance in the transimpedance amplifier circuit, the noise generated by the input voltage noise of the transimpedance amplifier, and the noise generated by the input current noise of the transimpedance amplifier. Theoretical analysis shows that a reasonable selection of feedback resistance and inductance, photodiode with low dark current and low junction capacitance, and the TIA with low input noise can reduce the electronic noise of the detector. Meanwhile, the L-C coupled structure is better than the R-C coupled structure in experimental conditions (Fig. 2).

The device is constructed to test the performance of MBHD (Fig. 3). AC output of MBHD is connected to a spectrometer to measure the bandwidth and SNR. The DC signals of each pixel are measured by a DAQ to monitor the optical powers of each pixel. When the optical power is distributed on all pixel channels, the distribution of the shot noise power in each channel is proportional to the distribution of the incident optical power, which verifies that the multi-pixel BHD can achieve spectrally resolved multi-channel parallel balanced homodyne detection (Fig. 4). When the incident optical power is 1.660 mW, 0.834 mW, 0.418 mW, 0.208 mW, and 0.102 mW respectively, the shot noise spectrum and electronic noise spectrum of one pixel are measured at different analysis frequencies (Fig. 5). The test results show that the 3 dB bandwidth of MBHD is 5 MHz. The resolution bandwidth is set to 100 kHz, the video bandwidth is 100 Hz, and the number of averaging times is 10. When the incident optical power is 1.660 mW, the shot noise power is 23 dB higher than the electronic noise power at the analysis frequency of 2 MHz. By comparing the shot noise power under different incident optical power, the shot noise power decreases by 3 dB when the incident optical power decreases by half, which indicates that the detector has a good linear gain within 0.102 mW to 1.660 mW of the optical power.

Based on the noise model of the BHD, the electronic noise source is analyzed theoretically. The results indicate that the L-C coupled structure is better. By adopting the multi-pixel photodiode array and L-C coupled structure, a high-performance multi-pixel BHD is developed. In each pixel channel, when the 815 nm laser with optical power of 1.660 mW is incident, the shot noise power is 23 dB higher than the electronic noise at the analysis frequency of 2 MHz. By employing the grating to scatter the incident light horizontally, the shot noise power in each channel is proportional to the incident optical power. It is verified that the multi-pixel BHD can realize the spectrally resolved multi-channel parallel balanced homodyne detection. The detector provides a high-performance detection tool for quantum precision measurement based on quantum optical frequency comb.

The fiber optic microwave frequency transmission technology is based on the loopback method to detect and suppress fiber optic noise. Under the adoption of existing communication fiber links, the frequency transmission stability can reach 10^-18/d-10¹⁹/d, which meets the remote transmission and comparison of current microwave atomic reference frequency standards, with broad application prospects. At present, most of the solutions are point-to-point master-slave station transmission structures, and in many application scenarios, it is necessary to deliver a reference frequency source to multiple users (multiple access), and even add a midway download point in the transmission fiber link, such as square kilometer array (SKA), radio telescope array, and very-long-baseline interferometry (VLBI). The high-precision ground-based time service project undertaken by the National Time Service Center, Chinese Academy of Sciences includes the construction of a thousand-kilometer level fiber optic microwave frequency transmission network, which employs the unique electrical phase compensation transmission scheme of the center. As a supplement to the backbone transmission network, the local frequency distribution network needed for the future is constructed, and a set of multi-access transmission and mid-download equipment schemes compatible with the existing system is designed to enhance the regional service capability of the high-precision ground-based timing system. As a result, the standard frequency signal in the backbone network can reach the client within 100 km of the urban node to complete the local frequency signal distribution task of the city node.

The system diagram of multi-access fiber microwave frequency transmission technology is shown in Fig. 1, where TX is the common transmitting end and RX1-RXN are multiple receiving ends, or there are multiple addresses. At the transmitter TX, the reference signal is modulated onto the laser carrier by a Mach-Zehnder modulator (MZM) and an external modulation. Then, by adopting a fiber splitter, the signal light is divided into N channels and transmitted to N addresses respectively. Firstly, a principle analysis of microwave frequency transmission technology of multi-access fiber is carried out to show the feasibility of the experimental scheme. Then the experimental verification is carried out in the laboratory: the 2 km fiber spool and 50 km fiber spool are connected by the 2×2 fiber coupler, and the beam splitting ratio of the fiber coupler is 9∶1. After the 50 km fiber spool, the fiber dispersion compensation fiber of the corresponding length is fused to reduce the dispersion effect in the fiber link.

By utilizing the above experimental design and device link, Symmetricom 5125A is adopted to measure the residual phase noise at the receiving end of the multi-access fiber optic microwave transmission technology. The results are shown in Fig. 6. The phase noise spectrum of the 7.5 GHz signal at the receiving end is greatly optimized via phase noise elimination of the scheme. Meanwhile, the stability of multi-access fiber microwave transmission technology is measured by phase comparison method. The voltage signal is tested by digital multimeter 3458A according to the test block diagram in Figs. 4 and 5. The results are shown in Fig. 7. The frequency stability of the remote 7.5 GHz signal is 3.5×10^-14/s and 1.2×10^-17/10⁵ s. The stability of mid-download is 4.1×10^-14/s and 6.5×10^-17/10⁵ s. In the process of multi-access fiber microwave frequency transmission technology, the unidirectional erbium-doped fiber amplifier (EDFA) is employed to amplify the optical power, which will increase the asymmetry in the fiber link and affect the propagation stability of the system. Due to the nonlinear effect of devices, nonlinear effects inevitably occur during signal processing, which affects the phase detection accuracy. To avoid the influence of nonlinearity, we adopt 1.875 GHz and 3 GHz as the propagation frequencies. Signals at 1.875 GHz and 3 GHz do not have harmonic overlap and cannot generate intermodulation components of similar frequencies.

We propose an fiber optic microwave frequency transmission system with multi-access frequency transmission and midway download, which adopts different optical wavelengths to transmit microwave signals and thus avoid the effects of parasitic reflection and backscattering of signal light. The scheme has two main features. Firstly, the link noise compensation is implemented in the receiving end by electrical phase compensation method, and the fiber optic link is compensated for due to temperature noise disturbance caused by external environmental changes such as stress. Secondly, the dispersion compensation fiber in the transmission system is also placed at the receiving end to compensate for the dispersion impact in the fiber link. The stability of remote frequency transmission is 3.5×10^-14/s and 1.2×10^-17/10⁵ s, and that of mid-download is 4.1×10^-14/s and 6.5×10^-17/10⁵ s. The index of multi-access fiber optic microwave frequency transmission system can meet the requirement of microwave atomic frequency signal long-distance transmission in various applications, with a wide application prospect.

The resonant fiber optic gyroscope (RFOG) represents a cutting-edge generation of fiber optic inertial devices, leveraging the Sagnac effect within a fiber optic ring resonator. It gauges the angular velocity of external rotation by measuring the resonant frequency difference of light beams traveling clockwise and counterclockwise in the fiber optic ring resonator. In comparison to interferometric fiber optic gyroscopes, the RFOG offers advantages such as reduced length, compact dimensions, minimal thermal nonreciprocal noise, heightened detection accuracy, a wide dynamic range, and superior theoretical accuracy. Nevertheless, the progress of RFOGs is constrained by noise factors such as polarization fluctuations, the optical Kerr effect, and Rayleigh backscattering within the resonator. To address these limitations, the broadband source-driven RFOG emerges by mitigating parasitic noise through its low coherence. However, the current challenge lies in detection noise, particularly relative intensity noise (RIN), serving as the primary impediment to accuracy. Consequently, there is a pressing need to formulate a comprehensive theoretical model for RIN in broadband source-driven RFOGs. Such a model serves as the foundational framework for devising various schemes aimed at suppressing RIN, thereby advancing the precision of these gyroscopes. We fulfill this need by establishing a theoretical model grounded in the spectral width of the broadband source and resonator parameters.

Regarding our need to construct a theoretical model for RIN in a broadband light source-driven RFOG, we choose an amplified spontaneous emission (ASE) with a center wavelength of 1550 nm as light source (Fig. 1 and Fig. 2). The power spectral density of the system is comprehensively analyzed to delineate the spectral alterations induced by the resonant cavity's characteristics in response to RIN (Fig. 5). To ascertain the primary contribution of the existing RIN, we employ the random walk method, which is visually depicted in Fig. 6. The validity of our theoretical model is subsequently corroborated through practical measurements involving the RIN spectrum across varying spectral ratios of the resonant cavity, and the Allan variance is assessed for diverse laser spectral widths (Fig. 8 and Fig. 9). These experimental validations solidify the reliability and applicability of our proposed theoretical framework.

In the broadband source-driven RFOG, an ASE with a center wavelength of 1550 nm serves as the light source. The sensing device is a 500 m fiber ring resonator with a diameter of 12 cm. Experimental measurements of the RIN spectrum for the resonator with different splitting ratios and the Allan variance for varying laser spectral widths are presented in Fig. 8 and Fig. 9. Notably, the observed RIN spectrum aligns closely with the theoretical predictions, validating the accuracy of our proposed model. Crucially, our results demonstrate that increasing the laser spectral width is beneficial for enhancing the angle random walk performance of the gyroscope. This observation underscores the practical significance of our theoretical framework and suggests a promising avenue for optimizing gyroscope performance through spectral width modulation. These findings provide valuable insights into the field, emphasizing the potential for improved gyroscope precision through strategic adjustments to laser spectral characteristics.

We construct a theoretical model of RIN in RFOGs driven by a broadband source. The model here proposed considers the effects of laser spectral width and resonator parameters simultaneously, making it more realistic. Power spectral density analysis of the transmission process of RIN in the gyroscope system is performed, and the influence of different system parameters on the RIN in the RFOG driven by a broadband source is obtained. A large laser spectral width and a high-precision resonator with high-frequency modulation can effectively reduce the influence of RIN. The establishment of this theoretical model provides a basis for suppressing RIN in RFOGs driven by broadband sources.

As an innovative multiple-input-multiple-output (MIMO) technology, optical spatial modulation (OSM) resolves antenna interference and synchronization challenges in MIMO systems by selecting a single antenna to carry information and collectively transmits the antenna index as additional information. However, existing OSM research predominantly adheres to the orthogonal transmission criterion, and imposes limitations on enhancing the transmission rate of the system although the research is effective in avoiding inter-symbol interference. To this end, the introduction of non-orthogonal transmission via Faster-Than-Nyquist (FTN) technology compresses symbol intervals during pulse shaping, enabling an increase in transmission rate within the same bandwidth per unit time. As a result, we propose a novel Faster-Than-Nyquist rate optical spatial pulse position modulation scheme that combines OSM with FTN to further enhance the transmission rate and spectrum efficiency of the system. Additionally, in response to the highly complex receiver issue, a multiclassification neural network (MNN) decoder is proposed to significantly reduce computational complexity and achieve approximate optimal detection.

At the transmitting end, the input binary bit stream is divided into two groups of data blocks after serial/parallel transformations. The first group of data blocks is mapped to the index of the selected lasers for each symbol period, while the second group is mapped to pulse position modulation (PPM) symbols. An FTN shaping filter is employed to compress the PPM symbols. Then, the compressed PPM-FTN signals are loaded onto the chosen lasers for transmission. The signal traverses the Gamma-Gamma channel, and it is received by photodetectors (PDs) and converted into an electrical signal for further signal processing at the receiving end. Initially, downsampling is conducted to obtain a signal with the same dimensionality as the input signal. The downsampled signal is then classified based on its effective features, with each class being assigned the corresponding label. Subsequently, different samples with varying signal-to-noise ratios (SNRs), along with their associated label values, are utilized as input and output for offline training of a neural network model. The objective is to achieve optimal decoding accuracy by defining average loss and learning rate parameters to construct an MNN, which helps determine the number of hidden layers and neurons. Finally, the well-constructed MNN is employed for online signal detection. Then, inverse mapping is conducted on output label values from the decoder to recover the corresponding modulation symbols and laser index.

Monte Carlo simulations are conducted to evaluate the proposed scheme in a Gamma-Gamma channel. We first derive an upper bound of the average bit error rate (ABER) of the system and provide a comparison of the simulated BER with the ABER in Fig. 3. The results show that the two curves asymptotically coincide at high SNRs, which demonstrates the correctness of the derived ABER. Then, an analysis is performed on the influence of various parameters such as the number of lasers, the number of detectors, and modulation order on the error performance of the OSPPM-FTN system. The findings reveal that an increase in these parameters can enhance both the transmission rate and BER performance of the system, despite at varying costs. Furthermore, in Fig. 5, we compare the transmission rate, spectrum efficiency, and BER performance of the proposed system with traditional OSPPM. The results indicate that under the acceleration factor of 0.9, compared to the OSPPM system, the proposed system shows a 17% increase in spectrum efficiency and a 5.5% increase in transmission rate with only 1 dB SNR lossy. As the acceleration factor decreases from 0.9 to 0.7, the spectrum efficiency and transmission rate of the OSPPM-FTN system rise by 73% and 21.5% respectively. Thus, the proposed scheme demonstrates a significant improvement in both transmission rate and spectrum efficiency with the reduction of the acceleration factor. Through the comparison with the maximum likelihood (ML) algorithm, Figs. 7 and 8 illustrate the computational complexity reduction and BER performance of the proposed MNN decoder. The results show that the MNN decoder achieves near-optimal decoding performance, and as the detectors increases, the computational complexity of the MNN decoder is significantly lower than that of ML. For instance, when there are 8 or 16 PDs, our decoder can reduce computational complexity by 69.75% and 89.95% respectively.

A Faster-Than-Nyquis rate optical spatial pulse position modulation scheme is proposed by combining optical spatial pulse position modulation with the FTN technique, which effectively improves the transmission rate and spectrum efficiency of the system. Compared to traditional optical spatial modulation, simulation results show that the proposed scheme achieves a significant improvement in transmission rate and spectrum efficiency with the decreasing acceleration factor. Simultaneously, increasing the modulation order, the number of lasers, and the number of detectors can improve the transmission rate and error performance of the system. However, the cost associated with each parameter varies, and the selection of these parameters should be contingent on specific circumstances. Additionally, the MNN decoder proposed for the OSPPM-FTN scheme achieves near-optimal decoding performance while substantially reducing computational complexity. It is noteworthy that this advantage is particularly pronounced in large-scale MIMO systems.

Optical fiber directional coupler can realize beam coupling and splitting, which is one of the most important passive devices in the optical fiber communication system after the optical connector. In recent years, with the wide application of various high-capacity wavelength division multiplexing (WDM) communication networks, the bandwidth characteristics of optical fiber directional couplers are facing great challenges. As a practical product, the fabrication technology of optical fiber couplers based on the melt-drawing cone process is very mature and has the advantages of good directionality, high-temperature stability, and low cost. However, due to the strong dependence of the beam-splitting ratio on the operating wavelength, most of the current optical fiber directional couplers operate at specific wavelengths and have narrow bandwidths. The advent of photonic crystal fibers (PCFs) makes it possible to design fiber couplers with higher performance. Compared with traditional fiber couplers, PCF-based couplers have the advantages of low wavelength dependence, short coupling length, and low insertion loss, and they have become a hot spot in related research fields. Among them, the dual-core PCF-based directional coupler has been reported in many experimental and theoretical studies. However, most researchers usually give the structure and parameters of the designed coupler directly and do not make a more detailed summary and generalization of the specific rules of parameter design. If the specific rules of PCF parameter design are summarized in detail, it can provide a meaningful reference for the efficient design of broadband optical fiber directional couplers.

