a laser communication system and an optical tracking system. The former is for information transmission between two satellites, and the latter is for pointing, acquisition, and tracking (PAT). The space laser communication system is advancing toward miniaturization and is lightweight. However, traditional optical tracking and sighting systems usually use gimbal turrets and gimbal turning mirrors to attain significant beam angles. Furthermore, such structures are large in size, large in inertia, poor in dynamic performance, slow in response time, and sensitive to vibration, which is not conducive to the installation of the carrier platform and the balance of the carrier posture. Compared with the traditional structure, Risley prisms are small in size, have excellent viewing axis adjustment function, and can realize large-angle deflection of the beam; therefore, the rotating biprism is more suitable for space laser communication. However, since Risley prisms are composed of two coaxial wedge prisms, there is no linear relationship between the outgoing light and the wedge prism s rotation angle, making it challenging to solve the outgoing beam of Risley prisms. Additionally, there are several error sources of Risley prisms, and the pointing is not sufficiently accurate. Therefore, it should be corrected to obtain a more precise pointing, which can be used in space laser communication.

A new method of correcting the pointing deviation of Risley prisms is proposed to aim at the problem of poor pointing accuracies, including the significant pointing error of Risley prisms and more error sources. This study uses a non-paraxial ray tracing method to establish a Risley prism pointing model and a two-dimensional turntable pointing model. Many points are uniformly chosen in the entire field of view, and the deviation between the rotating double prism s theoretical and actual output beams is compared. The Levenberg-Marquardt iterative algorithm corrects the rotation angle error, wedge angle, and refractive index of the front and back mirrors of Risley prisms. Higher-precision pointing is achieved by correcting the inaccuracy of the initial incident beam relative to the ideal optical axis and separately correcting the region with a small pitch angle to address the issue of low pointing accuracy in the area with a big pitch angle.

From the simulation findings of the final convergence of the Levenberg-Marquardt algorithm with various initial values, different initial values have little impact on the final optimization results of this experiment (Fig. 2). The entire field of view of Risley prisms is pitch angle 0°-29.22°, azimuth angle 0°-360°. After optimizing the whole area of view by the Levenberg-Marquardt algorithm, the maximum pointing deviation is 5.33 mrad and the average pointing deviation is 1.82 mrad (Fig. 6). It can be observed that the pointing error of the initial incident beam relative to the ideal optical axis will have a relatively large impact on the pointing accuracy of Risley prisms from the effect of the simulation error on the pointing deviation between the actual outgoing beam and the theoretical outgoing beam (Fig. 7). After adding the correction of the error of the initial incident beam relative to the ideal optical axis by the Levenberg-Marquardt algorithm, the maximum pointing deviation is 3.75 mrad and the average pointing deviation is 1.38 mrad (Fig. 8). After using the Levenberg-Marquardt algorithm to correct the points with a pitch angle of less than 15°, the maximum pointing deviation is 1.51 mrad and the average deviation is 0.84 mrad (Fig. 9).

In this study, the non-paraxial ray tracing method is used to develop the pointing model of Risley prisms. Numerous points are evenly chosen in the entire area, and a two-dimensional turntable pointing model is shown to accurately measure the actual outgoing beam of the Risley prisms. Comparison is made between the deviation of the theoretical and real output beams of Risley prisms. The rotation angle error, wedge angle, and refractive index of the front and rear mirrors of Risley prisms are corrected via the Levenberg-Marquardt iterative procedure. After correction in the entire field of view, the maximum pointing deviation changes from 8.37 mrad to 3.75 mrad, and the average pointing deviation changes from 4.00 mrad to 1.38 mrad. Moreover, the correction effect is better when the pitch angle is small. For example, after individually correcting the field of view area with the pitch angle less than 15°, the maximum pointing deviation becomes 1.51 mrad and the average deviation becomes 0.84 mrad. This method improves the pointing accuracy of Risley prisms, and it has a particular reference value for correcting the pointing deviation of Risley prisms.

Results and Discussions A simulation is used to validate the performance of the project-constraint decoupling method for the aberration correction, coupling error elimination, stability, and computation complexity. It can compensate the aberration better than the traditional method to decoupling method for the wave front sensor-free system (Fig. 2). Additionally, it can effectively eliminate the decoupling error between the Woofer and the Tweeter (Fig. 3), as the aberration is broken down into low order Zernike modes and high order modes before being corrected by the Woofer and Tweeter. During the decoupling operation, it is more stable than the conventional approach, and the advancements have improved its performance in the control process. Finally, the decoupling method suggests in the research has a lower computational complexity than the conventional method (Fig. 4). An experimental system was built to evaluate the effectiveness of the method. The experiment demonstrates that the decoupling algorithm can effectively compensate for phase distortions (Fig. 6 and Fig. 7) and significantly suppress the coupling error between the dual deformable mirrors and decompose the aberration accurately (Fig. 8).

Dual deformable mirrors are often used to create wave front-sensor-free adaptive optics systems that can be used to correct aberrations with broad strokes and high spatial frequencies. The Woofer, which has big amplitude and is used to correct low order aberrations, and the Tweeter, which has a high spatial resolution and is used to correct high order aberrations, are two examples of dual deformable mirrors. However, without the decoupling process, it is difficult to avoid the coupling error, which would cause the deformable mirrors to generate an opposite surface shape and waste the ability of aberration correction in the dual deformable mirror adaptive optics system. To solve this problem and make the Woofer and Tweeter could work efficiently together; a decoupling method must be developed. Even the decoupling algorithms are the subject of considerable study, most of them focus on dual deformable mirror adaptive optics systems with wave front sensors. These techniques frequently employ the data from the wave front sensor to aid in decoupling. A few decoupling methods are used for the wave front sensor-free adaptive optics system, and their performances are usually not satisfactory for the engineering project. To improve the performance in the aberration correction, coupling error reduction, stability, and computation complexity for the wave front sensor-free adaptive optics system, a new decoupling technique must be developed. This might lead to further applications for the adaptive optics technology in things like large-scale telescopes, vision equipment, and laser beam cleanup.

To make the dual deformable mirrors in the system work together to correct the aberration, a straightforward but effective decoupling method based on the mode project-constraint is proposed. The Woofer is controlled by a low order Zernike mode coefficient to avoid correcting the high order modes, and the Tweeter is constrained by the project-constraint method to eliminate the low order modes in its corrections. Obtaining the related matrix of the mode coefficients to the Woofer control signal is essential to the decoupling control process. It can be obtained through the Woofer’s influence functions and the low order Zernike modes which will be corrected by the Woofer. The project-constraint, which requires the following processes, can also limit the use of low order modes in the Tweeter. To start, a relationship matrix between the Zernike mode coefficients and the Tweeter’s control signals needs to be produced. Then, the component of the signals in the Tweeter-induced coupling error can be solved by the relation matrix. Finally, by subtracting the component-induced coupling error from the initial Tweeter control signals, the signals free of coupling error can be obtained. These techniques result in the realization of the Woofer and Tweeter’s decoupling.

In this paper, a simple and effective method was proposed based on project-constraint to restrict the coupling error and eliminate the aberration in a wave front sensor less adaptive optics system with a dual deformable mirror. This method can outperform the conventional method in terms of aberration correction, coupling error elimination, stability, and processing complexity. It can be used to make the Woofer and Tweeter cooperate efficiently to correct the aberration by Zernike mode decomposition. Then the low order Zernike modes of the aberration can be compensated by the Woofer, and the other Zernike modes of the aberration can be corrected by the Tweeter.

Results and Discussions The Fourier synthesis illumination device composed of MEMS and off-axis ellipsoidal mirrors can achieve various illumination patterns such as disk, dipole, quadrupole, and annular and the illumination area size (representing the partial coherent factor) and spacing of the illumination area can be adjusted. The tested illumination profile has no distortion and the illuminating intensity distribution is relatively uniform. When the MEMS scanning angle is ±1° and the magnification of the ellipsoidal condenser is 10 (i.e., with an object distance of 1 m), the maximum illumination diameter can reach >30 mm on the condenser, and the 4×NA on the ellipsoid focal surface can reach >0.6. Moreover, the illumination area on the surface to be detected located at the imaging focal point of the ellipsoidal mirror was tested, and all scanning rays were concentrated in the same area on the surface to be detected. Neither the scanning mode nor scanning angle influences the position of the overlapping area. Ellipsoidal mirrors with different magnifications can be used to adjust the size of the illumination area on the surface, and the actual magnification of the illumination area is basically consistent with the theoretical value.

Off-axis illumination is an important resolution enhancement technology in lithography, and it can effectively enhance both resolution and the focal depth of the lithography tool. Conventional off-axis illumination methods, such as those using pupil filters, have the disadvantage of serious energy loss. Moreover, realizing a few special illumination patterns is difficult using transmission elements represented by an axicon, and diffractive elements have the problem that a single diffractive element corresponds to only one illumination pattern. In the EUV spectral band, because optical materials intensely absorb EUV radiation, the transmission elements and transmission type diffraction optical elements cannot be used. In the present study, we investigate an illumination system based on Fourier synthesis technology. It has advantages of realizing any off-axis illumination patterns, increasing imaging numerical aperture (NA), high energy efficiency, and wide applicability in various spectral bands, especially for applications in the EUV spectrum. We hope that our research results will improve the understanding of Fourier synthesis technology and achieve an illumination technology that limits illumination divergence and can easily provide uniform illumination, making it useful in applications such as lithography projection exposure and mask defect detection.

We use a micro-electro-mechanical systems (MEMS) mirror combined with an off-axis ellipsoidal mirror to construct our Fourier synthesis illumination device. The surfaces of the MEMS and ellipsoidal mirrors are coated with a high reflectivity film for working wavelength. Based on the characteristic high-frequency two-dimensional rotation of the MEMS mirror, with the support of an optimization scan program, we set ray-scanning paths of the MEMS mirror in the x and y directions, achieving various illumination patterns such as disk, dipole, quadrupole, and annular, and adjust the partial coherent factor. The scanning ray is then collected and imaged by using the ellipsoidal mirror with two imaging focal points, whose surface to be detected (such as the mask) is located at the focal point. The Fourier synthesis illumination device provides uniform illumination with the required illumination pattern and illumination divergence to the surface to be detected. In this study, the imaging characteristics of two ellipsoidal mirrors with different magnifications of M=10 and M=2.5 are verified, and the simulation results are found to be basically consistent with the experimental test results.

The Fourier synthesis technique based on MEMS and off-axis ellipsoidal mirror is studied and an experimental confirmatory device is set up. The feasibility of Fourier synthesis technology is verified, and it can achieve various illumination patterns and illumination size by adjusting the pupil and partial coherent factor. The experiment demonstrates that Fourier synthetic illumination technology can meet the requirements of off-axis illumination and illumination divergence of imaging systems. Our research shows that Fourier synthesis technology is an illumination method that can be easily meet illumination requirements. There are only two main reflection elements needed to minimize energy loss, and their reflection characteristics are widely applicable over a wide spectral range.

In recent years, owing to the advancements in attacks and attack detection technology for optical fiber, various types of optical-fiber eavesdropping devices have emerged; the original “unique” physical security of optical fiber has been broken, and the optical network constantly encounters security threats. In this study, the use of all-optical encryption and decryption technology in optical networks for optical-fiber secure communication is proposed; it can solve the “rate bottleneck” problem of encryption and decryption technology based on electrical signal processing and can encrypt and decrypt the optical signal in the optical domain. Optical-fiber secure communication can be inferred to be an effective method for solving the “rate bottleneck” problem of encryption and decryption in the electric domain and mitigating the potential security threats in optical networks. However, most of the all-optical encryption and decryption schemes reported thus far are simple XOR verifications for optical signals and rarely consider the cipher synchronization problem between the encryption and decryption parties in different places. In practical applications, the ciphertext data encrypted at the sender’s end must be transmitted to the receiver 100 km or more away through the optical network, and a certain propagation time delay occurs in the transmission process. Determining the starting position of the ciphertext data is difficult for the receiver; this makes synchronization between the processes of encryption and decryption impossible, leading to an increase in the error rate and decryption failure. Thus, the key to realizing optical-fiber secure communication is cipher synchronization. To effectively solve the cipher synchronization problem in optical-fiber secure communication, an all-optical synchronization scheme is designed in this study to precisely determine the starting position of the ciphertext data sequence and adjust the starting position of ciphertext data and decryption key; this can achieve cipher synchronization, which will help the receiver to successfully decrypt.