In a dual-core fiber, each core region can be considered as an independent optical waveguide, and the optical field energy conducted within each core is affected by the other core and changes periodically with the length of the coupling region. According to the coupling theory, it can be seen that for two parallel lossless optical waveguides, the internal optical field energy can be expressed by Eqs. (1) and (2), respectively. Eq. (3) indicates that when the two waveguides and their nearby spatial structure and material are consistent, the effective coupling coefficient is equal to the coupling coefficient. When the two waveguides and their nearby spatial structure or material are inconsistent, the effective coupling coefficient will be greater than the coupling coefficient, in which case there will be no specific interaction length so that the incident light field energy can be completely into the coupling arm. At this point, by changing the fiber structure parameters, the effective coupling coefficient can be adjusted without changing the interaction length, and then the desired coupling ratio can be obtained near the center of the target wavelength range with a shorter interaction length. In this paper, the coupling characteristics of the coupler structure under different fiber structure parameters are simulated by using the beam transmission method to obtain the variation of the optical field energy in the structure with the transmission distance. For the determined fiber structure, the variation curves of the optical field energy in the straight through arm and the coupling arm satisfy Eqs. (1) and (2), respectively. Specifically, I₁ and I₂ are functions of the variable L and the unknown constants κ and δ, which exactly satisfy the applicable conditions for estimating the constants using the least squares method. Since the beam transmission method can provide a sufficiently large number of simulation data points, Eq. (5) is overdetermined, and the equations can be solved by curve fitting using the trust-domain reflection algorithm. After κ and δ are obtained using the least squares method, the difference in transmission constants between the cores of the dual-core PCF fibers at this point can also be obtained from Eq. (3).

The influence of structural parameters on the inter-core coupling efficiency in dual-core PCF fibers is discussed in detail. According to the analysis results of Fig. 6, it can be seen that changing the hole spacing and air hole symmetry can realize the coarse adjustment of the coupling region length; changing the air hole symmetry can realize the coarse adjustment of the maximum coupling ratio; changing the core refractive index difference, the central air hole diameter ratio, and the core diameter ratio can realize the fine adjustment of the coupling region length and the maximum coupling ratio. To verify the above theory, we design a broadband 50∶50 coupler containing 1310 nm and 1550 nm with ±5% coupling ratio. We find that the designed structure has the largest bandwidth value of 240 nm while satisfying the design requirements when L=3000 μm, d₂=1.8 μm, and d₀=0.51 μm. It can be seen from Fig. 8(a) that the coupling ratios of the two arms for wavelengths from 1310 nm to 1550 nm can all fall between 45% and 55%. The additional loss of the structure and the insertion loss of the straight through arm and the coupling arm with wavelength are shown in Fig. 8(b). The insertion loss of the designed structure is not higher than 0.2 dB, and the insertion loss of both arms is around 3 dB.

In this paper, the influence of various parameters on the coupling efficiency between cores of a dual-core PCF is analyzed by using the beam transmission method, and the coupling coefficient and other parameters between waveguides are estimated by using the least squares method according to the principle of dual-core coupling. It makes clear that in a dual-core PCF, each structural parameter regulates the coupling ratio and the length of the coupling region. By summarizing the specific rules of parameter design in detail, the coarse and fine-tuning design methods for the coupling performance of dual-core PCFs are proposed. Then, an asymmetric dual-core PCF broadband directional coupler is designed according to the proposed design method, and the coupling ratio and coupling zone length of the designed coupling structure are coarse-tuned and fine-tuned by adjusting the symmetry of the air holes and the diameter of the central air holes, respectively, enabling the coupler to achieve a coupling ratio of 50%±5% in the interval of 1. 31-1.55 μm, a bandwidth of 240 nm, and an ultra-short coupling length of 3 mm. The research results can provide a meaningful reference for the efficient design of broadband optical fiber directional couplers.

With the rapid development of technologies such as the Internet and artificial intelligence, the demand for data in various fields of life is growing exponentially. However, the capacity of traditional single-mode fiber (SMF) networks is approaching the Shannon limit. Therefore, various multiplexing technologies including wavelength division multiplexing (WDM), polarization multiplexing (PDM), and mode division multiplexing (MDM) have been explored to meet the growing demand for data. In MDM, FMF fibers for long-distance transmission have lower nonlinear losses than multi-mode fibers, which makes it more cost-effective. Additionally, MDM introduces severe crosstalk among different modes, which should be compensated for by advanced DSP algorithms at the receiving end. We propose a crosstalk correlation ratio measurement method based on signal correlation peak extraction to address the channel crosstalk caused by mode coupling in MDM systems. The crosstalk correlation coefficient is applied to the correlation peak ratio multi-input-multi-output constant modulus algorithm (CPR-MIMO-CMA) to improve channel equalization performance. An SMF optic transmission experimental platform is built, and the CPR-MIMO-CMA is utilized to process the data from the receiving end to verify the algorithm superiority. The experimental results show that the proposed algorithm has a significant improvement in both convergence speed and balancing effect compared to traditional CMA, and is expected to be employed in future high-capacity FMF transmission scenarios.

Firstly, we model and calculate the coupling mode equation and coupling coefficient, and derive the expression of the coupling coefficient in FMF and also the relationship between the signal correlation peak and it. Then, the FMF transmission system is built using simulation software. The signal generation end of the system is responsible for generating repetitive and misaligned digital signals. Then, the mode laser generator generates LP01 mode and LP11 mode optical signals, which are modulated by 16QAM and enter the FMF link. The FMF adopts a segmented simulation structure, and the two signals at the receiving end are processed with digital signals to obtain XT-CPR. It performs multiple changes in fiber length and coupling strength, recording data to explore the relationship among XT-CPR, coupling strength, and propagation distance. To verify the performance of the CPR-MIMO-CMA, we also build a third mock examination transmission experimental platform. At the transmitting end of the experimental system, firstly the software generates a pseudo-random binary sequence with a code length of 2¹⁴, maps it into a 16QAM symbol every four bits, and realizes baseband shaping through root raised cosine (RRC) filter. Meanwhile, the signal is loaded after resampling to an arbitrary waveform generator (AWG) with a sampling rate of 64 GSa/s, and it is converted into two electrical signals to drive the IQ modulator to modulate two groups of optical carriers. The 3 dB bandwidth of the IQ modulator is 29 GHz. The working wavelength of the laser is 1550.1 nm, and the modulated optical signal is amplified by a low noise erbium-doped fiber amplifier (EDFA) before entering a 1×3 coupler. At the same time, to eliminate the correlation between modes, we add LP11 and LP21 optical fibers with delay lines of different lengths and employ a polarization controller to control the polarization state of the signal. The fiber adopts a step type four-mode fiber with a length of 5 km, model FM SI-4, which can transmit up to four modes of optical signals including LP01, LP11a, LP11b, and LP21. Additionally, we employ three channels of LP01, LP11a, and LP21 for experiments. At the receiving end, the multiplexed signal is divided into three channels by the mode demultiplexer and enters the coherent receiver. The relevant image and waveform data are observed and recorded for offline digital signal processing (DSP). In the DSP, the signal is sequentially processed by the RRC low-pass filter, resampling, timing recovery, and the proposed CPR-MIMO-CMA. Then, the blind phase search algorithm is adopted to enter the sampling decision with experimental results observed.

Fig. 6 shows a visual graph of the signal correlation peaks under three modes. According to Formula (11), when other conditions are constant, the larger crosstalk leads to smaller XT-CPR. The height comparison of the correlation peaks in Fig. 6 is basically consistent with the size relationship shown in the reference values of Table 1. Fig. 7 demonstrates a comparison of error rates between traditional equalization and equalization with CPR parameters. The figure indicates that the proposed CPR-MIMO-CMA has a performance improvement of 1.3 dB, 0.9 dB, and 1.0 dB compared to traditional CMA in LP01, LP11, and LP21 channels respectively under the threshold of forward error correction (FEC) of 3.8×10^-3. When the received optical power is low or the signal-to-noise ratio is high, there is not much difference in the effect between traditional equalization and equalization with CPR parameters. This is because the damage caused by noise is much greater than that caused by mode crosstalk. When the received optical power is high, the equalization effect with CPR parameters reaches the best. As the received optical power continues to increase, the equalization effect of the two tends to be similar. At this point, the signal already meets the FEC threshold of 3.8×10^-3. Fig. 8 shows a comparison of the average convergence speed of CPR-MIMO-CMA and the traditional CMA for processing the data at the receiving end of the third mock examination transmission system. This figure reveals that the proposed CPR-MIMO-CMA has a faster convergence speed, and the average convergence time under the three modes is reduced by about 50%.

We propose a crosstalk equalization method based on signal correlation peaks, which combines mode coupling theory and signal correlation peak theory to eliminate the randomness error of traditional crosstalk measurement, making the algorithm have a better mode equalization effect. A third mock examination transmission experimental platform is built, on which the feasibility and accuracy of the method are verified. The BER performance and convergence speed of CPR-MIMO-CMA based on signal correlation peak and traditional CMA equalization are compared. The results show that the method can effectively equalize mode crosstalk, and the performance of this method is improved by 1.3 dB, 0.9 dB, and 1.0 dB respectively compared with traditional equalization in LP01, LP11, and LP21 channels. Meanwhile, the average convergence time in the three modes is reduced by about 50%.

Coherent optical communication technology possesses a significantly higher communication rate and receiver sensitivity, which has been applied in fiber optic networks and space optical communication by researchers. Compared with the optical fiber channel, the space atmospheric channel possesses significant randomness and fluctuation, and the relative motion between the terminals will introduce an additional Doppler frequency shift. Thus, the frequency offset and phase noise of the space optical communication systems are characterized by a large fluctuation range and a fast-changing rate. Traditional coherent optical communication systems realize carrier synchronization mainly by reference light method, optical phase-locked loop method, and digital signal processor (DSP) open-loop carrier synchronization method. However, it is difficult to implement the reference light method in space atmospheric channels with a large dynamic range. The tuning rate of the optical phase-locked loop method is slow, leading to poor performance. Besides, these two methods will lead to a more complex system. An open-loop synchronization scheme is recommended by researchers, although there is phase ambiguity when an open-loop synchronization scheme is used in large dynamic link conditions. Therefore, the optimization of open-loop synchronization schemes is of great significance for meeting the needs of different space optical communication applications. We aim to develop a carrier synchronization algorithm to solve the phase ambiguity problem of coherent optical communication systems with a large frequency offset and large phase noise and to provide a competitive carrier synchronization method for space coherent optical communication systems. We believe that this will be helpful for the development and application of space coherent optical communication technology.

Considering the simple implementation and small computation of the Mth power carrier synchronization algorithm, we realize the carrier synchronization algorithm by optimizing the Mth power carrier synchronization algorithm. The principle of the Mth power carrier synchronization algorithm is analyzed, and the regular phase ambiguity is found, namely that the phase ambiguity can be treated as one of the M situations. It should be noted that both the actual frequency offset ambiguity and phase noise ambiguity are randomly distributed in the M situations. The adopted enumeration method is simple and effective. To decrease the computation of the procedure as much as possible, the unwrapping phase ambiguity procedure is combined with the frame synchronization process. In the unwrapping phase ambiguity procedure, different combinations of frequency offset ambiguity and phase noise ambiguity are tried until the frame synchronization is successful. The different combinations can be tried in parallel to improve signal processing speed. The carrier synchronization algorithm is applied in free-space dual polarization-quadrature phase shift keying (DP-QPSK) coherent optical communication systems to verify the effectiveness.

A DP-QPSK free-space coherent optical communication simulation system is built in OptiSystem, and frequency offset and phase noise are characterized by changing laser frequency and linewidth. Also, a DP-QPSK free-space coherent optical communication experimental system is built between two buildings 600 m apart. The simulation and experimental results show that our carrier synchronization algorithm is effective for DP-QPSK coherent optical communication systems, and the error vector magnitude (EVM) value of the carrier synchronization constellation is always less than 15% (Figs. 7, 10, and 11). Besides, the quality of demodulation constellation is independent of frequency offset, phase noise, and modulation parameters, and the bit error rate is 0% (Fig. 8). In the experimental system, comparative analysis of our carrier synchronization algorithm and Mth power carrier synchronization algorithm is carried out. Although it is a fact that the demodulation constellation EVM values using the Mth power carrier synchronization algorithm are almost the same as our carrier synchronization algorithm, but the bit error rate will be up to 37.5% or 25% when the Mth power carrier synchronization algorithm is applied directly. Thus, it is essential to unwrap phase ambiguity for space coherent optical communication applications.

We propose an unwrapping phase ambiguity carrier synchronization algorithm for the free-space coherent optical communication system. To verify the effectiveness of the carrier synchronization algorithm, we build a free-space DP-QPSK coherent optical communication simulation system and experimental system with different frequency offsets and phase noises. Our carrier synchronization algorithm requires correlation operations of the frame synchronization process to be implemented multiple times, whose mathematical expectation is M2/2. However, once the modulation format of the system is determined, the operational logic of the unwrapping phase ambiguity process is fixed. Thus, the unwrapping phase ambiguity process can be operated in parallel to improve signal processing speed. Besides, the frequency offset and phase noise compensation range of the proposed carrier synchronization algorithm are not constrained by the modulation rate and modulation order of the coherent optical communication system. A higher modulation order system needs to increase the implement times of correlation operations in the frame synchronization process, while the carrier synchronization effect is almost not influenced. The carrier synchronization algorithm may be applied to future coherent optical communication systems with a higher communication rate and modulation format.

Based on the physical principle of the heterodyne laser Doppler vibration measurement process, we analyze the measurement process of high-frequency and low-speed movement in the presence of low-frequency and high-speed background movement. In the process, the measurement noise generated by the presence of stray light exhibits chirp characteristics, with the effects and patterns of chirp noise explained. In response to the chirp noise, we propose a derivative preprocessing method for demodulation. The theoretical analysis shows the method exerts a significant effect on suppressing chirp noise, which is verified by simulations and experiments. Meanwhile, we set a heterodyne laser Doppler vibration measurement system with stray light and measure the target vibration. The normal method and derivative preprocessing method are adopted respectively for demodulation. The experimental results verify the existence of chirp noise and the effectiveness of the derivative preprocessing method in suppressing chirp noise, which decreases the chirp noise power by about 81.8%. The method can effectively reduce the influence of stray light on vibration measurement.

Heterodyne laser Doppler vibration measurement technology is a widely adopted non-contact and non-destructive movement measurement method, with the advantages of fast response speed and high resolution. It has a strong detection ability for single frequency movement and can quickly identify the characteristic frequency of target movement. However, in the presence of low-frequency high-speed background movement, the measurement of high-frequency low-speed movement is severely affected by chirp noise, which is caused by stray light and closely related to low-frequency high-speed background movement. The chirp noise can seriously affect the measurement of high-frequency low-speed movement, with errors even reaching tens of times larger than those of real movement. There is a lack of research on the principle of chirp noise caused by stray light and suppression methods of chirp noise. We deeply analyze the principle of chirp noise caused by stray light and propose a novel demodulation method called the derivative preprocessing method (DPM). This demodulation method is easy to implement and exhibits a good effect for suppressing chirp noise. This demodulation method is expected to provide a reliable noise suppression method for measuring high-frequency low-speed movement in the presence of low-frequency high-speed background movement. This plays a significant role in analyzing high-frequency vibration modes of precision devices in some special measurement scenarios, such as in the presence of background movement.

Our study consists of theoretical analysis, simulation, and experimental verification. Firstly, the working principle and demodulation method of the heterodyne laser Doppler vibration measurement system, which is in the presence of stray light, are deeply analyzed. According to the analysis, the stray light would generate chirp noise in the process of normal demodulation method (ARCTAN). Based on the generation and characteristics of the chirp noise, a new demodulation method DPM is proposed. Then, the influence of chirp noise on the measurement of target movement velocity and the effect of DPM on chirp noise suppression are simulated. In the simulation, a low-frequency sinusoidal movement is utilized as the background movement, while a high-frequency sinusoidal movement is employed as the target movement. In the simulation, the background movement generates corresponding chirp noise to affect demodulation results severely. The normal demodulation method DPM is leveraged to restore the target movement by demodulating the overall movement and performing high-pass filtering. Finally, a heterodyne laser Doppler vibration measurement experiment is conducted to utilize a piezoelectric ceramic plate fixed on the pendulum device. In the experiment, the piezoelectric ceramic plate vibrates at a single and high frequency, which is regarded as the target movement, and the pendulum's movement is considered as the background movement. According to the experiment results, the existence of chirp noise is verified, and the DPM suppresses the chirp noise too.

In the process of the normal demodulation method (ARCTAN), the cause of chirp noise is the combination of stray light and background movement. The frequency of chirp noise changes in real time with the background movement speed, and specifically, it is proportional to the absolute speed of background movement and inversely proportional to the laser wavelength (Formula 11). When the background movement is low-frequency high-speed movement and the target movement is high-frequency low-speed movement, the chirp noise will seriously affect the measurement of high-frequency part movement [Fig. 2(b)]. Compared with the normal demodulation method, DPM can effectively restore target movement [Fig. 2(c)], but will generate erroneous velocity spikes in the positions that are near zero speed locations. Since adopting the normal demodulation method's results to partly replace the demodulation results of the DPM at the corresponding positions (near zero speed locations), the velocity spikes can be suppressed, and the demodulation results approach target movement more closely. In the experiment, the background movement of the pendulum indeed generates corresponding chirp noise [Figs. 4(a) and (b)], and DPM can effectively suppress the chirp noise [Fig. 4(c)]. DPM has a significant suppression effect on chirp noise, which reduces the power of chirp noise by about 81.8% at the peak of the chirp noise (Fig. 5).

The principle of heterodyne laser Doppler vibration measurement is deeply analyzed. It is pointed out that chirp noise is generated due to stray light and background movement. The frequency of the chirp noise changes in real time with the background movement speed, which is proportional to the absolute background movement speed and inversely proportional to the laser wavelength. Simulations and experiments have confirmed the existence of chirp noise and its frequency variation pattern. A novel demodulation method DPM has been proposed for this type of chirp noise. Simulations and experiments prove that DPM can effectively suppress chirp noise. Above the target movement frequency, the chirp noise power can be reduced by about 81.8%.

As devices can change the relative delay time of reference light and detection light in optical detection systems, optical delay line (ODL) is widely employed in terahertz time-domain spectroscopy (THz-TDS), optical coherence tomography, ultrafast time resolution spectroscopy, and pump-probe technique. In particular, ODL is adopted to scan and detect THz-TDS signals by changing the relative delay of femtosecond and terahertz (THz) pulses in THz-TDS. As such, ODL is a key component that affects the accuracy, signal-to-noise ratio, and spectral resolution of THz signals. In the THz-TDS system, the ODL nonlinearity directly affects the accuracy and consistency of the sampling signal of the THz-TDS system. The nonlinear delay time change leads to the nonlinear actual sampling interval of the system, which brings the nonlinear change in the optical path of the femtosecond laser pulses (FLP) and thus causes the line position error of the THz spectrum. The greater nonlinear error of the THz sampling signal results in more severe distortion of the collected THz signals and greater difficulty in subsequent data processing. Therefore, it is urgent to solve the nonlinear problem of various rotating optical delay line (RODL) delay time. We design a fast rotating optical delay line (FRODL) composed of multiple turntable reflection surfaces (TRSs) and construct a polarized Michelson interference system. Based on the actual calibration results of the total delay time and delay time interval of the FRODL structure, nonlinear error calibration of the actual delay time of FRODL is achieved.

We first design a FRODL composed of multiple TRSs and analyze the structure and working principle of FRODL. Then, the feasibility of the FRODL optical path is further verified, and the optical path structure of FRODL at different rotation angles is simulated to obtain the theoretical working angle of FRODL. Combined with the theoretical mathematical model of FRODL, the theoretical delay time of FRODL is obtained, and the theoretical nonlinearity is fitted using the least squares method. Then, considering the signal ratio of the excitation signal, a fiber optic coupling structure is adopted. Based on the coupling power fluctuations during the actual coupling process of FRODL, the actual working range of FRODL is determined. Then, a polarization Michelson interferometer measurement system is built, and the delay time and delay time interval generated by the actual rotation angle of the TRS on each side of the FRODL are calibrated multiple times to obtain the average delay time of the TRS on each side of the FRODL. Additionally, the least squares method is adopted to fit the nonlinear error size and actual nonlinearity of the actual delay time interval. Finally, we also build the THz-TDS system, collect the THz signal under FRODL operation, and utilize the cubic spline interpolation algorithm to calibrate the nonlinear error of the THz signal.

The designed FRODL structure consists of a turntable, a coupling lens, a focusing lens, and a planar reflector (Fig. 1). The simulation results show that the theoretical working range of FRODL is [-2.5°, 2.5°] and the theoretical delay time can reach 43.522 ps. The fitted ideal delay time is 43.465 ps, and the sensitivity of the ideal delay time to rotation angle is 8.693 ps/(°). The theoretical nonlinearity of FRODL is 0.304%, which means the linearity can reach 99.696% (Fig. 3). The calibration results of the polarization Michelson interferometer measurement system show that the average delay time of TRS is 43.504 ps, and the ideal delay time after fitting is 43.522 ps, with a small difference between the two values. The nonlinear error of the FRODL target sampling interval is 52.724% less than 0.05 ps, and there is a nonlinear error of 47.276% with a sampling interval exceeding 0.05 ps. The maximum nonlinear error is 0.094 ps, and the actual nonlinearity of FRODL is 0.215% (Fig. 6). Finally, by adopting cubic spline interpolation twice, we obtain the actual delay time of FRODL is matched with the sampling point signal and the calibrated THz equally spaced time-domain waveform (Fig. 7).

We provide a design concept for FRODL and verify by simulation and experiments that the working angle of the FRODL structure can reach 5°. Based on polarization Michelson interference calibration technology, the actual delay time of FRODL is tested. The experimental results show that the delay time of the FRODL is greater than 43.5 ps, and the maximum error of the FRODL before calibration is 0.094 ps, with a linearity of 99.785%. To address the nonlinear errors in THz waveform acquisition in the THz TDS system, we employ the cubic spline interpolation method to obtain the actual delay time corresponding to the encoder angle of each TRS sampling point. By recording the actual delay time corresponding to the encoder angle position, the nonlinearity of the THz sampling signal is calibrated. The FRODL delay time error after calibration is determined by the error accuracy of the cubic spline interpolation algorithm. By leveraging cubic spline interpolation to perform equidistant interpolation on the calibrated non equidistant time-domain THz waveform, the spectral transformation error of the non-equidistant time-domain THz waveform is solved. The calibrated equidistant time-domain THz waveform not only maintains the accuracy of time-domain THz signal sampling but also has spectral accuracy.

Fresnel high magnification focused photovoltaic/thermal system has the advantages of a high concentration ratio, small footprint, low lens processing cost, etc., and it has a broad application prospect in the field of solar electric and thermal utilization, but the accumulation of dust particles on its mirrors leads to the reduction of the system's thermal and electrical efficiency. The current study focuses on two points. One is the effect of the settling law of the accumulated dust particles and their particle size distribution on the concentrating effect, and the other is the effect of the dust density on the mirror surface on the electrical and thermal output characteristics of Fresnel high magnification focused photovoltaic/thermal system. Accumulated dust affects the Fresnel lens transmittance, which in turn weakens and disperses the distribution of concentrating solar energy flow on the surface of photovoltaic cells and reduces their power output. Therefore, it is necessary to effectively remove the accumulated dust. Specific strategies should be adopted for the physical and chemical properties of the accumulated dust, such as the inclination angle and wind speed of the wind blade in wind power dedusting, as well as the configuration and selection of cleaning agents in water jet cleaning. There are many different types of dust on the mirror surface, and it is necessary to prioritize the removal of the accumulated dust that has the greatest impact on the electrical energy output. In view of the geographical characteristics and the influence of anthropogenic activities and the composition of naturally accumulated dust particles at the test site, in this study, six kinds of particle samples such as calcite, albite, marble, loess, coke, and coal gangue are selected as the research objects, so as to analyze the correlation of the influence law of the physicochemical nature of the accumulated dust particles on the Fresnel high magnification focused photovoltaic/thermal system, provide a theoretical basis for the prediction of the law of dust accumulation in a specific region and the electrothermal output characteristics of the Fresnel high magnification focused photovoltaic/thermal system after dust accumulation, and direct the cleaning of the dust on the mirror surface of the Fresnel concentrator.

The research is mainly carried out by experimental methods. First, an X-ray diffraction analyzer, energy spectrometer, and scanning electron microscope are used to study the particle morphology, material, and elemental composition. Second, the powder is uniformly arranged on the surface of the lens by means of artificial dusting, and the density of accumulated dust is 1, 3, and 5 g/m². The output characteristic test of the Fresnel high magnification focused photovoltaic/thermal system is carried out to analyze the influence of different accumulated dusts on the electrothermal output. Finally, the grey correlation method is used to process the experimental data and analyze the influence of the physicochemical properties of the accumulated dust on the comprehensive performance of the Fresnel high magnification focused photovoltaic/thermal system.

From the material composition, the main component of coal gangue is ferrous oxide, with a content of 56.30%. The main component of albite is calcareous albite, with a content of 42.38%. The main components of calcite and marble are magnesium calcium carbonate, and the contents are 94.55% and 89.12% respectively. The main component of coke is silicate, with a content of 46.08 %. The main component of loess is silica, with a content of 51.48% (Fig. 4). In view of the element composition, calcite and marble are the same, mainly composed of oxygen elements. Albite is mainly composed of oxygen and silicon. Coal gangue is mainly composed of oxygen, calcium, and silicon. The carbon content in coke is the highest, about 80%. The main components of loess are oxygen and silicon (Fig. 5). Coal gangue and coke accumulation of dust particles have a great influence on the electric power of Fresnel high magnification focused photovoltaic/thermal system. When the dust accumulation density is 1, 3, and 5 g/m², the corresponding electrical efficiency of the coal gangue decreases by about 26.7, 30.1, and 33.9 percentage points, and that of the coke decreases by about 29.3, 30.1, and 33.1 percentage points compared with the clean state (Fig. 7). Compared with the cleaning system, the thermal efficiency of coal gangue and loess dust particles decreases significantly. When the dust density is 1, 3, and 5 g/m², the corresponding thermal efficiency of coal gangue decreases by about 17.0, 30.6, and 42.2 percentage points, while that of loess decreases by about 19.9, 30.1, and 42.4 percentage points (Fig. 9). The comprehensive correlation degree of CaMg(CO₃)₂, CaCO₃, SiO₂, and Fe₂O₃ with electrical power exceeds 0.68, and thermal power exceeds 0.62, showing a strong correlation (Fig. 10). The correlation degrees of particle elements O, Al, Ca, and Mg with the electrical and thermal power of the Fresnel high magnification focused photovoltaic/thermal system all exceed 0.71, showing a strong correlation (Fig. 11).

From the perspectives of particle morphological features, material composition, element composition, and proportion, the physicochemical properties of six typical dust particles on the concentrator mirror are investigated, and it is found that the shapes of different types of dust particles are different; the material composition of the dust particles is complex, and the types of element composition are more varied. The rocky dust particles have more dolomite, albite, and calcium carbonate. The highest content of elemental O is found in the particles, except for the coke. Mg, Si, and Ca elements also appear more frequently. A comparison test of Fresnel high magnification focused photovoltaic/thermal system shows that all kinds of accumulated dust have different impacts on the thermoelectric output, in which the coal gangue in the mirror surface dust increases by 1 g/m², and the gangue dust particles corresponding to the comprehensive performance of the Fresnel high magnification focused photovoltaic/thermal system decreases by 15%. All kinds of accumulated dust have the most serious impacts on the system's electro-thermal performance. The composition of the material affects the electrical power (E) and thermal efficiency (T) of the Fresnel high magnification focused photovoltaic/thermal system in the following order: ESiO2>EFe2O3>ECaCO3>ECaMg(CO3)2 and TSiO2>TCaCO3>TFe2O3>TCaMg(CO3)2, and the elemental composition has the same effect on the electrical and thermal outputs (P), with the following order: PO>PAl>PCa>PMg>PFe>PSi>PC. The results of the study provide a reference for predicting the electrothermal performance of the Fresnel high magnification focused photovoltaic/thermal system in a specific area of dust accumulation and provide a basis for the de-dusting of the Fresnel condenser mirror surface.

Terahertz filter is an important functional device for realizing terahertz imaging, terahertz communication, and other terahertz application technologies, and in-depth study of terahertz filters plays a great role in promoting the development of terahertz technologies. Therefore, the design of terahertz filters with a wide range of adjustable center frequency, sensitive bandwidth adjustment, deep modulation depth, simple structure, and multi-band transmission performance has become an urgent problem. In this study, a metamaterial terahertz band-stop filter based on two intersecting split-ring resonance (TI-SRR) is designed. It can effectively expand the bandwidth adjustment range, adjust the center frequency, reduce the transmittance, and make the stopband attenuate rapidly. At the same time, it has multi-band filtering and is easy to fabricate and process. The metamaterial terahertz band-stop filter has high application value in the field of new communication equipment and precision instruments.

In this experiment, the effect of each parameter on the performance of the filter is investigated by varying the line width, inter-ring spacing, and radius size of the TI-SRR. The transmission coefficients of the filter under each parameter are compared, and the design scheme with the best performance is summarized. The electric field and surface current distributions at the three resonance points of the metamaterial band-stop filter are analyzed, so as to investigate the working mechanism of the filter. In order to verify the calculation results of the theoretical model, physical samples of the filter are prepared by micro-nanolithography and tested using a terahertz time-domain spectroscopy (THz-TDS) system. The results of the actual measurement and simulation are compared to find the cause of the error.

Simulation experiments are carried out on several parameters of the metamaterial terahertz band-stop filter, while other parameters are kept unchanged. When the line width w gradually increases from 2 to 14 µm, the filter's first stopband bandwidth increases from 0.190 to 0.253 THz, and the relative bandwidth radually increases from 44.98% to 54.33%. The bandwidth range increases, and the center frequency is shifted to the high-frequency direction, while the filter's modulation depth deepens. However, as the line width increases, the resonance in the ring is strong, and clutter appears at high frequencies. The line width w is selected to be 10 µm (Fig. 2). When the spacing m gradually increases from 10 to 40 µm, the first stopband bandwidth of the filter decreases from 0.238 to 0.227 THz, and the relative bandwidth gradually decreases from 52.44% to 44.51%. The bandwidth of the filter decreases slightly, and the adjustment of the spacing allows the filter bandwidth to be adjusted precisely. The transmittance of the filter is gradually increasing, which is not favorable to the performance of the band-stop filter. Therefore, smaller spacing indicates a better filtering effect. However, as the spacing m decreases, the resonance in the ring becomes stronger, and clutter occurs at high frequencies. The spacing m is selected to be 10 µm (Fig. 3). When the outer radius R₁ gradually increases from 56 to 68 µm, the inner radius R₂ gradually increases from 56 to 58 µm, and the first stopband bandwidth of the filter increases from 0.222 to 0.261 THz. The relative bandwidth increases from 47.65% to 61.34%, and the effective bandwidth of the filter increases. The filter performance transmittance is reduced within the effective bandwidth, and the filter performance is improved. However, with the gradual increase in the radius, the filtering effect of the third resonance point becomes worse, and the outer radius R₁ is selected to be 60 µm after comprehensive consideration (Fig. 4). The physical samples of the filter are prepared by micro-nano lithography (Fig. 10). The measured results are shifted at each resonance point compared with the simulation, and the measured stop-band suppression effect is not as good as that of the simulation. Especially, the gap is obvious at the high frequency, but the overall curve trend remains consistent.

In this study, a terahertz band-stop filter based on metamaterials is designed to optimize the performance of the filter by varying the metal line width, inter-ring spacing, and metal open-ring radius, and the optimal design is concluded. The working mechanism of the filter is analyzed based on the electric field and surface current distributions of the terahertz filter. The physical filter samples are prepared by micro-nano lithography and tested by the THz-TDS system. Test results are comparable with the simulation results considering the errors in the test process. The band-stop filter has the advantages of a simple structure, adjustable center frequency, fine-tunable bandwidth, wide range adjustment, low stopband transmittance, and deep modulation depth.