In this study, we design an all-optical synchronization scheme based on the existing wavelength division multiplexing (WDM) system, which transmits ciphertext data and synchronization signals through a classical optical fiber channel after applying WDM. The formula for the propagation time delay difference in the optical fiber channel is deduced, and the function of cipher synchronization in optical-fiber secure communication is achieved by employing time delay correction. To prove the feasibility of the all-optical synchronization scheme, a simulation model of the all-optical encryption and decryption system is built on an OptiSystem platform, and the all-optical synchronization scheme is simulated and verified at 10 Gbit/s and 40 Gbit/s. The output data after decryption are identical to the original plaintext data, and both indicate good output performance. To verify the influence of cipher synchronization on the encryption and decryption system, the correlation between the cipher synchronization state and the performance of the plaintext signal decrypted is tested and analyzed in a 40 Gbit/s simulation experiment. To solve the problem of the maximum transmission distance of the 40 Gbit/s data rate being limited, the all-optical synchronization scheme at 40 Gbit/s for long-distance optical fiber links based on dispersion compensation is simulated and verified.

The simulation results show that the maximum length of the G.655 optical fiber link in the WDM system can reach approximately 160 km for a 10 Gbit/s channel rate with successful decryption, the Q factor of the recovered plaintext data signal after decryption is 7.12, and the corresponding bit error rate is approximately 5.77×10^-13. The maximum length of the G.655 optical fiber link in the WDM system can only reach approximately 9 km for the 40 Gbit/s channel rate with successful decryption, the bit error rate of the recovered plaintext data signal after decryption is 1.85×10^-13, and the Q factor is 7.29. With the increasing misplacement of the ciphertext data and decryption key, the bit error rate of the recovered plaintext data signal after decryption increases, the corresponding Q factor decreases, the quality of the signal eye pattern degrades, and the performance of the output signal after decryption deteriorates. The maximum length of the G.655 optical fiber link based on the dispersion compensation in the WDM system can reach 80 km+80 km for the 40 Gbit/s channel rate with successful decryption, the Q factor of the recovered plaintext data signal after decryption is 7.33, and the corresponding bit error rate is approximately 7.63×10^-14.

The results show that the proposed all-optical synchronization scheme is feasible and can be directly applied to WDM systems. The scheme is suitable for both 10 Gbit/s and 40 Gbit/s channel rates, for both conventional fiber links and fiber links based on dispersion compensation; it can effectively solve the problem of all-optical cipher synchronization in optical-fiber secure communication and meet the requirements of a low bit error rate, high speed, long distance, and large capacity. Solving the “rate bottleneck” problem and mitigating the potential security threats to the physical layer in the optical-fiber communication network are crucial for promoting the development and application of the optical-fiber secure communication system.

Passive optical networks (PON) have become one of the main solutions for optical access networks because of their low cost and large bandwidth capacity. With the continuous increase in bandwidth demand, such as high-definition videos and online conferences, in recent years, existing PON technology has faced capacity bottlenecks. Recently, few-mode fiber (FMF)-based mode-division multiplexing (MDM) technology has been proposed, which is expected to further improve the capacity of PON by introducing a new multiplexing dimension to support higher transmission rates and more users. However, for the mode-division multiplexing passive optical network (MDM-PON), which divides users by mode, the mode crosstalk in the FMF causes the user signals to be loaded on different modes to interfere with each other, which affects the transmission performance. To further improve the transmission performance of the MDM-PON, we propose a MIMO pre-equalization based mode crosstalk mitigation method for the MDM-PON and build a simulation system with VPI Transmission Maker for verification.

Owing to the point-to-multipoint structure of the MDM-PON downlink, it is impossible to simultaneously receive and eliminate mode crosstalk for all modes at the receiver. Therefore, an MIMO pre-equalization based mode crosstalk mitigation method is proposed in this study. To estimate the downlink channel impulse response, we design a time-division training sequence that is inserted into the frame header. The time-division training sequence consists of the same number of time slots as the modes, and each time slot corresponds to only one mode and contains the corresponding training symbol sequence. The receiver of each mode uses coherent detection and adopts a training sequence-based least mean square (LMS) adaptive algorithm for channel estimation. The channel estimates are fed back to the transmitter for pre-equalization. The transmitter-side MIMO equalizer used in this study has a linear structure and uses the feedback channel impulse response to calculate the tap coefficients based on the zero-forcing (ZF) criterion. Considering the inter symbol interference (ISI) caused by fiber chromatic dispersion, we use cascaded FIR filters after the MIMO equalization for pre-compensation at the transmitter. Because the impulse response and dispersion coefficient of the chromatic dispersion are known, the tap coefficients of the FIR filter used for dispersion pre-compensation can be directly calculated.

By adjusting the transmitted optical power in the range of -20 dBm to -44 dBm, we analyze the performance of each mode under OBTB and 5 km FMF transmission, during which the bit error rate (BER) threshold of 7% hard decision forward error correction (HD-FEC) is adopted. The curves of the BER with respect to the transmitted optical power with and without crosstalk under the OBTB and 5 km FMF are shown in Fig. 6. When the BER meets the 7% HD-FEC threshold, compared with tranmission without crosstalk, the transmitted optical power of each mode is increased by 1 dB, 2.8 dB, 2.5 dB, and 2 dB in tranmission with crosstalk. After connecting the 5 km FMF, the transmitted optical power of the LP₀₁ mode is increased by 2.8 dB compared with the transmission without crosstalk. The BER curves of the other three modes can only be close to or at the threshold. The above results show that the influence of the mode crosstalk from the FMF is greater than that of the mode multiplexer/demultiplexer, which is the main factor of performance degradation in the current system. We further study the BER performance before and after using MIMO pre-equalization and compare it with the ZF-pre-coding based crosstalk mitigation. According to the results in Fig. 7, after using MIMO pre-equalization and ZF pre-coding, the BER performance of each mode in transmission with and without crosstalk is improved. When the BER meets the 7% HD-FEC threshold, compared with the ZF pre-coding, the transmitted optical power of each mode using MIMO pre-equalization is reduced by 1.6 dB, 1.2 dB, 1.5 dB, and 1.4 dB under OBTB and is reduced by 3.0 dB, 4.1 dB, 1.2 dB, and 9.2 dB under 5 km FMF. The above results show that MIMO pre-equalization performs better than ZF pre-coding in both cases because it can eliminate the ISI caused by modal dispersion and the differential mode group delay after connecting the FMF. Additionally, the adaptive channel estimation used in MIMO pre-equalization is more accurate than the least squares (LS) estimation used in ZF pre-coding. Considering the influence of fiber chromatic dispersion, we analyze the BER performance before and after using pre-dispersion compensation based on MIMO pre-equalization. As shown in Fig. 8, when the BER meets the 7% HD-FEC threshold, the transmitted optical power of each mode using pre-dispersion compensation is 0.9 dB, 2.0 dB, 1.2 dB, and 2.4 dB less than without pre-dispersion compensation.

We propose an MIMO pre-equalization based mode crosstalk mitigation method for MDM-PONs and build a simulated MDM transmission system for verification. In both cases of OBTB and 5 km FMF transmission, we compare the performance of the proposed method with that of ZF pre-coding based crosstalk mitigation method. The results show that when using four LP modes (LP₀₁, LP₁₁, LP₂₁, LP₃₁) for 4×25 Gbaud QPSK transmission and the BER meets a 7% HD-FEC threshold, compared with the ZF pre-coding, the transmitted optical power of each mode using MIMO pre-equalization is reduced by 1.6 dB, 1.2 dB, 1.5 dB, and 1.4 dB under OBTB, whereas it is reduced by 3.0 dB, 4.1 dB, 1.2 dB, and 9.2 dB under 5 km FMF. The above results demonstrate that the proposed method can effectively mitigate the mode crosstalk in MDM-PONs and exhibits better performance for ISI caused by modal dispersion and differential modal group delay compared with linear pre-coding. Moreover, considering the influence of fiber chromatic dispersion, the performance of MIMO pre-equalization is further improved after cascading dispersion pre-compensation.

Confining light in air- and hollow-core microstructured fibers has many advantages such as low nonlinearity, low scattering, low dispersion, low loss, and low delay that are expected to break through the limits of fiber optic gyroscopes caused by the backscattering, Faraday effect, Kerr effect, and Shupe effect. They have become a hot topic in the research on a new generation of high-precision fiber optic gyroscopes. At small bending radii (on the order of millimeters), the optical fiber generates large stress and torsion owing to deformation, making it difficult to measure the bending loss. Therefore, there are few experimental reports on the bending loss of hollow-core photonic bandgap fiber (HC-PBGF) under an extremely small bending radius. In addition, in the winding process of the fiber optic gyro ring, to overcome the stress during bending and make the optical fibers compact, it is often necessary to apply a certain tension that would also increase bending loss. Therefore, it is of great significance for the development of high-precision fiber optic gyroscopes to research the bending loss of hollow-core microstructure fibers.

Hollow-core microstructured fibers are mainly divided into HC-PBGFs and hollow-core anti-resonant fibers (HC-ARFs). In this study, these two hollow-core microstructured fibers with excellent performance are drawn using the stack and draw technology. The finite element method combined with a perfect matching layer is used to simulate the scattering and confinement losses of two hollow-core fibers in straight and bent states. In the bending loss measurement, the light of the supercontinuum source is drawn out through the pigtail of the single-mode fiber and coupled into the hollow-core fiber through the fusion splicer. Optical fibers are wound onto cylinders with different bending radii, and the output of the optical fibers is connected to the spectrometer. The bending loss is determined by the difference in the spectra before and after bending. Furthermore, the HC-PBGF is tightly wound on the gyro ring skeleton by applying different tensions in turn with a fiber optic gyro winding machine, and the bending loss is measured using the truncation method.

Two types of hollow-core microstructured fibers propagating mainly at a wavelength of 1550 nm are successfully fabricated. The duty ratio of the HC-PBGF is as high as 97.6%, its core diameter is 32.8 μm, and the thickness of the lattice wall is between 40 nm and 75 nm. As for the fabricated HC-ARF, the core diameter, wall thickness of the cladding, and inner diameter of the cladding tube are 34.5 μm, 553 nm, and 23.8 μm, respectively. In terms of the simulated results, the bending loss of the HC-PBGF is 2-3 orders of magnitude lower than that of the HC-ARF at small bending radii (Fig. 4). The confinement loss of the PBGF begins to increase sharply when the bending radius is reduced to 1 cm, and the mode field of the fundamental mode shifts severely, but no coupling exists between the wall dielectric mode and the core fundamental mode. For the HC-ARF, the core and cladding modes achieve phase matching when the bending radius is 3.5 cm and the energy of the core leaks into the cladding. The experimental results show that in the wavelength of 1624 nm, the bending losses of the PBGF under bending radii of 5 cm, 3 cm, and 1 cm are 1.38 dB/km, 11.74 dB/km, and 23.29 dB/km, respectively. When the bending radius is less than 1 cm, the bending loss increases significantly. For example, at an extremely small bending radius of 0.25 cm, the bending loss at 1624 nm rapidly increases to 231.58 dB/km (Fig. 6). However, the bending loss of the HC-ARF is 2-3 orders of magnitude higher than that of the HC-PBGF (Fig. 7). At the wavelength of 1550 nm, after applying stresses of 0.1 N, 0.5 N, and 0.9 N using the fiber gyro loop winding machine, the ring losses increase by 3.69 dB/km, 16.43 dB/km, and 70.15 dB/km, respectively.