After decades of development, mode-locked fiber lasers can provide laser pulses with high coherence, high pulse energy, and controllable pulse width and repetition rate. Mode-locked pulsed lasers can play a key role in some specific research areas. For instance, in biomedicine, lasers are used as light sources to perform coherent tomography imaging and the information of the samples under test can be collected and recorded at the same time. However, in the process, the signals of some substances with similar excitation wavelengths can interfere with each other, thus affecting the measurement results. Therefore, the development of wavelength tunable mode-locked lasers to improve spectral resolution is of great significance to the research in this field. We study the rapid tuning of the center wavelength of a narrow-spectrum passive mode-locked ytterbium fiber laser based on fast acousto-optic filtering technology. Combining fast acousto-optic filtering technology, we obtain a stable mode-locked pulse with a center wavelength tuning function. To investigate the reconstruction process of laser pulses during intracavity filtering and confirm the reliability of this technology, we record the real-time reconstruction process of laser pulses during the tuning of the center wavelength. We hope that our research can provide a reliable solution for applications requiring high spectral resolution.

The laser consists of a laser cavity and a two-stage amplifier. The fiber cavity consists of a semiconductor saturable absorption mirror (SESAM), a wavelength division multiplexer (WDM), a 40 cm long ytterbium-doped fiber (CorActive Yb406, YDF), a 90∶10 fiber coupler (90∶10 OC), a collimator, and a λ/2 waveplate (HWP). It is composed of acousto-optic tunable filter, reflect mirror, and piezoelectric ceramic transducer (PZT). The piezoelectric ceramic is combined with a mirror to lock and stabilize the output laser repetition rate by adjusting the length of the phase-locked loop feedback. The phase-locked loop is composed of a photodetector (PD), an RF amplifier, a bandpass filter, a mixer, a signal source, a low pass filter, and a proportional integral derivative (PID). The voltage intensity of the externally modulated signal can alter the intracavity pumping energy. The rising edge of the modulated signal can be recognized by the acousto-optic tunable filter driver and used to switch the filter wavelength. The arbitrary waveform generator drives the acousto-optic tunable filter and laser semiconductor with the edited modulation signal, such that the center wavelength of the laser can be tuned at high speed while maintaining the mode-locked state. To explore the pulse conversion process in the cavity during wavelength switching, a part of the laser after the first stage amplification is fed into the dispersion compensation fiber, and the stretched optical signal is converted into an electrical signal through a photodetector and transmitted to a high-speed oscilloscope. The real-time observation of the laser pulse reconstruction process can be realized by generating signals through the external arbitrary signal generator, and simultaneously modulating the pump working current of the cavity and the wavelength switching of the acousto-optic tunable filter.

The parameters of the laser are tested (Figs. 2 and 3), and the wavelength tuning ability and frequency stability of the laser are verified (Fig. 4). The phase noise and time jitter of the locked pulse are significantly improved. The time jitter of the locked laser is 9.58 ps, and the phase noise at 10 Hz is -72 dBc/Hz. The information on the pulse reconstruction process of the laser in the state of high pump power and the operation of the single pulse after adjusting the external modulation signal is recorded (Figs. 5 and 6). The information shows the pulse reconstruction time and spectrum of the wavelength tuning process. The spectral stability and the highest wavelength tuning speed can be defined. Also, the result of the dispersive Fourier transform test proves that by editing the external modulation signal to change the internal pump energy of the laser cavity and the filtering band of the acousto-optic tunable filter, a reliable mode-locked fiber laser with high-speed tuning of the center wavelength can be obtained.

We study the rapid tuning of the center wavelength of a narrow-spectrum passive mode-locked ytterbium fiber laser based on fast acousto-optic filtering technology. The narrow-spectrum mode-locked fiber laser system has an output power of 200 mW, a pulse width of 5.87 ps, a repetition rate of 40.874 MHz, and a spectral bandwidth of 0.15 nm. By programming the RF signal to drive the acousto-optic tunable filter, a stable mode-locked pulse with a center wavelength tunable in the range of 1016-1042 nm can be obtained. To investigate the reconstruction process of laser pulses during intracavity filtering, we employ the dispersive Fourier transform technology to visualize the real-time reconstruction process of laser pulses during the tuning of the center wavelength, and the results confirm that the highest central wavelength tuning frequency of the laser is about 5 kHz.

Dual-energy computed tomography (DECT) is a medical imaging technology that provides richer tissue contrast and material decomposition capabilities by simultaneously acquiring X-ray absorption information at two different energy levels, and it is increasingly widely used. In DECT, based on the energy absorption differences of different materials, the scanning objects can be decomposed into different base material components, such as bone and soft tissue. However, accurate decomposition and reconstruction of base material images remain a challenging problem due to factors such as noise, artifacts, and overlap. Therefore, we aim to improve the quality and accuracy of base material decomposition in DECT imaging. Current base material decomposition methods may have some limitations in complex scenarios, such as the failure to accurately decompose overlapping materials, vulnerability to noise interference, and poor image quality. To solve these problems and improve the properties of base material decomposition, a new base material decomposition method is proposed in this study.

We aim to improve the quality and accuracy of base material decomposition in DECT images. To achieve this goal, we propose a method based on the multi-channel cross-convolutional UCTransNet (MC-UCTransNet), which is performed by fitting the mapping function in DECT. The network is designed to be a double-in-double-out architecture based on UCTransNet. During training, with the real decomposition image as labels, a pair of double energy images as input, and its concating into the form of multi-channel, our multi-channel network structure aims to realize the information exchange between two material generation paths in the network. The channel cross-fusion converter and channel cross-attention module are used to improve the decomposition of base materials, realizing double-input-double-output and end-to-end mapping. Further, the channel cross-fusion module and the channel cross-attention module can better capture the complex channel correlation to more fully conduct feature extraction and fusion and realize the information exchange between the generation paths of base materials. To improve the model fitting performance, the network is trained using a hybrid loss. Meanwhile, in order to better adapt to the particularity of CT image data, the model uses the normalization method based on the Sigmoid function to preprocess the network input data and improve the model fitting performance.

In order to verify the decomposition accuracy of each method, we not only compare the base material images decomposed by various methods but also reconstruct the base material images to the low energy image, and we compare them with the original low energy image. By obtaining the difference map to intuitively feel the decomposition effect of each method, the experimental results show that the proposed method is able to obtain images of water and soft tissue. Compared with the contrast method, the decomposed images perform better in accuracy and noise contrast suppression. Meanwhile, the results of the ablation experiments also demonstrate the attention mechanism, the mixed loss, and the effectiveness of the Sigmoid normalization method in this task. The introduction of the attention mechanism enables the network to better capture the information of key features in the image and improves the accuracy of decomposition. The mixed loss function of mean absolute error (MAE) and structural similarity index measure (SSIM) is used to improve the network decomposition effect and performance. In addition, the application of the Sigmoid normalization method can better adapt to the particularity of CT image data. On the premise of maintaining the distribution characteristics of the data, the interference of abnormal data to the model can be reduced, and the stability and accuracy of the model can be improved. The loss and peak signal-to-noise ratio (PSNR) values of the proposed method are superior in both the training and validation sets, with fast convergence and good stability, as well as a good decomposition effect on different test sets, showing strong generalization ability. This indicates that the dual energy-based MC-UCTransNet method has high utility in the base material decomposition task of DECT imaging.

We aim to improve the quality and accuracy of base material decomposition in DECT, and remarkable progress is made by proposing a dual material decomposition method based on MC-UCTransNet. Our study innovatively adopts the MC-UCTransNet network to integrate multi-channel cross-convolution with cross-attention mechanism modules to better capture the correlation among complex channels and realize information exchange between generation pathways of base materials. Moreover, the multi-channel cross structure avoids the use of multi-network for high and low energy information extraction, which makes the network model more convenient. In addition, we further improve the fitting performance of the model by the use of mixed loss and normalization methods based on the Sigmoid function. The experimental results show that the proposed method can ensure a promising improvement in water bone-based material and soft tissue iodine-based material decomposition tasks.

In optical coherence tomography angiography (OCTA), the applications of decorrelation mapping, primarily reliant on intensity data, have caught significant attention. However, this method is particularly vulnerable to the deleterious effects of noise, especially in fields characterized by low signal-to-noise ratios (SNRs). Noise artifacts have a pronounced effect on static tissue signals, which makes them exhibit elevated decorrelation between frames and in turn tends to overlap with the high decorrelation values associated with blood flow signals. This overlap detrimentally affects the quality of microvascular image acquisition. Meanwhile, classical techniques for refining decorrelation mapping, such as frequency-domain decorrelation angiography, still struggle to yield optimal results due to this inherent challenge. In response to the spurious static voxel artifacts, some studies have resorted to employing thresholding to eliminate static voxels falling below a predefined threshold. However, the global and indiscriminate nature of such thresholding often lacks a robust theoretical foundation, making the precise suppression of static voxel artifacts a complex endeavor. To this end, we present a novel OCTA approach that incorporates considerations of SNR and dynamic threshold adjustments. This innovative method is further combined with spectral analysis principles to provide a more precise means for the identification and suppression of static voxels. The ultimate objective is to enhance the microvascular imaging quality, thereby serving as a more dependable foundation for medical diagnostics.

We introduce a method for spectral amplitude decorrelation, which features dynamic threshold adjustments based on local SNRs. The methodology commences with an in-depth exploration of the complex relationship between local image SNRs and static voxels, including a comprehensive analysis of the various factors influencing this association. Subsequently, spectral analysis techniques are employed to mitigate artifacts arising from axial motion and accentuate the visualization of blood flow data. Built upon the established connection between local image SNRs and static voxels, our approach proposes adaptive thresholds for each voxel to ensure precise differentiation between dynamic and static voxels. Voxels exhibiting decorrelation values below the established threshold are categorized as static ones and subsequently suppressed. Conversely, voxels surpassing the threshold are identified as dynamic ones and are retained. Meanwhile, we further employ a sigmoid function to apply non-linear mapping to all voxels, thereby facilitating a seamless transition at the boundary between dynamic and static voxels. After the suppression of static voxels, an averaging process is applied to the decorrelation images, which allows us to reconstruct enface microvascular images by the mean projection technique. Additionally, we have established a dedicated posterior segment SS-OCT system to collect retinal data from volunteers. The effectiveness of our algorithm is rigorously validated via the data, and we conduct comparative experiments with other classical intensity-based OCTA methods to comprehensively assess its performance.

In comparison to the conventional decorrelation mapping approach, the retinal blood flow cross-sectional images processed by our algorithm exhibit prominent blood flow signals, whereas the conventional method's results are largely submerged within the noise emanating from static tissue (Fig. 6). This disparity highlights that the SSADA algorithm affected by noise-induced interference in individual spectral amplitude decorrelation images produces lower-quality enface microvascular images after averaging. In contrast, our algorithm effectively suppresses the noise arising from static voxels within individual spectral amplitude decorrelation images, ultimately yielding high-quality enface microvascular images. Compared to other intensity-based OCTA techniques, our proposed algorithm demonstrates superior performance across both high SNR skin data and low SNR retinal data, with the same preprocessing, target extraction, and image registration protocols employed. For skin data, the enface microvascular images obtained by our algorithm exhibit an SNR enhancement of approximately 4 dB in contrast to the SSADA method without static voxel suppression (Fig. 5). In the case of retinal data, our algorithm produces enface microvascular images with significantly improved contrast ratio, achieving a contrast enhancement of 0.0182 compared to the SSADA method without static suppression (Table 1).

We conduct a systematic examination of the intricate relationship between local SNRs and the decorrelation values of static voxels in OCT structural images. The results show that as noise levels on voxels increase, static voxels exhibit higher decorrelation values. Based on this pivotal finding, we introduce a dynamic threshold adjustment method within the context of spectral analysis. This combined approach adeptly leverages the sensitivity of decorrelation mapping to subtle differences and the efficacy of spectral analysis in mitigating artifacts stemming from axial motion. The retinal enface microvascular images produced by our algorithm adeptly differentiate capillaries in proximity to the macular region, underscoring the algorithm's competence in effectively suppressing static voxel noise within microvascular images. Furthermore, our algorithm consistently delivers favorable outcomes in retinal data characterized by low SNRs, resulting in enhanced image contrast ratio and superior vessel visibility. This enhancement has great potential in improving disease diagnosis and evaluation, contributing to more precise medical assessments.

In recent years, death and economic losses caused by respiratory diseases have occurred globally, with a significant portion of respiratory disease patients facing challenges related to delayed early detection and inadequate treatment in later stages. With the advancing medical technology, numerous studies have demonstrated a close association between the volume fraction of human fractional exhaled nitric oxide (FeNO) and respiratory disease. In normal individuals, airway epithelial cells produce a small amount of nitric oxide (NO), with volume fractions generally below 2.5×10^-8. However, in patients with respiratory diseases, inflammatory cells in the airways produce a large amount of NO, with volume fractions generally 2-10 times higher than those in normal individuals. FeNO detection is a non-invasive, simple, rapid, and efficient method for exhaled breath diagnosis. It can be employed to differentiate respiratory diseases with similar clinical presentations, such as asthma, chronic obstructive pulmonary disease (COPD), and overlapping syndromes. Additionally, it can predict treatment outcomes and post-treatment management for patients with these conditions. FeNO detection provides information that cannot be obtained from medical history, physical examinations, and lung function tests alone, and it contributes to improving the diagnosis and treatment of respiratory diseases, elevating the clinical management of respiratory diseases to a new height.

For FeNO detection, we utilize tunable diode laser absorption spectroscopy (TDLAS) technology, which is known for its high sensitivity, precision, and fast response rate. The fundamental theory of TDLAS is based on Beer-Lambert's law that when light passes through a certain volume fraction of gas, gas molecules absorb light at specific wavelengths. The relationship between the emitted light intensity and incident light intensity can be directly adopted to establish the relationship between the signal magnitude and gas molecule volume fraction. Direct absorption spectroscopy (DAS) directly applies this law. Due to the susceptibility of DAS to low-frequency noise such as interference fringes, wavelength modulation spectroscopy (WMS) is a commonly adopted method to suppress low-frequency noise. The basic principle of a WMS involves the combination of a low-frequency triangular wave signal and a high-frequency sine wave signal generated by a signal generator. These signals are introduced into the laser to drive both scanning and modulation of the laser wavelength, and the laser is directed into the gas absorption cell, interacting with gas molecules. The detector receives the laser light after the interaction and converts the optical signal into an electrical signal, and the lock-in amplifier demodulates it into a harmonic signal. The relationship between the harmonic signal and gas molecule volume fraction is established by gas calibration.

We calibrate the exhaled carbon dioxide (CO₂) volume fraction within a single exhalation cycle using both DAS and WMS (Figs. 4 and 5). By simulating the second harmonic signals of mixed gases of CO₂ and NO, we determine correlation coefficients to achieve the inversion of FeNO volume fraction (Figs. 6 and 7). By a 15-minute continuous measurement of the volume fraction changes of mixed gases of CO₂ and NO, and Allan variance curve analysis, the system's CO₂ gas measurement precision and detection limit are determined to be 0.045% and 5.4×10^-3 [Figs. 8(a) and 10(a)] respectively. For NO, the measurement precision and detection limit are found to be 1.1×10^-9 and 3.4×10^-9 [Figs. 8(b) and 10(b)], respectively. By repeatedly replacing mixed gases of CO₂ and NO with nitrogen (N₂) and measuring the gas volume fraction changes over time, the system's response time is determined to be 12 s (Fig. 9). Finally, based on the gas curve during a single exhalation cycle at an exhalation flow rate of 3 L/min, the volume fractions of CO₂ and NO in the exhaled breath of 18 volunteers are determined (Figs. 11 and 12).

We establish a FeNO detection system based on TDLAS, with the selected target absorption line for NO at a wavenumber of 1900.07 cm^-1. Experimentation is conducted with NO at a volume fraction of 4.76×10^-6 under a pressure of 0.3 atm, and 46 mV is chosen as the optimal modulation amplitude. DAS and WMS are adopted to calibrate the CO₂ volume fraction. By simulating the second harmonic signals, we calculate the relationship between the signals of CO₂ and NO, completing NO volume fraction calibration. Precision, response time, and stability of both CO₂ and NO are analyzed to evaluate the system performance. Through Allan variance analysis, within an integration time of 25 s, the system's detection limits for CO₂ and NO are determined to be 5.4×10^-3 and 3.4×10^-9 respectively. Finally, an analysis of different stages of the complete exhalation cycle in adults is conducted to calculate the concentrations of CO₂ and NO, and 18 volunteer samples are processed and analyzed. Experimental results demonstrate the feasibility of using a mid-infrared quantum cascade laser (QCL) for low-concentration measurement of NO, providing references for real-time online detection of human exhaled gases.