This study proves that the HC-PBGF has a better bending resistance than the HC-ARF. By using the bipolar symmetric winding method, the bending loss of the HC-PBGF at an extremely tight bending radius of 0.25 cm is successfully measured,which is 231.58 dB/km @1624 nm. This is the current lowest bend loss reported for such a tight bending radius. Furthermore, the losses of the HC-PBGF loop under different winding tensions are measured for the first time oriented to the application of a fiber optic gyro. The results show that the losses of the HC-PBGF loop increase significantly as the winding tension increases. Therefore, the winding of the HC-PBGF loop should be performed under small tensions. The research results are of great significance for promoting the application of hollow-core microstructured fibers in fiber optic gyros.

Many materials have been proved to be suitable for passively Q-switched lasers in the 3 μm waveband, and only a few relatively stable materials such as Fe^{2 +}∶ZnSe crystals can achieve a large energy output. However, as the Fe²⁺∶ZnSe crystal has a low damage threshold (1.5-2.0^{J/cm2@100 ns) in the 3 μm waveband, it can easily be damaged when operating at high peak power and high repetition frequency. Hence, to reduce the risk of damage during normal operation, it is necessary to analyze the pulse characteristics of Fe2+∶ZnSe crystals in passive Q-switched lasers to reduce the possibility of damage to the saturable absorber and realize laser operation at a high peak power and high repetition rate.}

Based on the measurement results, a high-repetition-rate Fe²⁺∶ZnSe crystal passively Q-switched laser system with a concave-convex resonator structure is developed to compensate for the thermal focal length. The Er,Cr∶YSGG crystal has dimensions of Ф3 mm×100 mm. Concave mirror M₁ is used as the all-reflection mirror (R₁=200 mm), M₂ is used as the output mirror (R₂=-216 mm), and the reflectivity of the convex surface is 70% at 2.79 μm.

By optimizing the internal component layout of the 60 Hz Er,Cr∶YSGG passively Q-switched laser, the high repetition frequency and high peak power of the 2.794 μm passively Q-switched laser can be achieved. Figure 5 shows the experimental waveforms of the 60 Hz passively Q-switched laser with two Fe²⁺∶ZnSe crystals. The single pulse energy of the lasers is 4.7 mJ and 7.0 mJ, with pulse widths of 97.0 ns [Fig.5 (a)] and 72.6 ns [Fig.5 (c)], respectively.

Lasers with high repetition rate and nanosecond pulse width around 3 μm waveband are required to improve the conversion rate of optical parameters and reduce the thermal effect when they are used in mid-infrared parametric pumping and hard tooth tissue ablation. The Q-switched technology is widely used to generate lasers with high peak power and narrow pulse width. Currently, the high-peak-power laser output at 3 μm waveband has been obtained using electro-optic Q-switched laser technology. However, because of the thermal depolarization effect of polarized laser under high-power pump, the repetition frequency of electro-optic Q-switched technology cannot be increased. The high repetition frequency can be achieved using acousto-optic Q-switched technology, but the large laser pulse energy cannot be realized owing to the limitation of the diffraction efficiency of the acousto-optic device. Mechanical Q-switched technology cannot produce stable laser pulses because it is difficult to accurately control the motor during high-speed operations. Theoretically, a passively Q-switched laser can achieve nanosecond laser pulses with high repetition frequency and high peak power as long as the damage threshold of the optical components is sufficiently large. Moreover, as a passively Q-switched laser has a compact cavity structure, its use is advantageous in laser applications.

Using output mirrors with different reflectivities, the values of the output pulse width of a Fe²⁺∶ZnSe saturable absorber are theoretically calculated (Fig.1 and Table 1). The values provide theoretical guidance for the design of passively Q-switched lasers. The pulse widths under two initial transmittances of the Fe²⁺∶ZnSe crystal (91.9% and 93.6%) and two reflectivities of the output mirror (30% and 40%) are measured using Er,Cr∶YSGG laser crystal rods with two sizes (Ф3 mm×100 mm and Ф4 mm×100 mm) pumped by a xenon lamp (Fig.2). The theoretical calculation results are verified through relevant experiments.

The results in Table 1 and Fig.3 show that the pulse width of the output lasers with different initial transmittances narrows with an increase in the reflectivity of the output mirror. A passively Q-switched laser output with large energy and narrow pulse width can be obtained more easily when the initial transmittances of the saturable absorber are lower. The experimental results verify the accuracy of the calculation. Moreover, the pulse width of the laser output has little relation with the size of the laser crystal rod, and the pulse widths obtained with the crystal rods with two different sizes are similar. From the beam diameter in the cavity, it is observed that a larger crystal rod diameter changes the mode volume in the cavity and increases the output laser energy; however, the laser energy density in the cavity does not increase because the bleaching process of the saturable absorber is not affected by the increase in the beam diameter.

The results show that a saturable absorber with low initial transmittance can achieve a low pulse width, whereas a saturable absorber with high initial transmittance can compress the pulse width by enhancing the reflectivity of the output mirror. Based on these results, the xenon lamp pumping Er,Cr∶YSGG laser is optimized, and Fe²⁺∶ZnSe passively Q-switched laser pulses with high repetition rate (60 Hz) and high peak power (7.0 mJ) are realized.

Rare-earth-doped optical waveguide amplifiers (RDWAs) have been widely investigated over the past few years because of their low cost, compensation for optical loss, compatibility with silicon substrates, and potential applications in integrated optical systems. Among the rare-earth elements, neodymium has received significant attention because it can achieve optical amplification at 1.06 µm. 808 nm semiconductor lasers are often selected according to the intrinsic absorption of Nd³⁺ ions from ⁴I_9/2 state to ⁴F_5/2 state to achieve the population inversion of Nd³⁺ ions. However, semiconductor lasers with a high pump power (100-400 mW) cause thermal damage to the waveguides and induce the up-conversion parasitic effect. Moreover, it is difficult to reduce their commercial costs. Therefore, three low-cost light-emitting diodes (LEDs) with different central wavelengths are selected as pump sources to achieve optical gains in neodymium-complex-doped polymer waveguides.

Using thermal ion exchange technology, a group of Ag⁺-K⁺ ion-exchanged glass waveguides is fabricated in a BK-7 optical glass. A group of rectangular SU-8 polymer waveguides with a cross-section of 8 μm×5 μm is fabricated by a one-step lithography process. Next, an active polymer material, neodymium complex Nd(TTA)₃DBTDPO-doped PMMA polymer, is spin-coated as the top cladding on the surfaces of the two types of waveguides. The room-temperature absorption and photoluminescence (PL) spectra of Nd(TTA)₃DBTDPO-doped PMMA polymer films are measured. Under the excitation of three blue-violet LEDs with different central wavelengths, optical gains are achieved in waveguides based on evanescent-wave coupling.

For the evanescent-wave optical waveguide based on Ag+-K+ ion-exchanged glass with a length of 10 mm, the output optical intensity increases with the increasing pump power when the input signal power is 0.03 mW at 1.06 μm wavelength [Fig. 5(a)]. For a fixed signal power, the relative gain increases linearly with increasing pump power [Fig. 5(b)]. When the input signal power is 0.03 mW at 1.06 μm and the pump power is 225 mW, the relative gains of 3.6 dB/cm, 2.2 dB/cm, and 0.9 dB/cm are obtained under LED excitation with central wavelengths of 405, 581, and 745 nm, respectively. The relative gain under the excitation of the 581 nm LED is better than that of the 745 nm LED because of the increased absorption coefficient of Nd3+ ions. The organic ligand can realize the transition from a ground state (S0) to a high-energy singlet state (S1) by absorbing 405 nm pumped light energy and then transit the energy to a triplet state (T) by intersystem crossing. Moreover, Nd3+ ions can be excited from the ground state 4I9/2 to 4F9/2 through energy transfer from the organic ligands in the triplet state (T) (Fig. 7). After relaxation to the 4F3/2 level, the luminescence at 1060 nm (4F3/2→4I11/2) is achieved. Therefore, the relative gain under the excitation of the 405 nm LED is better than those under the excitations of the 581 nm and 745 nm LEDs. For the neodymium-doped polymer waveguide with a length of 8 mm based on evanescent-wave coupling, the relationship between the output signal intensity and pump power shows the same trend as that for the ion-exchanged optical waveguide (Fig. 6). When the pump power reaches 225 mW, a relative gain of approximately 4.1 dB/cm is obtained. Compared to the ion-exchanged waveguide, which only has a neodymium-doped polymer attached to the upper layer of the waveguide, the three sides of the polymer waveguide are surrounded by neodymium-doped polymer. Thus, the polymer waveguide exhibits an increased amplification ability.

In this study, a new LED top-pumping mode based on an evanescent-wave optical waveguide is proposed. The relative gain based on two types of optical waveguides with Nd(TTA)₃DBTDPO complex-doped PMMA polymer as the top cladding is demonstrated. An intramolecular energy transfer mechanism from the organic ligands (DBTDPO and TTA) to the central Nd³⁺ ions has been established. Using the vertical top pumping mode of the LED, the up-conversion parasitic effect and waveguide thermal damage caused by traditional laser pumping can be overcome because the incident power of the LED is almost uniformly distributed on the waveguide surface. The neodymium complex Nd(TTA)₃DBTDPO-doped PMMA polymer used in this study can be easily spin-coated on various waveguides, such as silicon on insulator (SOI), silicon nitride, polymer, and glass, to realize a loss compensation at 1.06 µm. The vertical top pumping mode of an LED based on intramolecular energy transfer can significantly reduce the commercial cost of the device and has potential market application value.

Results and Discussions The laser pulse characteristics are investigated using a pump pulse width of 7.5 μs, repetition frequency of 40 kHz, and pump power of 6 W. When the 1065 nm output mirror tilt angle is approximately 0.02°and the 1063 nm output mirror tilt angle is 0°, the laser achieves dual-wavelength pulse synchronization with a repetition rate of 40 kHz. The pulse widths at 1063 nm and 1065 nm are 120 ns and 150 ns, and the output powers are 143 mW and 96 mW, respectively. The pulse repetition frequency fluctuations are both less than 2%. By tuning the pump pulse repetition frequency, dual-wavelength synchronized pulse signals with a pulse repetition frequency of 30.7-100.0 kHz are realized. When the pump pulse repetition frequency lies between 30.7 kHz and 45.0 kHz, the average power of the dual-wavelength laser increases linearly with an increase in the pump repetition frequency, and the peak power of the dual-wavelength pulse remains unchanged. When the pump repetition rate lies between 45 kHz and 100 kHz, the average output power of the 1063 nm laser decreases with a rate of 0.8 mW/kHz, and the pulse peak power decreases with a rate of 0.25 W/kHz. The average output power of the 1065 nm laser decreases with a rate of 1.27 mW/kHz, and the pulse peak power decreases with a rate of 0.07 W/kHz. When the pump repetition rate is 100 kHz, the average output powers at 1063 nm and 1065 nm reach their highest values of 215 mW and 176 mW, respectively, and the total average output power is 391 mW.

Dual-wavelength synchronous pulsed lasers have important practical applications in fields including precision metrology, holographic interferometry, lidar, and coherent terahertz (THz) wave generation. One approach to obtain dual-wavelength synchronized pulsed lasers is based on a Y-type-cavity dual-crystal laser combined with a saturable absorber, which achieves power balance by adjusting the pumping power of the respective laser crystals. Another approach is based on a linear laser cavity combined with a saturable absorber and dual-gain-peak laser crystal, which achieves power balance by means of birefringent elements, etalons, or stress-induced birefringence. Passive Q-switched pulse mechanism often leads to time jitter between the dual-wavelength laser pulses, owing to the nonlinear characteristics of the saturable absorbers, and dual-wavelength pulse synchronization is difficult to achieve using conventional means. In this paper, a gain-switched dual-wavelength pulsed laser based on a Nd∶GdVO₄ crystal is proposed. By adjusting the misalignment of the Y-type cavity to change the dual-wavelength laser thresholds, synchronized pulse outputs at 1063 nm and 1065 nm are obtained. The gain-switching mechanism simplifies the laser resonator structure and flexibly controls the laser pulse parameters, including the pulse repetition frequency and the peak power, by adjusting the pump parameters. Currently, there are no studies on gain-switched synchronous dual-wavelength pulsed lasers, and obtaining dual-wavelength synchronous pulsed output by employing a gain-switching mechanism is challenging.

First, a simulation model of a gain-switched dual-wavelength pulsed laser is established based on the four-level rate equation. Through model simulation, it is found that the laser thresholds have an important influence on the time-domain characteristics of dual-wavelength pulses, and changing the loss of the output mirrors can control the dual-wavelength thresholds. Therefore, it is inferred that the reasonable output mirror loss can realize time synchronization of dual-wavelength laser pulses. The effect of the pump parameters on the repetition rate of the dual-wavelength pulse and the characteristics of the single laser pulse are also studied, which provides a reference for further design and experiments on dual-wavelength lasers.

In summary, a gain-switched dual-wavelength synchronous pulsed laser is proposed. Based on the simulation analysis of the four-level rate equation, a Nd∶GdVO₄ crystal with a high emission cross-section and a Y-shaped cavity design are employed, and the laser thresholds of the dual-wavelength signals are changed by adjusting the misalignment of the laser cavities. Finally, dual-wavelength pulse time synchronization is realized. By changing the repetition frequency of the pump pulses, dual-wavelength synchronous pulses of up to 100 kHz, pulse widths of 120 ns and 150 ns, and peak powers of 29.85 W and 15.10 W, respectively, are realized. Compared with the passive Q-switching mechanism, the gain-switched dual-wavelength synchronous pulse laser has a simple structure, good time synchronization characteristics, and a high pulse repetition frequency, which can be applied to the generation of terahertz wave signals.

Pulsed lasers are widely used in many fields because of their high peak power and short pulse width. Most single-mode pulsed lasers generated by Q-switching have Gaussian waveforms. However, pulsed lasers with unique waveforms exhibit improved effects in specific applications, such as laser-induced acoustics, laser welding, laser ablation, and laser-induced breakdown spectroscopy. Two lasers are employed using a high-precision signal generator to generate a double-pulse laser. A pulsed laser with an attenuated waveform is obtained using multiple reflections. In this study, an adjustment method for pulsed laser waveforms based on beam splitting and delay is proposed. The proposed method can provide increased pulsed laser waveforms in laser-induced acoustics, laser welding, laser ablation, and laser-induced breakdown spectroscopy.

First, an experimental optical layout (Fig. 2) based on beam splitting and delay is designed. Subsequently, a numerical simulation (Table 2 and Fig. 4) is conducted for a Gaussian waveform, and the parameters required to generate superimposed pulsed lasers with rectangular, triangular, hump-shaped, and dual-peak waveforms are obtained. Finally, the 532 nm laser generated by frequency doubling of the Nd∶YAG laser enters the device. Superimposed pulsed lasers with different waveforms are obtained by varying the splitting ratio and delay. Two high-speed photodetectors and a high-speed digital oscilloscope are used to measure the waveforms of the original and superimposed pulsed lasers.

Superimposed pulsed lasers with rectangular, triangular, hump-shaped, and dual-peak waveforms are successfully obtained (Fig. 6). The experimental results are consistent with the numerical simulation results. Because the waveform of the original laser pulse is not an ideal Gaussian waveform and the actual splitting ratio of the beam splitter is affected by the laser polarization direction, the top of the pulsed laser with a rectangular waveform is not sufficiently smooth. Subsequently, the pulsed laser with a rectangular waveform is simulated again with the waveform of the original pulsed laser, and the simulation results are consistent with the experimental results (Fig. 7). This method is suitable for experiments performed under strong light but is affected by the damage threshold. If the pulsed laser energy is exceptionally high, the damage threshold can be increased via beam expansion.

This study presents a method that can flexibly adjust the pulsed laser waveform. By varying the splitting ratio and delay or increasing the numbers of beam splitters, a laser can yield superimposed pulsed lasers with different waveforms. A numerical simulation is performed, and the parameters required to generate pulsed lasers with rectangular, triangular, hump-shaped, and dual-peak waveforms are determined. Experiments are performed on the designed optical layout based on the parameters obtained from the simulation. The experimental results demonstrate that this method can yield pulsed lasers with various waveforms, such as rectangular, triangular, hump-shaped, and dual-peak waveforms, by varying the splitting ratio and delay. Because the waveform of the original pulsed laser is not an ideal Gaussian waveform and the actual splitting ratio of the beam splitter is different from the theoretical splitting ratio, the top of the pulsed laser with a rectangular waveform is not sufficiently smooth. This method provides a new special waveform pulsed laser generation scheme for laser-induced acoustics, laser welding, laser ablation, laser-induced breakdown spectroscopy, etc.

To realize a silicon-based photonic integrated chip circuit, we perform epitaxial deposition of GaAs material on a silicon substrate and subsequently prepare a silicon-based light source. However, there is a 4.1% lattice mismatch between Si and GaAs, resulting in three-dimensional (3D) growth of the material and formation of several 3D island structures in the initial growth stage of GaAs/Si (001), deteriorating its surface morphology. The roughness in the initial growth stage is difficult to reduce to an ideal level, which significantly affects the crystal quality of subsequent growth materials and leads to the failure of the overall preparation process of the device. Currently, the main solutions for reducing the surface roughness of GaAs/Si(001) materials are chemical mechanical polishing (CMP) and the growth of strained-layer superlattice (SLS). Because the epitaxial layer is too thin to be cleaned using the CMP technology, the possibility of polishing the epitaxial layer cannot be increased because of the complexity of epitaxial layer preparation. Therefore, the SLS growth technology has become the primary choice for improving the surface morphology of epitaxial materials. Generally, the SLS growth technology used in previous study matches the lattice of epitaxial materials, and its strain is significantly less than that of the SLS used as a dislocation filter layer. Therefore, it can only improve the surface morphology; however, it cannot reduce the material defects and improve the crystal quality. Therefore, it is necessary to use a dislocation filter layer to improve the crystal quality of GaAs/Si (001). In this study, the preparation technology of a strain-balanced superlattice structure that combines tensile and compressive strains is proposed. This technique can not only effectively improve the surface roughness of GaAs/Si (001) materials but also reduce material defects and enhance the crystal quality in the traditional dislocation filter layer. This not only simplifies the growth and preparation process of GaAs/Si (001) but also reduces the thickness of the epitaxial layer, thereby reducing the risk of thermal cracking caused by excessive material thickness.

GaAs epitaxial layers with strain-balanced superlattices were grown through metal organic chemical vapor deposition on exact planar silicon (001), and pure GaAs epitaxial layers were grown under the same conditions. The surface morphology and crystal quality of the two samples were characterized by atomic force microscopy (AFM), photoluminescence (PL), and double crystal X-ray diffraction (XRD).

The implementation of the strain-balanced superlattice technique changes the growth mode of the GaAs/Si(001) material from layer-by-layer growth to step-flow growth. As demonstrated in the AFM characterization, the average surface root mean square (RMS) roughness decreases from 1.92 nm (10 μm×10 μm) to 1.16 nm (10 μm×10 μm) (Fig. 3 and Table 1). The quality of the GaAs crystals is characterized by PL and XRD at room temperature. In comparison with the GaAs/Si(001) material without a superlattice, the PL peak intensity of the GaAs/Si(001) material with a superlattice increases by 500.3%, whereas the average PL peak full width at half maximum (FWHM) reduces from 31.6 nm to 23.4 nm (Fig. 5 and Table 2). The FWHM of the XRD curve decreases by 30.4%, whereas its peak intensity increases by 472.2% (Fig. 6).

In this study, the effects of strain-balanced superlattice on the surface morphology and crystal quality of GaAs/Si(001) are experimentally investigated. The results indicate that this scheme can effectively improve the surface morphology of GaAs/Si(001). Compared with the GaAs epitaxial layer without the application of this technique, the average RMS roughness of the prepared sample decreases from 1.92 nm (10 μm×10 μm) to 1.16 nm (10 μm×10 μm). In terms of crystal quality, compared with GaAs epitaxial layer prepared without this technique, the average PL peak intensity under room temperature characterization increases by 500.3%, whereas the average PL peak FWHM decreases from 31.6 nm to 23.4 nm. The FWHM of the XRD curve decreases by 30.4%, whereas its peak intensity increases by 472.2%. In conclusion, this scheme effectively improves the surface morphology and crystal quality of GaAs/Si(001) materials. The scheme proposed in this paper provides a feasible way to improve the surface morphology of silicon-based GaAs materials and lays a technical foundation for promoting the industrialization of large-scale silicon-based photoelectric integrated circuits.

Cr³⁺-doped near-infrared (NIR) emitting persistent luminescence (PersL) materials with an emission range of 650-1000 nm are renewable by red light instead of ultraviolet (UV) light, which is highly promising for renewable tissue imaging in vivo and broad application prospects in biomedical diagnosis and treatment. We have recently reported a BaGa₂O₄∶Cr³⁺ (BGO∶Cr) NIR emitting PersL material with Cr³⁺ as the luminescent center and BaGa₂O₄ as the matrix. The BGO∶Cr PersL material exhibited UV excitation, light-emitting diode (LED) light restimulation, ultra-long PersL for more than 6 days, and excellent capability for information storage. This study aims to develop BaGa₂O₄∶Cr³⁺, Sm³⁺ NIR emitting PersL materials with stronger luminescence intensity and longer emission wavelengths than BGO∶Cr PersL materials by co-doping BGO∶Cr PersL materials with Sm³⁺ ions for the development of medical multimodal imaging, medical detection probes, integrated diagnosis, and treatment probes.

In this study, BGO∶Cr, Sm PersL materials were synthesized using a high-temperature solid-state synthesis method. The effects of Sm³⁺ doping concentration and calcination temperature on the luminescent properties and crystal structure of BGO∶Cr, Sm PersL materials were investigated, and the NIR luminescence mechanism was discussed. The surface shape, element distribution mappings, and thermal stability of BGO∶Cr, Sm PersL materials were observed and analyzed.

In PersL material characterization, all X-ray diffraction peaks of the BGO∶Cr, Sm PersL materials were consistent with those of the BGO plane crystals (PDF 46-0415), the energy dispersive X-ray spectrometry spectra and element distribution mappings of BGO∶Cr, Sm PersL materials indicated the presence of Ba, Ga, O, Cr, and Sm elements, and transmission electron microscopy images show that the average particle length of the PersL materials is 1.61 μm and the average width is 0.76 μm (Fig. 1). The BGO∶Cr, Sm PersL materials exhibit strong NIR luminescence at 734 nm, with the BGO∶Cr0.06, Sm0.004 sample exhibiting the highest luminous intensity. Furthermore, the PersL intensity of BGO∶Cr PersL materials was enhanced after co-doped with Sm3+ ion [Figs. 2(a), (b)], and the afterglow time of the BGO∶Cr0.06, Sm0.004 PersL material is 131.61 s. According to the thermoluminescence measurements, the electron trap energy-level depth is estimated to be approximately 0.553 eV by the half-width method, showing that BGO∶Cr, Sm PersL materials are suitable for providing PersL for a long time at room temperature [Figs. 2(d),(e)]. A schematic energy diagram of the PersL mechanism shows that the NIR luminescence of BGO∶Cr, Sm is produced by the spin-forbidden 2E(2G)→4A2(4F) transition of Cr3+ and that PersL is produced by the recombination of holes and charge carriers released from the trap after stopping UV irradiation [Fig. 2(f)]. Meanwhile, our studies have shown that BGO∶Cr, Sm PersL materials exhibit good thermal stability, and the maximum luminous intensity at 150 ℃ shows their potential as raw materials for red LEDs (Fig. 4). Finally, we found that BGO∶Cr, Sm PersL materials exhibit good crystallinity and NIR luminescence only when the calcination temperature reaches 1100 °C (Fig. 5).