For current nonlinear physical systems, nonlinear optical fibers serve as a mature nonlinear experimental platform in experimental science. As a type of nonlinear wave with periodic evolution or periodic distribution structure, breathers have become one of the research hotspots in nonlinear optical systems. As the demand for long-distance and high-capacity fiber optic communication increases, the dynamic properties of breathers are receiving increasing attention. Studying the breather solutions for the AB system is of great significance for better understanding long-distance transmission without shape changing in fiber optic communication. In the context of the periodic solution of the AB system, we focus on the breathers of the system. By studying the interactions between two breathers, it is found that the collision between breathers is elastic, which means that breathers can be transported over long distances without changing their shapes. The results obtained in this article will help to understand the dynamics and interactions of breathers under periodic backgrounds in nonlinear optics.

Via the Darboux transformation method in soliton theory, multi-breather solutions for the AB system were constructed under the elliptic function background. With the help of Matlab software, the spatiotemporal structure of the breathers was plotted, and the nonlinear dynamic characteristics of these breathers were further analyzed. Firstly, elliptic function solutions of the AB system were solved by the modified squared wave (MSW) function approach and the traveling wave transformation. Then, we obtained the basic solution to the Lax pair corresponding to the seed solution to the Jacobi elliptic function. Based on the elliptic function transformation formulas and the integral formulas, the potential function solution could be expressed in terms of the Weierstrass elliptic function. Secondly, by the once-iterated Darboux transformation, three types of breather solutions under the elliptic function background were constructed including the general breather (GB), the Kuznetsov-Ma breather (KMB), and the Akhmediev breather (AB). In addition, we analyzed the dynamic behaviors of these three kinds of breathers and presented their three-dimensional spatiotemporal structures. By the twice-iterated Darboux transformation, the spatiotemporal structure of the interaction between a GB and a KMB under the dn background was investigated, as well as the interaction between two GBs under the cn background.

As an important integrable model, the AB system can be used to describe various nonlinear phenomena in many physical fields such as the quantum field theory, weak nonlinear dispersive water wave, and nonlinear optics. It is meaningful to solve various types of solutions of this model to describe the propagation of nonlinear waves. As far as we know, the breather solutions for the AB system have not been constructed under the elliptic function background. In the context of the periodic solution to the elliptic function in the AB system, the basic solution to the Lax pair of the system is obtained using the MSW function. Using the Darboux transformation method, multiple breathers are constructed under the elliptic function background. Based on the expressions of the breather solutions, the dynamic characteristics of three types of breathers are discussed, including the GB, the KMB, and the AB (Figs. 1 and 2). Finally, the spatiotemporal structure of the interaction between a GB and a KMB under the dn background is investigated (Fig. 3), as well as the interaction between two GBs under the cn background (Fig. 4). It is found that collisions between breathers are elastic, which means that breathers can be transmitted over long distances without changing their shapes. These theoretical research results contribute to exploring the practical physical significance and applications of breathers in nonlinear optics.

Based on the elliptic function formulas, we derive the explicit expressions of the first- and second-order breather solutions under the backgrounds of the dn and cn elliptic functions using the Darboux iteration algorithm. By analyzing the dynamic characteristics of three types of breathers and studying the spatiotemporal structure of multi-breather interactions under the dn and cn backgrounds, we find that the collision of GBs and the collision between GB and KMB in the AB system are both elastic, and the breathers do not undergo any shape change during their propagation. This discovery is of great significance for understanding the propagation characteristics of breathers and further elucidating their ability to complete long-distance transmission without changing their shapes. This research will help to understand the dynamics and interactions of breathers under the periodic background from fluid dynamics to nonlinear optics.

Fractional diffraction effects and various novel phenomena produced by parity-time (PT) symmetric optics systems have become research hotspots in the field of optics. A large amount of theoretical research has proven the existence of the optical soliton in the fractional nonlinear Schr?dinger equation containing PT-symmetric potentials. However, the existence, stability, and dynamics of partially PT-symmetric solitons in non-Hermitian nonlinear optical waveguides with fractional diffraction effect have not been explored yet. The phenomenon and mechanism of spontaneous symmetry breaking of the partially PT-symmetric solitons are still unclear. Meanwhile, the obtained research results provide new insights into the propagation and controlling of the partially PT-symmetric solitons in the non-Hermitian nonlinear optical waveguides with fractional diffraction.

We numerically solve partially PT-symmetric soliton solutions and asymmetric solutions. Specifically, the accelerated imaginary time evolution method is used to solve the stationary fractional nonlinear Schr?dinger equation. Two types of solutions are obtained. The first type is the partially PT-symmetric solitons with real propagation constants, and the second is the asymmetric solutions with complex propagation constants. Then, the solutions of the perturbation are linearized through linear stability analysis, and the eigenvalue problem of the perturbation modes is transformed into the spectral space by using the Fourier collocation method. The spectrum of the eigenvalue problem of the perturbation modes is numerically solved. The propagations of the partially PT-symmetric solitons and the asymmetric solutions are numerically simulated using the split-step Fourier method. Finally, the obtained results are compared with the results of linear stability analysis.

First, two types of solutions are confirmed to exist in the fractional nonlinear Schr?dinger equation with the partially PT-symmetric potential. The first type of solution is the partially PT-symmetric solitons with real propagation constants, and the second type of solution is the asymmetric solutions with complex propagation constants. The results are shown in Fig. 2 and Fig. 3, respectively. Then, the critical power of the symmetry breaking bifurcation point of the partially PT-symmetric solitons is numerically determined and verified with the linear stability analysis, and the results are shown in Fig. 4(c) and Fig. 5(b), respectively. The reduction of the Lévy index from 2 to 1 causes the critical power of the spontaneous symmetry breaking for the partially PT-symmetric solitons to decrease from 1.6 to 0.4. The numerical simulations of the transmissions of the partially PT-symmetric solitons and the asymmetric solutions are shown in Fig. 6, Fig. 7, and Fig. 8, respectively. It is found that the stable partially PT-symmetric solitons obtained by linear stability analysis are robust, as shown in Fig. 6. The amplitude oscillates periodically during the propagations for the unstable partially PT-symmetric solitons in Fig. 7. In Fig. 8, the amplitude and light field distribution of the asymmetric solution change significantly.

In summary, the partially PT-symmetric optical solitons and spontaneous symmetry breaking phenomenon in the fractional nonlinear Schr?dinger equation are numerically studied. The research results show that there exist partially PT-symmetric solitons. The soliton power exceeds the critical value, and the partially PT-symmetric solitons turn into the asymmetric state. The enhanced fractional diffraction effect weakens the stability of the partially PT-symmetric solitons, and then spontaneous symmetry breaking occurs under the smaller soliton power. The critical power of the partially PT-symmetric soliton decreases to 0.409, when the Lévy index decreases to 1. The stable partially PT-symmetric solitons are robust and can be transmitted stably up to 1000 times the diffraction length, even in the presence of the perturbation. The research results of this work may be used to control optical solitons in the non-Hermitian nonlinear optical waveguides with fractional diffraction.

6061 aluminum alloy is widely employed in aerospace, optical manufacturing, and other fields in the production of mirrors due to its high reflectivity, easy machining, and sound stability after forming. However, at present, the surface roughness of aluminum mirrors using grinding and diamond turning machining methods is large, and the diffraction and scattering effects are too serious, which reduces the performance of aluminum mirrors. As an ultra-precision machining technology to obtain high quality surface, chemical mechanical polishing technology has been widely studied in the polishing of aluminum and its alloys. However, due to the presence of Mg₂Si hard particles and other elements in 6061 aluminum alloy, it is difficult to obtain ultra-smooth surfaces at present, and the influence of various parameters on the polishing process is still unclear. To this end, we investigate the influence of the parameters in the polishing solution on the surface quality of 6061 aluminum alloy and optimize a chemical mechanical polishing solution for 6061 aluminum alloy. The polishing solution can remove surface defects and obtain a good surface with a surface roughness of less than 0.4 nm. Therefore, our research can fill the current gap in the ultra-precision machining of 6061 aluminum alloy and contribute to the performance improvement of aluminum alloy mirrors.

Firstly, the chemical mechanical polishing experiments of 6061 aluminum alloy are carried out by single factor control of different oxidant H₂O₂, corrosion inhibitor BTA concentration, and pH from acidity to alkaline in the polishing solution. After polishing, the Zygo interferometer is adopted to characterize the surface morphology and roughness to explore the effect of each parameter acting alone. Then, according to the influence law of each single factor, based on the response surface method (RSM), we set up a three-factor, three-level experiment, and utilize ANOVA to test the effect of degree of each parameter on the surface quality. The surface composition of the aluminum part is measured by an X-ray photoelectron spectrometer (XPS) and the interaction of parameters is analyzed to predict the composition ratio of the polishing solution which can obtain the best surface quality. Finally, atomic force microscopy (AFM) is leveraged to further measure the surface roughness after polishing and evaluate the accuracy of the predicted results.

The surface quality of 6061 aluminum alloy is poor when only abrasive grains and pH alone act (Fig. 4), which helps further reduce the surface roughness after adding a certain concentration of H₂O₂. However, the surface inevitably produces deeper craters (Fig. 6), the surface quality is significantly improved with the addition of BTA, and the surface roughness is reduced to a sub-nanometer scale (Fig. 8). This is because aluminum as an amphoteric metal corrodes severely with both acids with too small a pH and bases with a large pH, and neutral aluminum is difficult to remove as it is too stable. After adding H₂O₂ and BTA, the aluminum first acts with H₂O₂ in a weak alkaline environment to promote the oxidation reaction of aluminum, thus generating Al₂O₃, AlOOH, and Al(OH)₃ oxide layers (Fig. 10). Then BTA forms a passivation film on the oxide layer surface. The raised area on the surface of the aluminum parts makes it easy to contact with the abrasive particles and polishing pad to achieve material removal. However, the pits are protected from excessive corrosion by the passivation film to achieve local ultra-smooth polishing (Fig. 11). Finally, RSM is adopted to optimize the composition ratio of the polishing solution to achieve a balance between oxidation reaction, passivation reaction, and mechanical action during the polishing. The ultra-smooth surface of 6061 aluminum alloy at a close-to-atomic scale is achieved (Fig. 12).

The effects of various parameters on the chemical mechanical polishing of 6061 aluminum alloy are studied and a polishing solution for close-to-atomic scale polishing of 6061 aluminum alloy surface is optimized. The results of single-factor experiments show that 6061 aluminum alloy can obtain the best surface quality when pH is in weak alkalinity, and the surface roughness decreases first and then increases with the rising H₂O₂ and BTA concentration. XPS energy spectra show that H₂O₂ in a certain concentration in the polishing solution can promote aluminum oxidation under the alkaline environment, and BTA can form a passivation film based on the oxide layer to inhibit the oxidation. The optimized polishing solution parameters include a pH value of 9.7, a H₂O₂ mass fraction of 0.57%, and a BTA mass fraction of 1.16%, and the surface roughness of the aluminum mirror decreases from 140 nm to 0.31 nm. The error with the predicted value of RSM is less than 10%, and the ultra-smooth surface close-to-atomic scale is obtained.

Environmental scanning electron microscopes (ESEMs) are widely employed for high-resolution observation of water containing, oil containing, and biological samples in low vacuum environments. However, at present, the development of ESEMs in China is almost blank, and most of them need to rely on imports. Therefore, the research on ESEMs can help improve China's independent development capability in this field, and provide a theoretical and experimental basis for the development of ESEMs in the future. Compared with conventional electron microscopy, the sample chamber of ESEMs should be in a low vacuum or ambient state. The vacuum value is generally on the order of 100 Pa, while that of the electron beam channel and the electron gun needs to be less than 1×10^-3 Pa and 1×10^-7 Pa respectively. The pressure difference between the electron beam channel and the sample chamber is much larger than that between the electron gun and the electron beam channel. The conventional method is to add a throttle tube between the electron beam channel and the sample chamber. Meanwhile, since the large pressure difference remains much greater than that between the electron gun and the electron beam channel, the conventional method is to add a throttle tube between the electron beam channel and the sample chamber, but the large pressure difference will result in a long throttle tube with a small aperture. This will bring practical problems in imaging, such as the longer throttle tube leading to an increase in the working distance of the objective lens. As a result, it increases the spherical aberration, reduces the imaging resolution, and causes a smaller deflection range to a certain extent. Additionally, the long throttle tube will lead to the presence of residual gas inside the tube, the electron beam will drift in a section of the gas space where there is low gas pressure, and the probability of collision between the electron beam and the gas is high, which will have a greater effect on the resolution at low accelerating voltages. Therefore, the comprehensive design of ESEMs, which plays a key role in the system resolution of the objective lens and vacuum differential structure, is the study focus and difficulty.

Starting from the theory of electron optics, we consider the structure of the objective lens and the vacuum differential structure in the ESEM comprehensively. Firstly, two throttle tubes are designed between the sample chamber and the electron beam channel (near the lower pole shoe of the objective lens), and a transition zone is added inside the objective lens to form a three-level vacuum differential structure of the sample chamber, the transition zone and the electron beam channel. The vacuum in the transition zone should be two orders of magnitude higher than that in the sample chamber, and that in the electron beam channel should be two to three orders of magnitude higher than that in the transition zone. Considering the processing cost and difficulty of the elongated throttle tube, we adopt the combination of multiple diaphragms, which can more conveniently change the vacuum level by adjusting the aperture and number of diaphragm sheets in the diaphragm groove to achieve the required differential pressure difference. Then, the optimized design of a high-resolution ESEM objective lens and deflector is carried out based on a double-throttle vacuum resistance structure. Finally, an experimental platform is set up, and the objective magnetic field test, vacuum differential pressure test, and resolution test are carried out for validation.

Considering the objective structure and vacuum differential structure in the ESEM, a double throttle tube vacuum resistance structure as shown in Fig. 2 is designed to form a three-stage differential test structure (Fig. 10). This design can reduce the length of the throttle tube as a whole, which lowers the requirements for the aperture and length of the throttle tube to a certain extent, and thus reduces the influence on the working distance and the deflection field. Meanwhile, it can also reduce the gas residual situation in the narrow throttle tube, and reduce the influence of the electron beam drift in the narrow gas space in the throttle tube. The results of the vacuum differential pressure test show that the vacuum in the transition vacuum zone is two orders of magnitude higher than that in the sample chamber, and the vacuum in the electron beam channel is two to three orders of magnitude higher than that in the transition vacuum zone, which can meet the design requirements. The resolution test results show that in the current experimental conditions and the low vacuum environment mode of 133 Pa, the imaging resolution corresponding to the 20 μm×20 μm scanning field is better than 50 nm, and that corresponding to the 80 μm×80 μm scanning field is better than 100 nm when the working distance is 15 mm (Fig. 13).

Starting from the electron optics theory, we consider the objective lens structure and vacuum differential structure in the ESEM comprehensively, and the two are combined for the optimal design to provide a design method for the objective lens with variable vacuum structures. Systematic analyses, calculations, and simulations are carried out. Based on the theoretical analysis and simulation results, a magnetic field test platform and an ESEM experimental test platform are built for experiments, and the results show that in the current experimental conditions and low vacuum environment mode, the imaging resolution of 20 μm×20 μm scanning field corresponds to a resolution of better than 50 nm when the working distance is 15 mm. The overall closed-loop design and test of the objective lens with variable vacuum structures provide a theoretical and experimental basis for the development of ESEM.

Integrated photonic chip is a key technology that combines laser light sources, modulators, waveguides, detectors, and other photonic devices into a compact, high-bandwidth, low-latency, and energy-efficient package. They hold significant importance in fields such as quantum information processing and optical communication and play a crucial role in the next generation of communication systems and data interconnectivity. The two-photon polymerization technology for three-dimensional micro and nanofabrication has pushed the resolution of laser direct writing (LDW) beyond the limit imposed by optical diffraction to achieve sub-hundred nanometer scales. Meanwhile, it has significant advantages such as simple processing workflow, minimal thermal effect, and low optical threshold damage, which makes it suitable for high-precision, high-density on-chip interconnections. Additionally, the exceptional flexibility of two-photon laser direct writing systems allows for effective adaptation to the varying spatial positions, dimensions, and orientations of interfaces in on-chip interconnections, substantially reducing the requirements for active alignment. In contrast to projection lithography which processes planar structures at one time, on-chip photonic interconnections demand high-precision positioning for the three-dimensional photonic lead at the tips of the waveguides. The writing position accuracy directly influences the signal coupling quality, emphasizing the need for high-precision alignment solutions.

We focus on the research on nanoscale alignment techniques in high-precision laser direct writing for on-chip photonic waveguides. In the context of a two-photon three-dimensional direct writing system (Fig. 1), machine vision and image processing technologies based on guide star nano-alignment are employed. Intelligent recognition and positioning of nano-alignment markers are carried out in Figs. 5 and 6 to enable the definition of the processing area and the establishment of a three-dimensional processing coordinate system. The two-photon laser writing beam is then precisely controlled, aided by a differential confocal system for axial spatial positioning. This approach facilitates the high-precision and high-density 3D direct writing of on-chip photonic lead interconnections within nanoscale structures between waveguides. By enabling intelligent recognition and alignment of specific markers or distinctive graphical features within the direct writing lithography system, the system is equipped with practical functions, including the fabrication of various complex structures. This has significant scientific and practical implications in high-precision processing areas such as chip packaging, multi-material functional structure fabrication, and complex structure modifications.

Due to limitations imposed by the field of view, the two-photon laser direct writing system cannot write photonic leads of approximately 270 μm in length at one time. Consequently, each one is divided into three segments and written separately. Fig. 7(a) displays the result of a single writing operation, and Fig. 7(b) illustrates the combined photonic lead that results from three-time writing. To analyze the alignment accuracy of the photonic lead, we conduct six writing experiments using the writing program, with the results shown in Table 2. The analysis indicates that the algorithm achieves an average alignment accuracy of 29 nm, with a maximum deviation of approximately 50 nm in a single experiment. This ensures sub-hundred nanometer-level alignment precision, which aligns very closely with the theoretically expected accuracy. Among the results, the average angular deviation between the written photonic lead and the silicon waveguide is 0.19°. This alignment level enables the precise writing of photonic lead and fulfills the requirements for high-precision on-chip waveguide connections.

After analysis, the alignment deviation of this algorithm is mainly caused by the optical diffraction limit. Although the edge of visible light with hundreds of nanometers wavelength is blurred under the influence of optical diffraction limit, the algorithm can still achieve the recognition and positioning accuracy of tens of nanometers since the designed nano-guide star is an isotropic square. However, the optical diffraction limit still largely restricts the alignment limit of image processing. Additionally, the pixel size of the image, the measurement error of alignment accuracy, the instability of the equipment and the environment, and the close distance between the alignment marks also limit the alignment accuracy of the algorithm.

We address the nanoscale alignment requirements for on-chip photonic interconnection waveguides in the context of two-photon laser direct writing. Meanwhile, a method is proposed based on guide star digital matching and intelligent nano-alignment to achieve 3D laser direct writing for on-chip photonic lead nanostructures with low cost, high precision, and high density. In response to the background and demand for on-chip photonic interconnection waveguides, we design the optical system structure of the two-photon laser direct writing system. On the hardware side, the unique design of the guide star enables high-precision positioning and writing of photonic leads. On the algorithmic side, machine vision and image processing technologies are adopted for intelligent recognition, matching, and positioning. Differential confocal systems assist in axial alignment, creating a three-dimensional machining coordinate system. This system then controls the direct writing laser beam for high-precision displacement, which helps fabricate photonic leads that connect specific polymer waveguides. The experiments produce photonic leads with an average angular deviation of only 0.19° from the polymer waveguides, achieving an average absolute positional alignment accuracy of 29 nm. Finally, our study holds scientific and practical significance in the fields of high-precision optical on-chip interconnections and complex structure modifications.

The mode splitter is employed in mode division multiplexing systems to separate and guide different modes in a bus waveguide. Traditional mode splitter methods are based on mode conversion processes, where the input higher-order modes are converted into the fundamental mode to separate them from the bus waveguide. This method is suitable for most mode division multiplexing systems, but in scenarios such as signal routing or signal selection, when different modes are separated, they are often switched or selected using multi-mode switches. If the mode splitter output is all in the fundamental mode, additional components should be added after the mode splitter to convert the separated fundamental mode back to higher-order modes before inputting them into multi-mode switches, which undoubtedly increases the system complexity. In the case of optical isolation, it is often necessary to remove the higher-order modes and just transmit the fundamental mode. If the mode splitter output is all in the fundamental mode, it cannot meet the requirements of practical applications. Therefore, if the original modes can be preserved with mode separation achieved, this will greatly simplify the system structure and reduce the system size.

The multi-mode interference (MMI) coupler is a basic silicon-based device, that features a compact structure, low loss, and easy fabrication. However, traditional MMI-based mode splitters are difficult to extend the mode separation function to higher-order modes due to the highly symmetric structure and mode self-imaging principle. This scheme is based on the silicon-on-insulator (SOI) platform. According to the modal analysis method, it is derived that the refractive index distribution in the multi-mode region can not only change the imaging position and shorten the self-imaging length but also separate different input modes. Thermal tuning is achieved by fabricating heaters on top of the waveguide, and the waveguide material refractive index changes with the temperature at a rate of 1.84×10^-4 K^-1 due to the thermo-optic effect. Therefore, by adding micro heaters to the multi-mode region of the MMI, designing the positions of the heaters, and accurately controlling the heating temperature, the separation of three modes, TE0, TE1, and TE2 can be achieved.

The designed structure is a 1×3 MMI, with the input port of the MMI located at the upper left of the multi-mode region, and four heaters are uniformly distributed in the multi-mode region. The optimized size parameters are w=w₃=1.9 μm, w₁=0.9 μm, w₂=0.6 μm, w_taper=w_taper1=w_taper3=4.4 μm, w_taper2=6 μm, w_m=15 μm, and l_m=227 μm (Fig. 6). The heating temperatures of the four heaters for the TE0 mode are 32 ℃, 26.14 ℃, 0 ℃, and 43.42 ℃ respectively, temperatures for the TE1 mode are 7.61 ℃, 0 ℃, 50 ℃, and 17.89 ℃, and those for the TE2 mode are 50 ℃, 50 ℃, 4.89 ℃, and 50 ℃. Under the wavelength of 1550 nm, the insertion losses are 1.03 dB, 1.04 dB, and 1.06 dB for the three modes, the crosstalks are -15.38 dB, -17.5 dB, and -20.4 dB respectively, and all have a 3 dB bandwidth greater than 97 nm (Fig. 8). It is proven that compared with traditional mode splitters, the proposed scheme has a larger number of separated modes, smaller insertion losses, and smaller mode crosstalks. The most outstanding feature is that it preserves the original modes during mode separation, which makes it have a wider range of applications in mode division multiplexing systems. Additionally, by increasing the number of micro heaters and output waveguides, the proposed scheme can achieve the separation of higher-order and more modes.

An MMI-based on-chip mode splitter scheme is proposed to separate the first three TE modes (TE0, TE1, and TE2) and preserve the modes. When the wavelength is 1550 nm, the insertion losses are 1.03 dB, 1.04 dB, and 1.06 dB, and the crosstalks are -15.38 dB, -17.5 dB, and -20.4 dB, with a 3 dB bandwidth greater than 97 nm. Meanwhile, when the temperature deviation is within 2 ℃, the insertion loss of each mode is less than 1.45 dB, and the crosstalkis less than -13.22 dB. Compared with traditional mode splitters based on mode demultiplexers, the proposed scheme can achieve separation without converting high-order modes into fundamental modes, which can greatly reduce system complexity in scenarios such as signal routing or signal selection. As more heaters are added, the proposed scheme can be expanded to separate higher-order modes. At the same time, this mode splitter also has high integration and low process difficulty and can be widely employed in optical communication systems.

Since the first metamaterial perfect absorber was proposed by Landy et al., it has been widely developed due to its potential applications in the fields of microwave radiation measurement, biosensors, thermal emitters, and imaging. Many existing absorbers face the issue of narrow bandwidths, which fail to satisfy the demands of some optoelectronic devices. To solve this problem, it is common to construct different patterns in the same layer or stack multilayer structures with different geometrical dimensions. However, these structures are often complex, and the absorption rate cannot be actively adjusted. Therefore, phase change materials have been introduced to regulate the absorption rate of absorbents, and vanadium dioxide is one of them. There are many absorbers designed with VO₂, but the absorption bandwidth and band number need to be further increased. Therefore, combining the characteristics of multi-band, wideband, and tunable absorption remains a meaningful endeavor.

To effectively study the performance of the absorber, the proposed structure is analyzed by using the microwave simulation software CST Microwave Studio 2020. The metamaterial absorber in this study consists of three layers: the top layer VO₂, the middle layer SiO₂, and the bottom layer Au. When the conductivity is adjusted from 200 S/m to 2×10⁵ S/m, VO₂ will change from an insulator to metal, which can be simulated by input conductivity parameters through the Drude model in CST software. The absorber's absorption can be obtained through one minus the reflection and transmission. Since the penetration depth of the incident wave is smaller than the Au thickness, thus the transmittance is zero. Perfect absorption can be achieved when the reflection is also zero. Material selection and structural design are used to achieve impedance matching, ensuring zero reflection and ultimately realizing perfect absorption of multiple broadbands.

The simulation results show that there are four absorption bands with more than 90% of absorptivity in the range of 0-10 THz, covering bandwidths of 0.87, 0.58, 0.61, and 0.45 THz, respectively. With variations in the conductivity of VO₂, the absorptivity dynamically adjusts between 7.7% and 99.9% (Fig. 2). The analysis finds that with the change of dielectric constant of vanadium dioxide, the resonant frequency remains almost constant, while the absorption rate changes significantly. The Fabry-Perot resonance theory and impedance matching theory are introduced to explain the effects of the dielectric layer and the VO₂ layer on the absorption (Figs. 3-5). The physical sources of multiple perfect absorption peaks are analyzed through the electric field distribution (Fig. 6). Additionally, changes in absorptivity with different incident angles and polarization angles are analyzed (Fig. 7), which shows that the absorber has the characteristics of polarization insensitivity and wide-angle absorption.

We describe a terahertz absorber with four absorption bands, dynamically adjustable absorptivity, and a simple structure. Simulation results indicate that within the range of 0-10 THz, there are four absorption bands with more than 90% absorptivity, and their respective bandwidths are 0.87, 0.58, 0.61, and 0.45 THz. The absorptivity can be dynamically adjusted between 7.7% and 99.9% by varying the conductivity of vanadium dioxide. The physical mechanism of the absorber is explained using impedance matching theory and Fabry-Perot resonance theory. Through the analysis of the electric field distribution, it is found that the first broadband absorption is mainly caused by the local absorption of VO₂, while the second, third, and fourth broadband absorptions result from the resonance absorption of multiple electric dipoles on the surface of VO₂, coupled with the coupling effects between the dielectric layer and VO₂ and the metal layer. Additionally, it has the features of wide-angle absorption and polarization insensitivity. This absorber has potential applications in micro-radiometers, biosensors, stealth technology, and other fields.

Cold rolled strips are widely employed in automobiles, home appliances and other industries, and their surface micromorphology affects the surface chromatic aberration of the strip steel. The strip steel surface with regularly distributed microstructure tends to exhibit alternative bright and dark fringes. When the microstructure is randomly distributed, the stripes caused by multi-beam interference will be weakened. The surface microstructure of the rolled strip corresponds to that of the roll surface. The disordered roll laser texturing technology features less pollution, a wide range of texturing roughness, and high surface hardness, which can reduce the surface chromatic aberration of the rolled strip and is expected to meet the growing demand for sound stamping performance and fine brightness after the painting of cold rolled sheet productions.

The laser texturing roller technology is presented for controlling the range of peak per inch (PPI) density and roughness of rolling rolls based on the offset phase difference of the random distribution. The formation mechanism of light and dark alternately stripes on the surface of rolled strip steel is analyzed using the multi-beam interference principle. By the ray tracing method, the random distribution phase difference generated by the offset of equally spaced convex microstructures is studied to weaken the interference fringes formed by single-wavelength reflected light on the surface of rolled strip steel, which thus eliminates Moiré fringes generated by multiple wavelengths. The reflected coherent irradiance is adopted to study the corresponding uniform distribution function characteristic parameters under different center spacing when the interference fringes are broken. Meanwhile, laser impact pit experiments are conducted on roll material samples to obtain the corresponding relationship between the textured pit morphology and laser impact conditions. The random deviation of the pit microstructure on the roll surface is the same as that of the convex microstructure on the rolling strip by attenuating“copying”. We utilize Matlab's pseudo-random number generator based on the linear congruence method to generate two sets of random arrays that obey the uniform distribution obtained from the simulation analysis. Disordered texturing is performed on the rolling roll material sample by laser impact, which is achieved by adopting deviation in the convex microstructure center distance following a uniform distribution by theoretical and simulation analysis.

When the center offset of the microstructure on the surface of the rolled strip steel obeys a uniform distribution function, the coherent irradiance disorder of the single wavelength reflected light of the microstructure is better (Fig. 2). When the interference fringes of the reflected light from the tabular microstructure are broken, different center spacing corresponds to various characteristic parameters of the uniform distribution function (Fig. 3).

By employing the uniform distribution function of pit center offset obtained from theoretical and simulation analysis, and the relationship between experimentally obtained laser parameters and pit morphology, the surface of a roll material sample with a roughness of 3.79 μm and PPI of 179 is experimentally realized as disordered laser texturing of the roll material sample in a small area of 10 mm×10 mm by laser texturing technology (Fig. 5).

The thickness measurement method based on dual-channel light directly radiating on the two end faces of the thickness sample has gradually become an international hotspot. This is because the measurement results are only related to the end face characteristics of the thickness sample, the measurement optical path and environmental parameters, and the influence of the auxiliary agent, radiation, with the internal optical path of the thickness sample in the traditional method excluded. Among these, Tolansky interferometry features both angle and thickness measurements, which provides a new possibility for research into high-precision thickness measurement methods for double-end faces. Additionally, this means that the series radius of the interference concentric ring is adopted to calculate the measured thickness. In the thickness measurement using the common-path Tolansky interference scheme, the image of the interference concentric ring has an obvious ring nesting phenomenon, and even misaligned nesting occurs. This phenomenon will affect the image recognition accuracy of the radius and interfere with the subsequent thickness measurement results. Therefore, it is important to investigate technical schemes to eliminate or suppress this phenomenon in thickness measurements using the common-path Tolansky interference scheme.

Based on the dual-beam interference principle of the point light source, the Tolansky interference image is displayed by MATLAB virtual simulations. Then the experimental pictures of whether the interference concentric rings are different or not are displayed via the common-path Tolansky interferometer and the dual-arm optical path structure experimental system similar to the Michelson interferometer. That means there is an interference loop nesting in the former, and no interference loop nesting in the latter. After a detailed study, it is found that the biggest difference between the two systems is the existence of a multi-faceted structure of the common-path Tolansky. Additionally, the laser will reflect multiple times between these faces, while the dual-arm optical path structure similar to the Michelson interferometer does not have this multiple reflection phenomenon.