In summary, BGO∶Cr, Sm PersL materials with an emission wavelength of 734 nm were prepared using a high-temperature solid-state synthesis method. The luminescence intensity reached the maximum when the composition of the PersL materials was BGO∶Cr_0.06, Sm_0.004, and the PersL intensity of BGO∶Cr was enhanced by Sm³⁺ doping. The calcination temperature has a significant effect on the luminescence properties and crystal structure of BGO∶Cr, Sm PersL materials. BGO∶Cr, Sm PersL materials with high purity can be obtained when the annealing temperature is 1100 ℃. The electron trap energy-level depth of BGO∶Cr, Sm PersL materials is approximately 0.553 eV when estimated using the half-width method. BGO∶Cr, Sm PersL materials exhibit strong and persistent luminescence by co-doping and have potential applications in night vision surveillance and medical imaging.

Fluid motion is a common phenomenon in observed nature and utilized in industries. Mastering the fluid flow is an important prerequisite for an in-depth study of fluid mechanics. The particle image velocimetry (PIV) is a non-contact global flow-field measurement and display technology that provides accurate data for flow-field measurements without affecting the flow field. The particle image velocimetry is mainly divided into two categories: cross-correlation and optical flow algorithms. The optical flow algorithm is primarily used in small-displacement scenarios. When the particle displacement is significantly larger than the particle size, the optical flow method cannot yield accurate results. The cross-correlation algorithm is mainly used in large displacement scenarios, and the combination of the two algorithms can satisfy more application scenarios. Although the hybrid algorithm has higher accuracy than the traditional algorithm in large- and small-displacement scenarios, the angle information is not well retained in the case of complex fluid. Because the image of the particle conforms to the Airy spot model and the light intensity satisfies the two-dimensional Gaussian distribution, if the Gaussian radial basis function interpolation is used, the velocity field refinement will be transformed into a surface reconstruction problem, and the reconstructed velocity field will have a higher accuracy. Therefore, we propose a cross-correlation optical flow mixing algorithm based on the Gaussian radial basis function interpolation to reduce the angular error.

Based on the traditional hybrid algorithm, in this study, the Gaussian radial basis function interpolation is used to replace bicubic interpolation and design a cross-correlation optical flow hybrid algorithm. First, a pair of particle images is inputted, and a cross-correlation method is used to extract the relatively large particle motion in each query window. A Gaussian radial basis function is used for data interpolation to fill the speed vector in each pixel. For each pixel, the image displacement is processed to remove the speed vector detected in the image. Subsequently, the initial velocity vector is determined using the HS optical flow method, and the residual velocity field is refined using the variable spectral flow method based on the dynamic illumination equation. The Gaussian radial basis function interpolation method is used to interpolate the velocity field at each layer, and the more refined velocity field vectors are obtained. Finally, the velocity field vectors obtained by the cross-correlation and optical flow algorithms are superimposed to obtain an accurate velocity field. The algorithm is quantitatively evaluated through a Rankine vortex simulation experiment. The influence of displacement and particle size on the accuracy of the algorithm is studied. Subsequently, a two-dimensional PIV experimental system is built, and rotation and water injection experiments are performed to simulate the vortex current field and jet field, respectively. The practicability of the proposed algorithm is verified.

In the Rankine vortex simulation experiment, the manifold reconstructed by the proposed method is more in line with the characteristics of the Rankine vortex and closer to the ground truth (Fig. 3). The root mean square error (RMSE) and average angular error of the cross-correlation optical flow hybrid algorithm based on Gaussian radial basis function interpolation are 27.36% and 38.32% lower than those of the Hybrid method 2020, respectively (Table 1). With an increase in the maximum displacement, the root mean square error gradually increases. In most cases, the hybrid algorithm based on Gaussian radial basis function interpolation is superior to the Hybrid method 2020. In the case of a small displacement, the RMSE can be decreased by approximately 45%, whereas in the case of a large displacement, the RMSE can be decreased by approximately 15% (Fig. 5). With an increase in particle size, the angle error first decreases and then the best reconstruction result is obtained when the particle size is 3 pixel. The proposed method can obtain good reconstruction results in the cases of both small and large particle sizes. In the case of particle size of 2-4 pixel, the average angle error of the proposed method is approximately 15% lower than that of the Hybrid method 2020 (Fig. 6). The results of water injection and rotation experiments verify the performance of the proposed algorithm in practical applications.

In this study, based on the traditional hybrid algorithm, the Gaussian radial basis function interpolation is used to replace bicubic interpolation, and a cross-correlation optical flow hybrid algorithm based on Gaussian radial basis function interpolation is proposed. This approach preserves the angle information in the complex flow field, which is not possible using the traditional hybrid algorithm. It changes considerably with velocity, and the method can accurately reconstruct flow fields. The proposed algorithm and the Hybrid method 2020 algorithm are used to reconstruct the velocity field in an experiment. The results show that the two algorithms can maintain high consistency in the entire manifold, and the proposed algorithm can retain more angle information. This verifies that the proposed algorithm can accurately reconstruct the actual complex flow field and has potential for practical applications.

Binocular camera calibration is important to realize high-precision 3D measurements, dynamic target trajectory estimations, and 3D positioning through binocular vision. Zhang s traditional calibration method based on a checkerboard target is currently the most widely used camera calibration method. However, Zhang s calibration method has certain shortcomings. First, Zhang s calibration method requires multiple shots of the checkerboard target, rendering the calibration process cumbersome. Second, when using the checkerboard target for calibration, the calibration accuracy is often degraded owing to the acquisition of local target images; this may sometimes also lead to failure of calibration. Finally, Zhang s calibration method optimizes the parameters of a camera through reprojection constraints; moreover, the constraints are extremely singular, and hence, accurate camera calibration results cannot be obtained. To address the above-mentioned issues, this paper proposes a high-precision binocular camera calibration method based on a novel stereoscopic target.

To solve the problems encountered in Zhang s calibration method, first, this study adopted a new type of coding stereoscopic target composed of four encoded plane targets with different spatial attitudes so that only one target image was needed to collect to complete the binocular camera calibration. In each coding plane target, multiple independent coding units were arranged to eliminate the traditional checkerboard structure, which could effectively address occlusion of the target. Second, each calibration corner was coded by a new variable-capacity coding flag, which improved the matching efficiency and accuracy of points with the same name. Finally, to enrich the camera parameter optimization constraints, a high-precision parameter optimization method was adopted, exploiting the three-dimensional information of the coding stereoscopic target and introducing standard length and coplanar constraints, which effectively improved the calibration accuracy of binocular cameras.

Compared with Zhang s traditional calibration method, the method proposed in this paper demonstrates significantly improved calibration efficiency and accuracy. In Zhang s calibration method, the checkerboard target must be shot multiple times, and each shot must ensure the integrity of the checkerboard target and the difference in the spatial posture of the checkerboard target. In contrast, the method proposed in this paper only requires to shoot the coding stereoscopic target once and can cope with the situation of the local target; therefore, the calibration efficiency is significantly improved. For the calibration accuracy, compared with Zhang s calibration method, the proposed method reduces the reprojection errors of the left and right cameras by 55.42% and 57.22%, respectively; the standard-length error by 41.28%; and the coplanarity error by 63.04% (Fig. 6). Simultaneously, when using the standard gauge block for verification, the measurement error of the proposed method is reduced by 54.61% compared with that of Zhang s calibration method (Fig. 8). When the locally encoded stereoscopic target is captured, the relative error between the left and right camera reprojection errors is 7.49%, the relative error of the standard-length error is 7.42%, and the relative error of the coplanar error is 6.36% compared with the complete target (Fig. 7). When a locally encoded stereoscopic target is recorded, the proposed method still demonstrates a high calibration accuracy for the binocular camera.

This paper proposes a binocular camera calibration method based on a coding stereoscopic target, combined with high-precision parameter optimization. The coding stereoscopic target includes four encoded plane targets with different spatial attitudes. By arranging multiple encoding units in the encoded plane target and encoding each calibration corner, the binocular camera can be calibrated based on a single target image acquisition. Compared with Zhang s calibration method, which requires multiple shots of the checkerboard targets, the method proposed in this paper effectively improves the camera calibration efficiency. In this study, a high-precision parameter optimization method is used to establish an objective function that combines reprojection constraints, standard length, and coplanar constraints, thereby effectively improving the calibration accuracy of binocular cameras. The experimental results reveal that compared with Zhang s calibration method, the proposed method effectively reduces the mean absolute reprojection error, mean absolute standard-length error, and mean absolute coplanarity error of binocular camera calibration. In addition, when the locally coded stereoscopic target is captured, the proposed method can still efficiently complete binocular camera calibration, and the relative error of each mean absolute error is less than 8% compared with that when the completely coded stereoscopic target is captured. This condition satisfies the requirements of high-precision calibration of binocular cameras for optical measurements.

Cross-linked polyethylene (XLPE) cable is an important part of the Chinese power system, and it plays a vital role in the transmission of power resources, therefore ensuring the normal operation of its lines is critical. According to some relevant cable fault statistics, the main cause of XLPE cable failure is a poor quality anti-stress cone in the cable joint, which is because all parameters of the anti-stress cone of cable joints are currently measured manually using contact measuring tools, such as tape measure. This measurement method has large errors and is prone to causing secondary damage to the measured object. The other cause is some nonstandard joints whose anti-stress cone size does not meet the design requirements are often connected to the power system. Under long-term high-voltage action, nonstandard joints can cause partial discharge due to insufficient resistance to axial stress, resulting in the insulation breakdown. Existing noncontact parameter measurement methods are difficult to apply to the parameter measurement of anti-stress cones. Therefore, we combined the structural characteristics of the cable joint with three-dimensional (3D) point cloud processing to propose a parameter measurement algorithm for the anti-stress cone of the XLPE cable joint, which can realize the effective measurement of all parameters of the cable joint anti-stress cone, which is critical to ensure safe and reliable operation of the power system.

First, this algorithm performs denoising and coordinate adjustment on a cable joint point cloud. Second, the target point cloud of the anti-stress cone and its adjacent area is obtained according to the XLPE cable joint characteristics. Then, the target point cloud is divided into strips and pieces using the point cloud space division method based on the angle and height information between each point and the coordinate axis in the target point cloud. Following that, the local point clouds of different regions on each strip point cloud are obtained using the included axis angle of the piece normal vector on the strip point cloud and the improved concave-convex criterion. On this basis, the random sample consensus (RANSAC) algorithm and Lagrange multiplier method are used to obtain the intersection line of the adjacent plane, and preliminary measurement results are obtained on the basis of the distance relationship between each point on the strip point cloud and the intersection line. Finally, residual estimation is used to correct the error of the preliminary measurement results to obtain the final measurement results.