Given this, based on the geometrical optics principle, we employ the multiple reflection method to carry out theoretical analysis and formula derivation and obtain the expression of optical path difference and interference intensity different from double beam interference. Meanwhile, the correlation relationship between the beam intensity after multiple reflections and the incident light intensity of the interference spectrometer, the transmittance K_t, the reflectivity K_r, and the reflectivity K of the mirror is acquired. Thus, a new simulation model of interference concentric rings is obtained. On this basis, the interference concentric ring is simulated by MATLAB. The simulation results show that the interference concentric rings obtained based on the multiple reflection theory are in good agreement with the experimental images in terms of the structure and intensity profile, which also confirms the correctness of the theory. Given the strong correlation between the beam intensity after multiple reflections and the parameters of incident light intensity, transmittance K_t, reflectivity K_r, and reflectivity K, the interference concentric ring images with different collocations of these parameters are further virtually studied. The results show that by adjusting the transmittance and reflectivity of the interferometric spectroscope and the reflectivity of the interferometric mirror, the nesting phenomenon can be suppressed.

Based on the theoretical analysis and virtual simulation, interference spectrometers with different spectral ratios and interference mirrors with different reflectivities are replaced in the common-path Tolansky interference experimental system to realize different collocations among these parameters. The experimental results are in good agreement with the virtual simulation results, which verify the proposed method for suppressing the nesting phenomenon.

We propose an analysis method of multiple reflections among multiple planes, and obtain the expression of optical path difference and interference intensity different from double beam interference. Meanwhile, the correlation between the beam intensity after multiple reflections and the incident light intensity of the interference spectrometer, transmittance K_t, reflectivity K_r, and reflectivity K of the reflector is obtained. Thus, a new simulation model of an interference concentric ring is obtained, with the theory of common-path Tolansky interference analysis perfected.

Based on a new theoretical basis, a method to suppress the nesting phenomenon of the interference ring is proposed to suppress the phenomenon by reasonably adjusting the transmittance, reflectance of the interference spectrometer, and reflectivity of the interference mirror. Finally, a guarantee is provided for accurate extraction of the series ring radius by the common-path Tolansky interference thickness measurement technology.

The nesting or misplaced nesting of the common-path Tolansky interference ring causes bifurcation and ambiguity in each interference ring, which not only changes the interference level at the center of the circle, but also affects the recognition accuracy of each ring radius. As a result, there will be errors in the measured thickness inversion via the ring radius, which is unfavorable for accurate thickness measurement using the common-path Tolansky interference. The MATLAB virtual simulation and experimental results show that the nesting phenomenon comes from multiple reflections among multiple surfaces, and the intensity of the reflected light beam can be quickly weakened by adjusting the transmittance and reflectance of the interference spectroscope and the reflectivity of the interference mirror reasonably. Finally, the interference result is approximately double beam interference, and the nesting phenomenon is effectively restrained. This provides a guarantee for accurate radius extraction of the common-path Tolansky interference concentric ring series and accurate thickness measurements.

Compared with the traditional method of changing spin freedom through external magnetic fields, the spin-orbit coupling, which utilizes the coupling between the spin freedom and the motion freedom of atoms, is a new method for regulating spin. With the continuous realization of artificial spin-orbit coupling in cold atomic systems in experiments, many novel physical phenomena based on spin-orbit coupling have been widely promoted. In addition, since the realization of the superradiant quantum phase transition in experiments in 2010, the system of coupling ultracold atomic gas and cavity quantum electrodynamics has become an ideal platform for exploring novel many-body physics, which has aroused a research boom among theoretical scientists and experimental scientists. This coupling system couples ultracold atoms into a high-precision optical microcavity. Under specific electromagnetic boundary conditions, light interacts with ultracold atoms and induces novel many-body quantum properties. In this coupling system, one can not only explore the complex quantum behavior induced by the long-range interaction among atoms mediated by cavity photons but also understand the collective dynamical properties of cavity photons and ultracold atoms at the single-photon level. At the same time, the optical microcavity has both driving and dissipation, and it is a natural non-equilibrium system, which allows one to study the non-equilibrium steady-state dynamical properties. However, the time-dependent cavity-assisted spin dynamics has not been considered experimentally and theoretically. On the one hand, the time-dependent Schr?dinger equation is difficult to obtain an exact analytical solution mathematically, and on the other hand, the physical process expressed by the time-dependent Schr?dinger equation involves complex energy changes, time evolution, and interaction problems, which makes it difficult to solve. In view of these problems, we proposed a method for realizing the superradiant phase transition with the assistance of an optical microcavity. This method coupled the optical microcavity system with a Bose-Einstein condensate trapped in a harmonic potential that oscillates with time to obtain a new model, which could be used to study the self-organized phase transition and spin dynamics of Bose-Einstein condensates in microcavities and provide a reference for studying other Bose-Einstein condensates based on spin.

We considered the preparation of Bose-Einstein condensates using a magneto-optical trap and the coupling of these Bose-Einstein condensates bound in an oscillatory harmonic potential field with a high-precision optical microcavity, thereby establishing a one-dimensional coupled system where the Bose-Einstein condensates only moved in the x direction. The atoms we considered were those with four internal energy levels, and under conditions of large detuning, the excited states of the Bose-Einstein condensates were removed adiabatically, and the resulting Hamiltonian was then quantized. Through mean-field calculations, we obtained the coupled mean-field equations, which were then specialized for the time-dependent part, thereby transforming the problem with time dependence into a classification discussion without time dependence.

We studied the steady-state properties of matter, obtained the relationship diagram of the order parameter with the coupling strength and explored the influence of the external magnetic field strength and the harmonic potential field vibration strength on the critical point of the superradiant phase transition. The results show that the effective magnetic field mz experienced by the atoms and the vibration strength ξ0 of the harmonic potential well will affect the phase transition. Specifically, the coupling strength corresponding to the critical point of the superradiant phase transition increases monotonically with the increase in mz. When ξ0/1/πmω≤31.5, the coupling strength corresponding to the critical point of the superradiant phase transition decreases with the increase in ξ0. When ξ0/1/πmω>31.5, the coupling strength corresponding to the critical point of the superradiant phase transition increases with the increase in ξ0(Fig. 4). In addition, we also analyzed the non-trivial spin dynamics induced by the interaction between light and atoms and the influence of the vibration strength of the harmonic potential field on the dynamical properties. It was found that when the system does not undergo superradiance, the oscillation of σxt at zero over time is still symmetric but not smooth, and the value of ξ0/1/πmω affects the atomic spin resonance effect (Fig. 5).

In this study, we propose a feasible method for realizing optical microcavity-assisted superradiant phase transition and spin dynamics and explore the superradiant quantum phase transition and non-trivial spin dynamics that oscillate with time. We adopt the mean-field approximation method for the cavity field and the matter field and treat the time-dependent system, so as to obtain the superradiant phase transition of the system and give the complete phase diagram of the phase transition. On this basis, we study the non-trivial spin dynamics of the system by qualitatively analyzing the average value of the Pauli operator. We find that the coupling strength corresponding to the occurrence of the superradiant phase transition increases with the increase in the external magnetic field, and it decreases first and then increases with the increase in the vibration intensity of the external harmonic potential field. The vibration intensity of the harmonic potential field affects the spin dynamics effect of the system, because the vibration intensity of the harmonic potential field changes the coupling strength corresponding to the critical point of the superradiant phase transition, thus resulting in changes in the spin dynamics effect of the system.

Quantum cryptography uses quantum states as the carriers of information transmission and transmits information between authorized users through quantum channels. Different from that of traditional cryptography, the security of quantum cryptography is guaranteed by the basic principles of quantum mechanics. Therefore, it is theoretically unconditionally secure. In recent years, quantum cryptography has received extensive attention from many researchers engaged in cryptography, and has gradually developed into a popular research direction in the field of cryptography. Specifically, the quantum key agreement is an important research topic in quantum cryptography. It enables all participants to jointly negotiate a session key through a secure quantum channel, and each participants contribution to the negotiated key is the same. On the one hand, due to the high cost and scarce resources, it is difficult for the vast majority of participants to have well-performing quantum devices. Therefore, in order to facilitate the implementation of the protocol, it is necessary to simplify the quantum operations of the participants. In response to this problem, some scholars have proposed a semi-quantum key agreement protocol. The semi-quantum key agreement protocol requires that one of the participants in the protocol has complete quantum capabilities, and the remaining participants only have semi-quantum capabilities. Moreover, the semi-quantum participants can only perform the following two operations: i) reflection operation. No operation is performed on the received particles, and the received particles are returned directly. ii) Measurement operation. Z-based measurement is performed on the received particles, and new particles are prepared according to the measurement results. On the other hand, since participants may be attacked by man-in-the-middle in the process of key agreement, it is necessary to authenticate participants before the key agreement. In recent years, researchers have also proposed some quantum key agreement protocols with mutual authentication. In practical application scenarios, in order to facilitate the implementation of the protocol, it is necessary to design a semi-quantum key agreement protocol with lower requirements for participants ability and equipment. In order to prevent external attackers from counterfeiting authorized users to steal shared keys, the protocol needs to have a mutual authentication function. Therefore, it is necessary to design a semi-quantum key agreement protocol with mutual authentication.

Based on the Bell state, we propose a two-party semi-quantum key agreement protocol with a mutual authentication function, where Alice is a full quantum participant and Bob is a semi-quantum participant. The two sides achieve mutual authentication of identity by preparing and measuring identity information particles. By using the entanglement characteristics of the Bell state, the shared key negotiation was realized. Compared with other entangled states, the Bell state used in this protocol is easier to prepare, and the protocol only uses two quantum measurement operations, namely Z-based measurement and Bell measurement, which are easier to implement in existing technology. In addition, we proved that the proposed scheme can effectively resist participant attacks and external attacks, and that the protocol is equipped with a wavelength quantum filter and a photon number separator on both sides of Alice and Bob to avoid Trojan horse attacks. In the performance analysis of this protocol, the Cabello qubit efficiency was used to measure the performance of the quantum key agreement protocol.

First of all, in the previous research on quantum key agreement protocols, some scholars focus on how to simplify the quantum operation of participants, so as to better apply to the actual scene of resource scarcity, while others pay attention to how to prevent the man-in-the-middle attacks that may be encountered during the key agreement process and further improve the security of the protocol. The two-party mutual authentication semi-quantum key agreement protocol based on the Bell state proposed in this paper can not only reduce the requirements for participants capabilities and devices, but also realize mutual authentication between participants before key agreement to prevent the protocol from being attacked by man-in-the-middle. Finally, a security analysis shows that the protocol can effectively resist participant and external attacks. In addition, the performance analysis shows that the protocol can improve the quantum bit efficiency compared with some quantum key agreement protocols that meet a single function under the condition of satisfying two functional characteristics at the same time.

In this study, a two-party mutual authentication semi-quantum key agreement protocol based on the Bell state is proposed. The protocol not only ensures that the shared key can be fairly negotiated between the full quantum party, Alice, and the semi-quantum party, Bob, but more importantly, the two parties need to authenticate each others identity before the key agreement, so as to resist external attackers posing as legitimate users to steal the shared key. Security analysis shows that this semi-quantum key agreement protocol can resist both participant and external attacks. Finally, through a performance analysis and comparison with existing quantum key agreement protocols, it is found that the protocol has certain advantages in terms of its function and performance.

The temperature and relative humidity (RH) measurement plays a crucial role in various fields such as food processing, environmental monitoring, and biomedical applications. Fiber optic sensors have been extensively studied due to their prominent advantages of low cost, small size, strong immunity to electromagnetic interference, and high sensitivity compared to traditional electronic hygrometers. Fiber optic sensors based on the Fabry-Perot interferometer (FPI) structure feature simple fabrication process and stable performance. However, previously proposed fiber optic temperature and humidity sensors exhibit low sensitivity or are limited to single-parameter measurements. Therefore, the development of temperature and humidity dual-parameter sensors with stable performance and high sensitivity holds practical significance. The cascaded structure allows for the connection of multiple fiber optic sensing units, enabling simultaneous multi-parameter measurement. The vernier effect is utilized to amplify the humidity measurement sensitivity, while the anti-resonance (AR) effect of polymer-coated no-core fiber (NCF) provides high temperature measurement sensitivity. We propose and fabricate an FPI cascaded AR temperature and humidity dual-parameter fiber optic sensor, which further enhances the temperature and humidity measurement sensitivity and eliminates the need for complex FFT demodulation processes.

The sensor is composed of cascading an Fabry-Perot (FP) cavity and an NCF with a polymer coating. Meanwhile, the single mode fiber (SMF) and the NCF with polyimide (PI) cured on its end-face are placed into a non-enclosed silicon tube. The non-enclosed silicon allows the humidity-sensitive material PI to have sufficient contact with water molecules in the air. The air cavity is selected as the sensing cavity, while the air-PI mixed cavity serves as the reference cavity. The superimposition of the spectra from the air cavity and the air-PI mixed cavity produces a vernier effect, enabling easy and highly sensitive RH measurement by tracking the spectral envelope of the sensor. The light transmitted through the FP structure further transmits into the NCF. In the NCF segment coated with acrylic resin, the refractive index of the coating is higher than that of the cladding, which causes partial reflection of the light at the interface between the coating and NCF, while the rest is refracted into the coating and reflected at the coating-air interface, which creates MPI inducing the AR effect in the coated NCF. When the external temperature changes, the refractive index of the coating alters, resulting in a wavelength shift of the non-transmitted light for temperature measurement. Real-time temperature and RH can be calculated by adopting a decoupling equation system. The characteristic wavelengths of the reflected and transmitted spectra are measured, and the temperature and RH are simultaneously changed to validate the accuracy of the calculation formula. Additionally, error analysis is performed on the experimental results based on the set standard values, with RH and temperature relative errors of 0.74% and 0.19% respectively, which indicates that the sensor has a certain level of practicality.

Under the temperature of 29.5 ℃, the sensor's spectral drift characteristics are tested as the RH increases from 10% to 80% (Fig. 5). As the humidity grows, the resonance wavelength of the FPI envelope shifts towards longer wavelengths, with the RH sensitivity of 510.25 pm/%. The characteristic wavelength of the AR spectrum shows a red shift in the range of 10% to 60% and a blue shift in the range of 60% to 80%. With the humidity kept at 33%, the temperature is increased from 26 ℃ to 35 ℃, and the interference spectrum wavelength is recorded every 1 ℃ (Fig. 6). The envelope wavelength of FPI interference spectra remains unchanged with the rising temperature. Due to the high thermo-optic coefficient of the acrylic resin, the temperature change alters the refractive index of the coating, affecting the non-transmitted wavelength. The characteristic wavelength of the AR spectrum shows a blue shift with increasing temperature and exhibits amplitude variations with a slope of -4.48 nm/℃.

We present a high-sensitivity cascade sensor based on FPI and AR effects for temperature and RH measurement. The sensor incorporates an SMF with a PI film-coated NCF that is inserted into an open-ended silicon tube. By superimposing two FPI spectra with similar optical paths, a vernier effect is generated to amplify the sensor's low sensitivity. The high-sensitivity RH measurement is achieved by detecting the envelope movement. The AR effect is formed by the optical coupling of the NCF high refractive index acrylic resin coating and the low refractive index cladding, which produces a shift in the non-transmitted wavelength due to the refractive index change of the coating caused by temperature. The experimental results show that within the range of 10% to 80%, the RH sensitivity is 510.25 pm/%, which amplifies the original sensitivity by approximately five times. In the range of 26 ℃ to 35 ℃, the temperature sensitivity is -4.48 nm/℃. In summary, the proposed sensor features simple fabrication and high sensitivity and holds potential practical significance in such fields as health monitoring and biomedical applications.

Optical micromanipulation utilizes optical force to dynamically control particles, which has the characteristics of non-contact and can be operated in a vacuum environment. Since the invention of optical tweezers in the 1980s, the field has experienced rapid development and has given rise to many emerging research directions, such as holographic optical tweezers, near-field evanescent wave optical tweezers, fiber optic tweezers, optoelectronic tweezers, and photo-induced temperature field optical tweezers, providing rich and powerful tools for fields such as biology, chemistry, nanoscience, and quantum technology. These methods can not only capture, separate, and transport small objects but also allow more precise manipulation, such as the rotation of small objects. However, traditional manipulation methods rely on tightly focused local light, greatly limiting the action range of optical force. In addition, in order to generate a structured light field, larger optical components such as spatial light modulators are usually required, making it difficult to miniaturize and integrate the optical manipulation system.