The proposed XLPE cable joint anti-stress cone parameter measurement algorithm has high-measurement accuracy and robustness. When it measures the parameters of the cable joint anti-stress cones with standard size, the absolute error is less than 0.2 mm, and the relative error is less than 0.5%; when it measures the parameters of the anti-stress cones of the cable joints polished by different technicians, the absolute error is less than 1.0 mm, and the relative error is less than 1.5% (Table 4), which meets the industry measurement accuracy requirements. Compared with the radius change method, it has higher measurement accuracy (Table 2). To address the problem that the number of points between the pieces obtained using the existing point cloud space division method is relatively large, resulting in the instability of local features, a new point cloud space division method that can achieve a good division effect is proposed (Figs. 6 and 7, Table 3), the best angle range of strip division is 4°-6° (Table 6), and the best setting constant range of piece division is 0.4-0.6 mm (Table 5). To address the problem that the initial measurement value is shifted to the anti-stress cone region due to the structure of the cable joint, a residual estimation error correction method is proposed, which effectively improves the measurement accuracy of the algorithm (Fig. 12, Table 4). The optimal threshold range of D_th3 and D_th4 is 0.35-0.45 mm (Tables 7 and 8).

In this paper, we proposed a 3D point cloud-based algorithm for measuring the anti-stress cone parameters of XLPE cable joints. The target point cloud is obtained by the proposed obtaining method; on this basis, the measurement of the parameters of the anti-stress cone of the cable joint is realized, which reduces the interference of the nontarget area and improves the processing efficiency of the algorithm. The proposed cable joint with a quasi-cylindrical structure ensures the consistency of the piece element s description of the measured object s characteristics. The original concave-convex criterion is improved to eliminate the influence of the piece elements in the transition area based on the changes in the included angle of the piece elements on the strip point cloud. The robustness of the algorithm is ensured using a preliminary measurement method based on the structural characteristics of the anti-stress cone. To avoid the problem that the preliminary measurement results are shifted to the anti-stress cone region due to the arc-shaped transition structure at the junction point of the anti-stress cone, the residual estimation error correction method is used to improve the measurement accuracy of the algorithm. Two types of cable joint point clouds with standard dimensions and surface defects were used for measurement experiments, and the experimental results show that the proposed algorithm has high-measurement accuracy and robustness.

China is currently planning on building several 4^th-generation light source facilities that are larger in scale and have highly complex equipment. Therefore, higher alignment and global control point accuracies are required to ensure the robust and stable operation of the facility. The accuracy requirement has reached the measurement accuracy limit of laser trackers. It is of great significance for the construction and development of 4^th-generation light source facilities to explore high-precision and stable data processing methods for laser trackers. In this study, an improvement on the existing adjustment method for the control network, which can retain the extremely high accuracy of laser tracking data while avoid some small and unidentifiable gross errors that will affect the overall processing results, is proposed.

Based on robust estimations, an adaptive weighting strategy for rank-defect weighted 3D bundle adjustment that can adaptively adjust the weight matrix of the observed values and weight matrix of the datum equation to achieve robust estimation is employed in this study. Simultaneously, due to data processing using routine robust estimation without any gross error, gross error misjudgment can also be avoided. First, after the first iteration of adjustment, the sum of the residuals less than or equal to the product of the mean value of the two selected weight thresholds and mean square error is calculated. If this value is less than half of the total numbers of observations, the thresholds are considered to be set too low, and vice versa. The two thresholds are corrected proportionally by multiplying them with a specific correction factor when the threshold is high and dividing them by the same factor when the threshold is low. Along with the iteration process, the selected weight thresholds are dynamically and adaptively adjusted to allow the dynamic and adaptive adjustment of the weight of the observed values. This process ends when the changes in the threshold are less than 0.001. Simultaneously, according to the corresponding relationship between the parameters of the datum equation and observed values, the sum of the weight values of all the observed values corresponding to each point in the parameters is calculated and divided by the numbers of respective observed values to obtain the weight matrix of the parameters of the datum equation. Thus, the adaptive adjustment of the weight matrix of the reference equation is realized (Fig. 1) owing to the progress of adjustment iterations and the adaptive adjustment of the weight matrix of the observed values.

The robustness and stability of the self-adaptive weighted bundle adjustment are verified using simulation data. Based on the accelerator alignment measurement scene and characteristics of the laser tracker, the alignment control point measurement data are simulated (Figs. 2-4), and the minimum norm adjustment method, the unified spatial metrology network (USMN) of SpatialAnalyzer software, and the method used in this study are used to adjust the simulated data. The error range and change trend of the treatment results are close, which conforms to the actual measurement experience (Fig. 5). The accuracy of the proposed method is basically equivalent to that of the USMN, with a deviation of about 0.002 mm (Table 1). To verify the ability to handle gross errors, a gross error of 1 mm is added to a point observed at the fifth station to simulate the gross error observation in the measurement process. This method maintains the processing stability in all three directions, avoids the influence of gross error observation, and has an overall accuracy equal to that of the USMN. When conducting data processing for two groups, the weight selection thresholds decrease proportionally with increased numbers of iterations and tend to be stable after eight iterations. Moreover, after the addition of gross error observations, the threshold must be decreased to ensure the stability of the selected observation range (Fig. 7). The measured data are processed in the Hefei Advanced Light Facility (HALF), and the results obtained are similar to those of mature commercial software (Figs. 9 and 10). The deviation is approximately 0.02 mm, which is within the accuracy requirements of the 4th-generation light facilities.

In this study, an adaptive weighting method for adjusting the weighted rank-defect bundle is proposed. Based on the weight selection and actual accuracy of the observed values, the weight selection thresholds are dynamically and adaptively adjusted to realize the adaptive adjustment of the weight matrix of the observed values. Simultaneously, the parameters of the weight matrix of the datum equation are adaptively adjusted according to the weight matrix of the observed values. In the adjustment process of the high-precision data of laser tracker and data with a slight gross error, the observed values are not misjudged as gross error during processing and the influence of the gross error can be simultaneously avoided. The simulation data and measured data show that the proposed method has a stability and robustness of adjustment similar to those of commercial software processing and can be a basic reference for studies on accelerator alignment.

Electromagnetic wave absorbers operating in the microwave, THz, infrared, visible, and ultraviolet bands have become a prevalent research topic. The typical electromagnetic wave absorber is a vertically stacked multilayer structure based on a metal-dielectric-metal (MIM) structure. The optical characteristics of metal, semiconductor, and new materials can be utilized to optimize the absorption of incoming electromagnetic waves. Absorption mechanisms such as local plasmon resonance, magnetic polariton resonance, surface plasma resonance, Fabry-Perot cavity resonance, and guide mode resonance can be used to realize ideal absorption effects. Infrared absorbers with efficient, broadband, and tunable properties are urgently required in optical sensors, photothermal energy converters, imaging, and infrared stealth cloaks. However, in practical applications, achieving a broadband response in the infrared band is difficult. Most proposed infrared absorbers are limited to the near-infrared (NIR) range and are untunable. Therefore, an ultra-broadband tunable absorber operating from near-infrared to far-infrared is proposed, and its absorption mechanism is analyzed.

An infrared broadband absorber is designed based on the phase material VO₂, metalloids, and high-temperature resistance materials NaF and TiO₂. First, owing to the unique properties of the materials, the material properties are set based on the role and characteristics of different materials. The ports at the upper and lower ends along the z-direction are set separately, the port type is periodic, and the two ports are set to open and close,respectively. Second, the domains, boundaries, and edges of the different materials in the structure are meshed in detail. Parametric sweeping is then performed according to the study band, and the electric field distribution and the magnetic field are obtained. Finally, the optimal result is obtained through repeated calculations by adjusting the structural geometric parameters, angle of incidence, and polarization angles of the transverse electric (TE) and transverse magnetic (TM) waves.

After several simulations, the optimization parameters are obtained: the cell period is 7 μm, the width of the bottom composite layer is 5.8 μm, the width of the top composite layer is 3.4 μm, the thickness of Au is 0.9 μm, the thickness of SiO2 layer is 0.9 μm, the thickness of NaF layer is 0.1 μm, the thickness of VO2 layer is 1.0 μm (the conductivity is set as 2×1015 S/m), and the thickness of TiO2 layer is 0.3 μm. The ratio between the edge length of each group of top square holes and the edge length of each group of composite layers is 0.05, the distance between the outside of the SiO2 square ring and the outside of the composite layer is 0.1 μm, and the width of the square ring is 0.1 μm. Figure 3 shows that the ultra-wideband absorption in the wavelength range of 12-52 μm, and the polarization insensitivity can be achieved using this absorber. Figure 4 shows that when the TM wave is incident, the angle of incidence increases to 55° in the range of 12-52 μm, and the absorptivity can reach approximately 80%. When the TE wave is incident, the angle of incidence increases to 55° in the range of 20-45 μm, and the absorptivity reaches approximately 80%. Figure 5 shows that the absorption mechanism of the absorber is surface plasma resonance. The physical mechanism of absorption can also be better understood from the impedance-matching plot (Fig. 6). The structural parameters have a substantial impact on the absorption performance. Figure 7 shows the absorptivity curves for different structural parameters and the corresponding magnetic field distribution maps to determine the optimal parameters. Figure 8 shows the absorption spectrum changes with VO2 conductivity. Finally, Fig. 9 compares the absorption effect of the SiO2 pattern in the uppermost layer of each multilayer structure. We determine that, when the SiO2 pattern is observed, the absorption bandwidth is wide and the absorption effect is high. Table 1 compares the main performance indicators of the infrared absorber designed for this study and the existing infrared absorber to further demonstrate the superiority of the proposed structure.

A truncated infrared broadband absorber is designed based on the phase material VO₂, metalloids, and high-temperature resistance materials NaF and TiO₂. Using the finite element method, the dependences of the absorptivity on the type of incident wave, angle of incidence, azimuth angle, incident wavelength, and geometric parameters are further analyzed. The results demonstrate that the absorption mechanism of the infrared broadband absorber is the surface plasma resonance effect. When the TM wave is incident, the angle of incidence increases to 55° in the range of 12-52 μm, and the absorptivity can reach approximately 80%. When the TE wave is incident, the angle of incidence increases to 55° in the range of 20-45 μm, and the absorptivity reaches approximately 80%. When TM or TE waves are incident vertically, three absorption peaks are formed around 14 μm, 24 μm, and 40 μm, which are named p₁, p₂, and p₃, respectively. At 21-25 μm and 35-43 μm, the absorptivity reaches 99.8%; the absorptivity is more than 90% at 12-51 μm, the average absorptivity of the broadband absorber reaches 96.4%, and the relative bandwidth reaches 124%. Further, the absorptivity is polarization insensitive. The infrared absorber designed in this study is expected to be widely used in infrared sensing, detection, energy harvesting, and energy conversion.

As an interdisciplinary subject of nanophysics and quantum optics, the physical properties of cavity optomechanics have attracted the attention of many researchers. At the same time, with the development of optomechanical systems, cavity magnetic quantum dynamics systems have become a new platform for realizing quantum coherence and coupling between magnons, cavity photons, and mechanical oscillators. This paper proposes the simultaneous input of the control field and detection on both sides. The cavity field (one of the microcavities has a mechanical vibration mode, there is mutual coupling between the optical fields of the two resonators, and the coupling strength is related to the distance between the two resonators) and the dual-resonator magnetomechanical system are composed of magnons. On this basis, the input-output theory is used to analyze the dual-resonator magnetomechanical system under different parameter mechanisms. In the cavity output, magnons, microwave photons, and acoustics can be observed in the presence of cavity-to-cavity coupling. Various coherent properties arise from the coupling between magnons, cavity photons, and mechanical oscillators. These results are new phenomena that have not been revealed in typical electromagnetically induced transparent systems and may be applied to novel optical information-processing devices.

In this letter, we begin with a dual-cavity magneto-optical mechanical system model. We analyze the composition of the cavity and provide the definition of each parameter. The magnon directly driven by the microwave source in the cavity a can directly establish a coupling mechanism with the microwave cavity photons. A YIG ball is placed in the maximum magnetic field of the microwave resonant cavity a. In order to bias the YIG ball, a uniform external bias magnetic field needs to be applied along the z direction. The cavity mode driving magnetic field in the y direction is mainly used to deform the YIG ball. The purpose of the dynamic magnetization of the magnon is to ensure that the cavity mode driving magnetic field in the y direction and the uniform external bias magnetic field along the z direction are perpendicular to the magnetic field of the cavity mode in the x direction at the same time. The Heisenberg equation of motion, factorization, and other methods are used to solve the obtained Hamiltonian, and the relational expression between the resonator field and the output field is established. Finally, we explore the different effects under different parameters. We investigate the coherent optical response under different parameter mechanisms, such as the coupling strength (J) between the resonators and the ratio (n) of the probing light intensity of the two resonators, in the case of system interaction, and the optical response transmission characteristics of the optomechanical system can be observed.

This study shows that different properties can be observed in the cavity of a magnetomechanical system under different parameter mechanisms. In the case where the mechanical oscillator is coupled with the magnon and the probe light on the right is turned off ( ), when the coupling strength , the greater the coupling strength of the system, the more obvious the degree of transmission of the system. When the value of the coupling strength increases to , the optomechanical system exhibits complete transmission at the central resonance, and when , the system exhibits mode splitting (Fig. 2). In the case where the microwave photons are coupled with the magnons and the probe light on the right is turned off ( ), with an increase in the coupling strength between the two resonators, the peak values of the transparent peaks on both sides gradually increase, while the central resonance strength gradually decreases. When the intensities of the left and right probe light are the same ( ), the peak transmittance and reflectance of the left cavity increase with the increase of J. This is because of the quantum coherence between the left and right probe fields (Fig. 3). In the case where microwave photons, mechanical oscillators, and magnons are coupled together and the right probe light is turned off ( ), when the coupling strength between the two resonators is enhanced, the peak values of the transparent peaks on both sides gradually become larger, the peak value at the central resonance gradually becomes smaller, and the standard mode splitting phenomenon occurs. When the effective optomechanical coupling ratio is changed, the width of the transparent peak at the central resonance increases with an increase in the value; the spacing between the transparent peaks on both sides also increases. Coupling with magnons also allows a portion of the energy to be stored in the magnons (Fig. 4). When the intensity of the probe light on the left and right sides of the system is the same ( ), the transmission first increases and then decreases, and the reflection first decreases and then increases on both sides of the optical system. This phenomenon is very important (Fig. 5). Based on this phenomenon, the dynamic control of the dynamic propagation process of weak light signals can be realized, which can be used to construct photonic devices with special functions.

In this paper, based on an optomechanical system, a dual-resonator magneto-optomechanical system based on magnons is proposed. The numerical results achieved can be displayed analytically under the coupling of the magnon and mechanical oscillator, the coupling of the magnon and microwave photon, and the co-coupling of the three. The detection field is regulated by adjusting the system parameters. This dual-cavity magnetomechanical system can exhibit different optical transmission characteristics, such as mode splitting, perfect quantum expansion coherence, perfect quantum destructive coherence, and absorption of magnon energy, which are very important in the process of quantum information processing. Studying and manipulating these dynamic controls can help us understand phenomena related to cavity opto-mechanical systems from a new perspective. The proposed scheme may serve as a potential platform for realizing controllable photon transmission and developing novel photonic devices.

Chaotic lasers have been widely used in high-speed secure communication, physical random key generation and distribution, sensing measurement, optical computation, and so on because of their wide bandwidth, large noise-like fluctuation, super sensitive dependence on initial values, and long-term unpredictability. With rapid development of these applications, a more accurate characterization of chaotic lasers is needed. At present, chaotic lasers are mainly evaluated through an analysis of their dynamic properties in time and frequency domains. The quantum statistics of chaotic lasers are also investigated through high-order coherence and photon number distribution. However, the phase-space quasi-probability distributions of chaotic lasers remain to be further studied. The phase-space Wigner quasi-probability distributions of quantum states, such as the squeezed state, Schr?dinger cat state, single-photon state, and multi-photon Fock state, have been reconstructed experimentally. However, system losses and the influence of noise in a practical experiment should be considered, and the high-fidelity measurement of the Wigner quasi-probability distribution in a phase space of chaotic lasers still needs to be further studied.

In this work, the phase-space Wigner quasi-probability distributions of chaotic lasers in the quasiperiodic, moderate, and coherent collapse states are reconstructed experimentally through balanced homodyne quantum tomography and the maximum likelihood method. First, by controlling the bias current and optical feedback strength, the quasiperiodic, moderate, and coherence collapse chaotic lasers with different bandwidths are prepared. Then, the chaotic lasers in these three different states are used as signal light and allowed to interfere with a local oscillator beam. Finally, the beams enter the balanced homodyne detector after 50:50 beam splitting. The local oscillator phase is scanned by piezoelectric ceramic transducer to obtain the amplitude quadrature at all phase angles. Based on the measured quadrature results of the chaotic lasers, the Wigner quasi-probability distributions in phase space and the density matrices of the chaotic lasers are reconstructed using the maximum likelihood method.

From the quasiperiodic state to coherence collapse, the auto-correlation of chaotic lasers changes from multi-periodic oscillation to periodic weakening chaos. The peak values of the time-delay signature decrease from 0.567 to 0.213, and the chaotic intensity and bandwidth increase continuously (Fig. 2). With an increase in the chaotic bandwidth and intensity, the measured phase-space Wigner quasi-probability distributions of the chaotic lasers are magnified by 1.5-3.0 times compared to the shot noise limit, and this chaotic amplification effect is continuously enhanced (Figs. 3 and 4). After removing the -44 dBm background noise, the fidelity of the Wigner quasi-probability distributions of the chaotic lasers is improved from 74.9%, 81.2%, and 84.8% to 79.9%, 86.8%, and 90.4%, respectively (Fig. 5). Then, after compensating for the 8.9% loss of the experimental system, the optimal fidelity of the reconstructed Wigner quasi-probability distribution function reaches up to 97.6%, realizing the high-fidelity phase-space reconstruction of chaotic lasers (Fig. 6).

In summary, the phase-space Wigner quasi-probability distributions of chaotic lasers in different states are reconstructed accurately. Three chaotic lasers, i.e. quasi-periodic, moderate, and coherent collapse chaotic lasers, are prepared experimentally, and their bandwidths are 3.2 GHz, 7.3 GHz, and 11.5 GHz, respectively. With an increase in bandwidth and a decrease in the time-delay period, the complexity of the chaotic laser increases. The quadrature signals of the chaotic lasers in the three states are measured, and the Wigner quasi-probability distributions in phase space and the density matrices of the chaotic lasers are reconstructed using balanced homodyne detection and the maximum likelihood method. Compared to the shot noise limit, the measured phase-space Wigner quasi-probability distributions of the chaotic lasers are magnified by 1.5-3.0 times. Meanwhile, the randomness of chaos increases, and the effect of chaotic amplification increases gradually. Finally, the high-fidelity phase-space reconstruction of the Wigner quasi-probability distributions of chaotic lasers with the fidelities of 95.5%, 97.0%, and 97.6% is achieved after removing the -44 dBm background noise and compensating for the 8.9% loss of the experimental system. Therefore, this method can enable the precise characterization of entropy sources in chaos-based secure communication.

With the continuous development of space technology, spaceborne long-distance high-precision detection technology has also made great progress. The imaging resolution is greatly limited because of the influence of the diffraction limit, effective aperture, and other factors of conventional optical imaging technology. Therefore, it is increasingly difficult to meet the needs of high-precision remote detection tasks. As one of the effective ways to realize long-distance and high-precision detection, laser reflective tomography technology has great advantages in the field of long-distance and high-precision detection because its imaging resolution is independent of distance and has high application value in the future. As an important part of the design of a laser reflective tomography system, imaging quality evaluation is of great significance to the application of laser reflective tomography technology. The conventional quality evaluation method of laser reflective tomography usually uses one or more specific values (such as relative root mean square error and image similarity coefficient) as the evaluation standard to realize the quantitative evaluation of the quality of laser reflective tomography. These methods often need a priori image as a reference, and there are large errors and limited scope of application. In this study, we invesitgate a quality evaluation method of laser reflective tomography. This method does not need an a priori image as a reference, and the result is more accurate. We expect that this method and our findings herein can aid the application of laser reflective tomography.

We introduce the concept of modulation transfer function into the quality evaluation method of laser reflective tomography and establish the quality evaluation model of laser reflective tomography based on distance resolution. First, the part containing edge information in the reconstructed image is intercepted, and its edge spread function is obtained. Next, the corresponding line spread function is obtained by differentiating the edge spread function. Then, the line spread function is used to obtain the modulation transfer function curve based on spatial frequency by the Fourier transformation. Finally, according to the relationship between spatial frequency and range resolution, the curve is transformed into a modulation transfer function curve based on range resolution to realize the quantitative evaluation of the quality of laser reflective tomography. In addition, we also set up the corresponding laser reflective tomography system and carry out a laser reflective tomography experiment under the detection distance of 0.2 km. The feasibility and accuracy of this method are verified by comparing the experimental results with the simulation results under ideal conditions.

Through the experiment of laser reflective tomography, we get the reconstructed image of the target (Fig. 4) and successfully draw the modulation transfer function curve based on distance resolution. In this study, the abscissa value corresponding to MTF value of 10% is considered as the test system’s limit value of distance resolution. According to the obtained modulation transfer function curve based on distance resolution (Fig. 7), the corresponding distance resolution at MTF value of 10% is approximately 1.587 cm, which is almost equal to the distance resolution (approximately 1.54 cm) obtained by theoretical calculation. With the increasing abscissa of the curve, the MTF value becomes larger and larger, and the imaging quality becomes better. Compared with the ideal image obtained by simulation (Fig. 8), the coincidence degree of their modulation transfer function curves is high, which also reflects the accuracy of the method in this study. In addition, we theoretically analyze the advantages of this method compared with the conventional evaluation methods. On the basis of the results, the modulation transfer function curve based on distance resolution can accurately evaluate the quality of laser reflective tomography.

We examine a method for evaluating the quality of laser reflective tomography. By introducing the modulation transfer function curve from conventional optical imaging into the quality evaluation of laser reflective tomography, the modulation transfer function curve based on distance resolution is drawn, and a model for evaluating the quality of laser reflective tomography based on the modulation transfer function is established. Quantitative evaluation of the image quality of laser reflective tomography without prior images is achieved. In the experiment, we set up an experimental system of laser reflective tomography and obtain modulation transfer function curves that can characterize the image quality of laser reflective tomography through the reconstructed image of this system, thus verifying this method’s feasibility. By solving the transverse coordinates at MTF value of 10%, the distance resolution of the laser reflective tomography system is 1.587 cm, which is approximately equal to the distance resolution (1.54 cm) of the system calculated by theoretical calculation. Moreover, we compare the experimental results with the simulation results and obtain almost identical modulation transfer function curves, thereby verifying the method’s accuracy. The results demonstrate that the evaluation method of laser reflective tomography based on modulation transfer function can accurately evaluate the quality of laser reflective tomography without prior images.

To cope with severe global climate change and achieve green development, China pledged at the 75th Session of the United Nations General Assembly to achieve a carbon peak by 2030 and carbon neutrality by 2060. Through photosynthesis, vegetation can effectively offset a fraction of the carbon dioxide emissions; therefore, it is of great practical significance to investigate forests and explore their carbon sink capacity to achieve carbon neutrality. However, traditional remote sensing technology is limited by the external environment and the lack of the internal structure data of forests. The emergence of LiDAR technology has made a breakthrough in forest resource surveying. Individual tree segmentation is an important component of forest resource investigation. The accuracy of the identified tree height, crown diameter, crown height, diameter at breast height (DBH), and other tree parameters is directly affected by the segmentation of single trees. However, at present, the research on single tree segmentation based on terrestrial LiDAR is still faced with the difficult problem of low precision of single tree segmentation in complex forest areas. Therefore, it is important to develop a single tree segmentation method with high precision and robustness.