In recent years, metasurfaces have emerged as integrated devices composed of subwavelength nanoantennas, promising new opportunities for optical micromanipulation. This ultra-thin artificial microstructure device can flexiblely control multiple degrees of freedom such as amplitude, phase, and polarization of light, by specially designing the geometric shape, size, and material of its own micro/nanostructure. Compared with traditional optical components such as liquid crystal spatial light modulators, gratings, and lenses, metasurfaces exhibit higher operating bandwidth, structural compactness, and integration. With the merits of miniaturization, integration, and excellent performance in light tailoring, optical metasurfaces have been extensively incorporated into the realm of optical micromanipulation. Especially, owing to their peculiar photomechanical properties, the metasurfaces hold the ability to be actuated by light fields, paving the way to the next generation of light-driven artificial micro-robots. The fast development of this subject indicates that the time is now ripe to overview recent progress in this cross-field.

We summarized principles of optical micromanipulation and metasurfaces (Fig. 1) and overviewed meta-manipulation devices, including metasurface-based optical tweezers (Fig. 2), tractor beams (Fig. 5), multifunctional micro-manipulation systems (Fig. 3), and metamachines (Figs. 7 and 8). Furthermore, we provided a detailed discussion of novel mechanical effects, such as topological light manipulation, which stems from the topological characteristics of nanostructures (Fig. 6).

We review the cutting-edge developments in the field of optical micromanipulation based on metasurfaces. The metasurface-based micromanipulation technology is expected to evolve toward higher temporal resolution, higher spatial accuracy, and lower manipulation power. To this end, more urgent requirements have been imposed on the underlying design scheme and experimental preparation standards of the metasurface. Although the introduction of metasurfaces has benefited micromanipulation systems and significantly reduced their sizes, there is still much room for further development and improvement in wide bands, multi-dimensional responses, and device thresholds.

In terms of micromanipulation systems, the subwavelength-scale structure of metasurfaces will continue to be a key focus of research. Especially in the field of topological light manipulation, it is expected to further expand its research scope, combining non-Abelitan, non-Hermitian, and nonlinear effects to discover new physical phenomena. In the fields of biology and chemistry, metasurface technology is expected to be flexibly applied on smaller scales, even achieving manipulation of single molecule-level objects. This technology is expected to be further applied to the fields such as battery quality inspection and targeted therapy, bringing changes to the basic research and practical applications of energy and life sciences. Specifically, in the development of ultrafast optics, metasurfaces are gradually exhibiting unique advantages. Nanoscale superlattice enables high-resolution spectral measurements, and the design of nonlinear superlattice surfaces can be used to enhance nonlinear effects or generate high-order harmonics, making high time resolution transient micromanipulation technology possible.

Overall, the technological evolution from traditional optical micromanipulation to meta-manipulation will continue to drive the vigorous development of nanophotonics. This technological paradigm not only meets the needs of various basic research but also arouses more innovative applications, opening up new prospects for branched sciences and technologies.

As the main green energy, methane (CH₄) has become increasingly important in human production and life. Meanwhile, as explosive and flammable harmful gas, it also causes significant problems such as production safety accidents and environmental pollution, it is particularly important to detect CH₄ concentration in real time and online. Additionally, carbon isotopes in CH₄ are also significant for environmental analysis of sources and sinks. Traditional isotope ratio measurement methods, such as mass spectrometry and gas chromatography, often require sample preprocessing and are difficult to achieve real-time online detection. At the same time, traditional absorption spectroscopy techniques often need large absorption cells and other devices to measure the gas isotopes, which results in difficult temperature and pressure control. We report a methane isotope measurement method based on off-axis integrated cavity output spectroscopy (OA-ICOS) technology, which eliminates residual mode noise in the measurement results by adding an RF white noise source and further expands the optical power of the incident laser using booster optical amplifier (BOA) to increase the effective optical path length of the measurement results. We hope our method can further reduce the minimum detection limit and provide solid theoretical and technical support for future measurement of isotope ratio changes in CH₄ under atmospheric background concentration.

We establish a system for carbon isotope detection in CH₄ based on OA-ICOS technology (Fig. 3), and the laser output laser changes the angle and position of the incident into the integration cavity through the fiber collimator fixed on the five-dimensional adjustment frame. Meanwhile, the outgoing light after multiple reflections is formed in the cavity by the lens to converge on the photosensitive surface of the detector, and the detector converts the collected integrated light signal for photoelectric conversion. The detected electrical signal is converted analog-to-digital via the data acquisition card and uploaded to the computer software by the USB serial port to realize gas concentration measurement. The opening ratio of the needle valve and the pumping speed of the vacuum pump are changed in the experiment to control the flow rate of the outlet end and thus ensure the measured pressure stability. Additionally, the mass flow controller is adopted to adjust the flow rate of the inlet in real time to realize the pressure control in the cavity. Radio frequency (RF) white noise is loaded on the current drive of the laser in the experiment and the laser linewidth is further widened, with eliminated remaining mode noise and improved signal-to-noise ratio (SNR) of the measurement results, which aims to minimize the mode noise interference in the cavity and improve the SNR of the measurement results. Additionally, to further improve the effective optical path length of the system and the signal-to-noise ratio of the measurement, we amplify the output power by adding a BOA after laser, after which the absorbance measured is greatly improved.

When the RF white noise power is greater than -30 dBm, the residual mode noise in the cavity is eliminated. When the RF white noise power is greater than -20 dBm, the absorption peak shows a significant decrease with the broadening linewidth (Fig. 5). Thus, the RF white noise with -30 dBm is adopted in the experiment. Meanwhile, the rising current of BOA leads to a significantly increasing absorption peak (Fig. 6) and effective optical path length. When the drive current is greater than 400 mA, the effective optical path length of the system at this time is approximately 6000 m, which increases by approximately 1.22 times. The SNR increase of ¹²CH₄ is 1.16 times and of ¹³CH₄ is 1.18 times, which is consistent with the rise in effective optical path length (Fig. 6). By employing the carbon isotope standard value given by NBS-20 [R_standard (¹³C/¹²C)=0.0112253] as the standard value for calculating the isotope ratio changes, δ(¹³C) in the CH₄ standard gas with a volume fraction of 494.14×10^-6 and a volume fraction of 5.55×10^-6 at a volume fraction of ¹³CH₄ is continuously measured for 1 h, and the measurement results are shown in Fig. 8(a). To further analyze the stability and detection limit of the measurement system, we perform the Allan variance analysis of the measured δ(¹³C), with the results shown in Fig. 8(b). The analysis results indicate that the limit of detection (LoD) is 4.57‰ when the average time is 1 s, and its LoD decreases to 0.567‰ when the average measurement time increases to 663 s, at which time the detection accuracy of the system can be further improved by increasing the average time.

To realize the real-time measurement of the change of stable carbon isotope ratio in CH₄, we establish a high-precision δ(¹³C) measurement system based on OA-ICOS technology. Meanwhile, for further improving the measured effective optical path length and reducing the measurement limit, we add the BOA behind the laser output to enhance the output laser power, increase the effective optical path length of the system from about 2700 m to about 6000 m, an increase of about 1.22 times, and increase the SNR of ¹²CH₄ and ¹³CH₄ by 1.16 times and 1.18 times respectively. By leveraging the gas distribution instrument, the system is calibrated by high-purity N₂ and CH₄ with a volume fraction of 5008×10^-6 to configure different volume fractions of sample gases, and the calibration curve is obtained by fitting the relationship between the gas volume fraction and the absorption spectrum peak, with the volume fraction inverted by the calibration curve. After performing the stability test of CH₄ with a volume fraction of 500×10^-6 for 1 hour, Allan variance analysis shows that the minimum variance of the system stability for δ(¹³C) measurement in CH₄ is 0.567‰. The utilization of this system can improve the SNR and reduce the minimum LoD to achieve long-term stable measurement of δ(¹³C) in CH₄. Additionally, by further improving the stability of the optomechanical structure, reducing system noise, and increasing the effective optical path length, the minimum detection limit can be further reduced. Finally, solid theoretical and technical support can be provided for future measurement of methane-stabilized carbon isotope characteristic values at atmospheric background concentrations.

In the inertial confinement fusion (ICF) experiment, the microchannel plate (MCP) framing camera is an important two-dimensional ultrafast diagnostic device that is used to acquire the duration and dynamic image of plasma at the stage of implosion compression. However, due to limitations of the electronic transmission time and its dispersion in the channel of the MCP, the temporal resolution is restricted to 60-100 ps for a long time. In order to further improve temporal resolution, a pulse-dilation framing camera (PDFC) is developed, which couples the MCP framing camera with the temporal dilation technique of the electron beam. With an ultrafast temporal resolution of better than 10 ps, it is easier to meet the detection requirements of the shorter duration states in the ICF. Therefore, the relevant ways and techniques of the PDFC are gradually focused on the field of ultrafast diagnosis. The PDFC is a new kind of framing camera with a long drift region using the imaging of magnetic focusing technique. Due to its similar structure to the streak camera, the improvement of its spatio-temporal performance to a higher order is restricted by the space charge effect (SCE). Moreover, the temporal width and radius of the electronic pulses (EPs) are dynamically changed by the dilating pulse and magnetic focusing in the PDFC. Therefore, building the model of the SCE that meets the dynamic parameters of the EPs and analyzing the influence of the dynamic radius caused by magnetic focusing on the spatio-temporal dispersions will be an important theoretical significance for systemically studying the SCE of the PDFC.

In the research, to analyze the influence of magnetic field on the spatio-temporal dispersions of the SCE, first of all, the model of the PDFC using magnetic focusing is built, and the dynamic characteristics of EPs during transmission are analyzed by the working principle of the PDFC. Then, the spatio-temporal dispersion model of the SCE is deduced by solving the equation of the electric field force based on the two-dimensional potential distribution of the EPs. To build a relationship between magnetic field and imaging area, while ensuring consistent imaging magnification, the different imaging magnetic fields are reasonably calibrated through the analysis procedure of optimal spatial performance of the PDFC based on the method of regional imaging. Finally, the dynamic temporal width and radius of the EPs are applied to the model of the SCE in different magnetic fields, and the spatio-temporal dispersions of different off-axis positions are analyzed.

The innovative and significant research results are mainly summarized in three aspects. First, the dynamic variation of the electronic density during transmission is analyzed in the PDFC, on which the dynamic temporal width and radius of the EPs are based [Fig. 2 (d)]. Second, under consistent imaging magnification, the optimal spatial performance of the PDFC is analyzed, and different imaging magnetic fields are reasonably calibrated by regional imaging (Fig. 3). Third, the dynamic temporal width and radius of the EPs are applied to the model of the SCE. When the radius of the imaging region is 1 mm, as the off-axis position increases from 0 mm to 15 mm, the magnetic field intensity is enlarged from 4.585×10^-3 T to 4.763×10^-3 T. The defocusing and dynamic radius of EPs of the off-axis are much larger than those of the on-axis. Therefore, as the electronic density of the EPs reduces, the temporal dispersion of the SCE is reduced from 2.94 ps to 483 fs, and the spatial dispersion is reduced from 668 μm to 22 μm (Fig. 4). When the radius of imaging region is gradually enlarged to 20 mm, the magnetic field intensity of the on-axis is reduced from 4.585×10^-3 T to 3.359×10^-3 T, and the spatio-temporal dispersions of the SCE are optimum value in the range of 3.4×10^-3-3.5×10^-3 T. The range of temporal dispersions of different positions is 256-392 fs, and spatial dispersions is 3.1-15.4 μm (Fig. 5).

In the PDFC, the temporal width, radius, and electronic density of the EPs during the transmission process are dynamically changed by the effect of the dilating pulse and the imaging system of magnetic focusing. Moreover, the spatio-temporal dispersions of the SCE are significantly affected by the defocusing of the EPs and the fluctuation of radius caused by a magnetic field. According to the research methods and results, on the one hand, the different magnetic field is reasonably calibrated through the analysis of the optimal spatial performance of the PDFC; on the other hand, it also provides a theoretical basis for analyzing the relationship between the magnetic field and the SCE. In the next stage, to provide a theoretical basis for achieving faster temporal resolution of the PDFC, the spatio-temporal dispersions of the SCE are systematically studied from different types of magnetic focusing imaging systems and the long drift regions.

In the automobile augmented reality head-up display (AR-HUD) optical system, due to its imaging performance and the non-standard shape of the windshield on the last imaging surface, the image observed by the driver will have some distortion. Meanwhile, as the viewpoint changes in the eyebox, the distortion will also be different at various eyebox positions, which will cause great trouble to the driver's perception during driving. At present, there have been a lot of studies on the distortion correction of AR-HUD, such as employing algorithm correction or adding optimization functions during optical design. However, the above-mentioned distortion correction methods are all for distortion correction at a single viewpoint. The binocular fusion process of human eyes is not involved. Since the image observed by the driver is essentially the fusion of distorted images of the left and right eyes at different eyebox positions, monocular correction alone cannot well represent the experience of the drivers during the binocular fusion processes. Therefore, it is necessary to conduct corresponding subjective experiments to evaluate the actual perception of the driver during the fusion process of different viewpoint images and provide certain constraints of dynamic distortion for the optical design process.

We adopt homogeneity of variance test, one-way ANOVA, and statistical chart analysis. First, we conduct a basic theoretical explanation of dynamic distortion and how to simulate dynamic distortion, build a dynamic distortion experimental simulation model, and synthesize a series of display images for later subjective experiments. Then we utilize the subjective experimental scale and carry out a subjective experiment for dynamic distortion evaluation. Experimental data from multiple subjects in different group conditions are collected in this section. Finally, statistical methods are leveraged to analyze previously obtained data, with one-way ANOVA and chart analysis processed in this section. Additionally, significant difference results and line-bar charts are employed to simultaneously analyze the experimental data quantitatively and visually find the relationship between dynamic distortion and drivers' subjective perception.

A total of three sets of results of 12 subjects for vertical, horizontal, and rotational distortion are calculated using the homogeneous test of variances. As shown in Table 1, the Levene statistics are 2.301, 0.988, and 1.401, respectively, and the corresponding difference significance values are 0.051, 0.435, and 0.241, respectively, all greater than 0.05, indicating that the statistical quantities of the three sets of data have homogeneity of variances and the F test can be adopted to perform one-way ANOVA. Then three groups of data are subjected to single-factor variance analysis with VIMSL in subjective experiments. In the ANOVA analysis results, the significant difference values of vertical distortion and rotational distortion are both 0, less than 0.01. The results show that the factor dynamic distortion level has a significant effect on the VIMSL increments. However, the significant difference value of horizontal distortion is greater than 0.05, which means that the changes in the horizontal direction have a small effect on drivers' perception and there is no obvious significant effect on the VIMSL increments. In the statistical chart analysis (Figs. 10-11), as the distortion level increases, VIMSL-related evaluation indicators rise accordingly. There is a more obvious difference between Group 2 and Group 3, which shows that drivers' discomfort increases most significantly during the switching process between the two groups. This means that vertical distortion of 2% and horizontal distortion of 1% can be regarded as a value at which obvious discomfort begins to occur. However, the SSQ scores do not change significantly before and after viewing, which shows that the influence of the experimental equipment on subjects' discomfort can be ignored and the display condition of the experimental equipment itself is relatively reliable.

We establish a subjective experimental procedure based on binocular 3D display observation and the subjective experimental data are adopted to analyze the subjective feelings of drivers caused by dynamic distortion in automobile AR-HUD devices. Meanwhile, the certain value of the distortion level that is acceptable to the drivers during binocular fusion when drivers are watching the images from different eyebox positions is evaluated. The experimental results show that different forms and levels of dynamic distortion both have a great effect on the driver's subjective perception. As the difference in dynamic distortion between the two eyes rises, it becomes increasingly more difficult for the driver to fuse the images, with rapidly increased discomfort level. Furthermore, we also reveal that the certain levels for the dynamic distortion acceptable to the driver at two different positions of the same eyebox are vertical distortion less than 2% and horizontal distortion less than 1%. The results show that the combination of different distortions has a great effect on the driver's subjective perception. Additionally, the experimental results also provide a clear design constraint index for dynamic distortion correction during the HUD optical design.