Point cloud filtering is conducted using the cloth simulation filter (CSF) to obtain the ground points. Thereby, the digital terrain model (DTM) can be generated using the ground points. By subtracting the DTM from the digital surface model (DSM) generated by the point clouds, the forest canopy height model (CHM) can be established. Then, the moving window is used to detect the local maximum and candidate treetops. When the moving window is small, many local points that are extremely high can be detected. Note that not all of these high points are treetops. To optimize treetop detection results, these high points should be processed further. In this study, connectivity growth clustering is conducted on these high points. As a result, only the highest point of each cluster is selected as the treetop. After treetop detection, the marker-controlled watershed segmentation method is applied to the CHM. Thereafter, single tree detection results can be obtained. However, some neighboring trees cannot be separated successfully by the marker-controlled watershed segmentation method. Thus, the single tree detection results should be optimized further. In this study, a method for under-segmented trees based on density isolines is proposed. In general, for a single tree, the density at the tree's center should be the largest. From the center to the canopy margin, the density decreases. Based on this characteristic, the under-segmented trees can be optimized by detecting the density isoline.

To verify the feasibility of the proposed method, three groups of terrestrial LiDAR forest point cloud data are selected for testing (Fig. 6). The three groups of data are labeled by manual classification. Three evaluation indices are used to evaluate the performances of the proposed method, including completeness, correctness, and average accuracy. In this study, the Meanshift and marker-controlled watershed segmentation algorithms are selected for comparative analysis. The average detection accuracy of the proposed method for the three groups of samples is 76.06%, 74.29%, and 50.70%, respectively (Table 1). The Meanshift method has an average detection accuracy of 37.04%, 51.8%, and 30.69% for the three groups of samples, and the marker-controlled watershed method has an average detection accuracy of 53.33%, 55.07%, and 37.93% for the three groups of samples, respectively (Table 1). The comparison shows that the average detection accuracy of the proposed method is higher than those of the Meanshift and the marker-controlled watershed segmentation methods.

In this study, connectivity growth is performed on the initial treetops, and optimization extraction of treetops is achieved by detecting the highest point of the connected region. This helps avoid the misjudgment of local maximum as tree vertices, effectively reduces the misjudgment rate of local maxima as tree vertices, and promotes the subsequent improvement of accuracy of single tree segmentation based on treetop markers. For locally under-segmented trees, this study proposes a single tree under-segmented optimization method based on density isolines, which can optimize the segmentation of under-segmented trees and improve the accuracy of single tree segmentation. Three samples of forest TLS point cloud data from different regions are used for experimentation. Experimental results show that the proposed method can achieve average detection accuracies of 76.06%, 74.29%, and 50.70%, which are better than those of the Meanshift segmentation method and traditional marker-controlled watershed segmentation methods. It can be seen that the proposed method has a certain robustness and achieves high-precision single wood segmentation for vegetation point cloud data in different regions.

Results and Discussions A comparison of the mass concentrations of CO₂, CH₄, and CO measured by the Picarro greenhouse gas analyzer and atmospheric OP-FTIR system yields correlation coefficients of 0.896, 0.840, and 0.906 for CO₂, CH₄, and CO mass concentrations, respectively, indicating the high reliability and accuracy of the atmospheric OP-FTIR system for monitoring greenhouse gas mass concentrations (Fig. 3). The results of the measured spectral fits show that the inversion spectral regions of 2102-2250 cm^-1, 2920-3140 cm^-1, and 2172-2210 cm^-1 selected for CO₂, CH₄, and CO have root mean square errors of the spectral fit residuals of approximately 0.102%, 1.359%, and 0.551%, respectively (Fig. 4). In terms of meteorological conditions, the mass concentration indices of CO₂, CH₄, and CO show significant negative correlations with wind speed and temperature in most cases and positive correlations with humidity, with high mass concentrations of pollution mainly in the westerly and northwesterly wind directions (Figs. 6 and 7). In general, the daily average mass concentrations of CO₂, CH₄, and CO were 823.470 mg?m^-3, 1.330 mg?m^-3, and 0.510 mg?m^-3, respectively. The mass concentrations of CO₂, CH₄, and CO in the ambient atmosphere vary periodically, in terms of mass concentration time series (Fig. 8). The correlations between the CO and CH₄ mass concentrations and CO₂ mass concentrations were analyzed, yielding correlation coefficients of 0.495 and 0.659, respectively (Fig. 9). The boundary-layer inverse temperature effect, intensity of atmospheric convection, and photochemical reactions are the main causes of the variations in CO and CH₄ mass concentrations. The main factors causing the variation in CO mass concentrations are photosynthesis in plants, photochemical reactions, convective air transport, and motor vehicle emissions.

Curbing global warming and reducing greenhouse gas emissions have become important issues that urgently require worldwide attention. Therefore, the establishment and improvement of real-time continuous greenhouse gas monitoring systems that can identify the sources and mass concentrations of specific pollutants are essential for controlling atmospheric pollution. There is a high degree of consensus on the choice of technology used for the high-precision, continuous, and automatic monitoring of greenhouse gases. Techniques, such as Cavity ring-down spectroscopy (CRDS), off-axis integrated cavity output spectroscopy (OA-ICOS), tunable diode laser absorption spectroscopy (TDLAS), and Fourier transform spectroscopy (FTIR) have been extensively investigated. Among these, FTIR is a promising measurement technique because it offers the technical advantages of high scanning speed, high luminous flux, and high sensitivity. In the present study, a set of 90 m open-optical-path Fourier transform infrared spectroscopy (OP-FTIR) greenhouse gas analysis and measurement equipment was designed, and the equipment was used to perform high-precision observations of CO₂, CH₄, and CO. Through a detailed analysis of the measurement data from the system, we hope to provide an indication of the accuracy and precision of the entire measurement apparatus and technique for measuring greenhouse gases in the atmosphere. Simultaneously, we obtain a better understanding of the influence of meteorological conditions on greenhouse gas mass concentration and the processes of greenhouse gases in the ambient atmosphere over time.

In this study, FTIR technology was used for real-time monitoring of greenhouse gases based on an open-optical-path design. First, an external field experiment measuring CO₂, CH₄, and CO in the ambient atmosphere was performed for three consecutive months using the constructed greenhouse gas analysis system. The strong absorption interference of water vapor was then reduced by selecting appropriate inversion spectral regions for each of the three target gases of CO₂, CH₄, and CO. In addition, the monitoring data from a Picarro greenhouse gas analyzer and atmospheric greenhouse gas OP-FTIR system were compared to accurately assess the accuracy and precision of the overall measurement setup and technique for monitoring atmospheric greenhouse gases. Finally, data from 10 days of the measurement period were selected to investigate the correlations between temperature and humidity, wind direction and speed, and the ambient atmospheric mass concentrations of CO₂, CH₄, and CO, and to analyze the daily variation characteristics of the pollutants in detail.

This paper describes an OP-FTIR measurement system for greenhouse gas analysis. A comparison of the system measurement data with those of the Picarro analyzer shows that the OP-FTIR system monitors greenhouse gas mass concentrations with high degrees of reliability and accuracy. The inversion spectral regions selected for CO₂, CH₄, and CO in the OP-FTIR system can maximize the information content of this component, reduce the interference of water vapor and other components, shorten the identification time, and improve the identification rate. This study provides the characteristics of horizontal variation in CO₂, CH₄, and CO mass concentrations. In terms of meteorological conditions, the levels of temperature, humidity, wind speed, and wind direction have significant effects on local pollutant mass concentrations; in general, the average greenhouse gas mass concentrations remained at a high level in March. In terms of mass concentration time series, the mass concentrations of CO₂, CH₄, and CO in the ambient atmosphere show cyclical variations. The variations in CO and CH₄ mass concentrations are mainly due to the boundary-layer inverse temperature effect, the intensity of atmospheric convection, and photochemical reactions. However, CO₂ mass concentrations vary mainly because of plant photosynthesis, photochemical reactions, convective air transport, and motor vehicle emissions.

Terahertz (THz) waves are in demand for applications in high-speed wireless communications, nondestructive material testing, macromolecular spectral analysis, and medical detection of biological tissues. However, the lack of high-power, miniaturization, and affordable THz radiation sources has severely limited the application of THz waves in the above-mentioned fields. Cascaded difference frequency generation (CDFG), in which a pump photon can continuously generate multiple THz photons simultaneously through nonlinear optical effects, breaks the limits of the Manley-Rowe relationship and substantially improves the energy conversion efficiency of THz waves. In this study, we propose a method for efficient THz wave generation by coupled cascaded difference frequency generation (CCDFG), which uses two sets of CDFG to jointly generate and amplify THz waves. The THz wave generated by this method can provide positive feedback to the CCDFG, further driving it to expand to higher-order Stokes differential frequencies, thus significantly improving the THz wave energy conversion efficiency. We hope that this new scheme will facilitate the generation of high-power efficient THz waves.

A pump wave with a wavelength of 532 nm stimulated an adhesive-free-bonded KTiOPO₄ (AFB-KTP) crystal generating dual signal waves and dual idler waves using a coupled optical parametric process. The dual signal waves and dual idler waves stimulated two CDFG in an aperiodic periodically poled lithium niobate (APPLN) crystal, generating two sets of cascaded optical waves and THz waves simultaneously. The above two CDFG were intensely coupled by THz waves with identical frequency, polarization direction, and propagation direction. The CCDFG generated and amplified the THz wave, and the amplified THz wave enhanced the CCDFG simultaneously, resulting in the further frequency transformation from dual signal waves and dual idler waves to high-order Stokes waves. Moreover, the cascaded optical waves were further transformed to high-order Stokes waves by depressing the phase mismatches of cascaded Stokes processes and enlarging the phase mismatches of cascaded anti-Stokes processes simultaneously, thus substantially improving the THz wave energy conversion efficiency.

With a pump intensity of 4000 MW/cm² and a poling period of 6104.9864 μm of AFB-KTP, two signal waves with wavelengths of 289.0173 THz and 288.0173 THz respectively, and two idler waves with wavelengths of 274.8924 THz and 275.8924 THz are generated. The power densities of the two signal waves are 1022.77 MW/cm² and 1027.10 MW/cm² respectively, and the power densities of the two idler waves are 972.78 MW/cm² and 983.85 MW/cm² respectively (Fig. 2). At 100 K, a THz wave with a power density of 1483.6 MW/cm² is realized, corresponding to energy conversion efficiencies of 37%. The frequencies of the cascaded optical waves are converted from 280 THz to about 70 THz, indicating that one signal or idler wave photon can produce 210 THz photons (Fig. 3). The majority of signal wave photons and idler wave photons in a single set of CDFG under the same conditions are transferred to approximately 120 THz (Fig. 4). At 300 K, the absorption coefficient of the APPLN crystal for THz waves is significantly large, limiting the transfer of CCDFG to higher-order Stokes waves. The generated THz wave, therefore, has a power density of 183.7 MW/cm², corresponding to energy conversion efficiencies of.4.6% (Fig. 5). The power densities of THz waves generated by CCDFG at the same temperature are 177.9 MW/cm² and 182.8 MW/cm², and the power densities of THz waves generated by a single set of CDFG are 58.8 MW/cm² and 53.1 MW/cm², respectively (Fig. 6). At both 100 K and 300 K, the THz wave power densities generated by the CCDFG is considerably higher than the sum of the THz wave power densities generated by the two sets of CDFG excited by dual signal waves and dual idler waves.

In this paper, a scheme to efficiently generate THz waves by CCDFG is proposed that substantially improves the energy conversion efficiency of THz waves. Unlike the reported scheme using two near-infrared (NIR) laser beams for cascaded difference frequency generation of THz waves, we use one high-energy laser beam and two NIR seed beams to generate two signal waves and two idle frequency waves in an AFB-KTP crystal. The two signal waves and two idler waves are generated in the same APPLN crystal by exciting a set of CDFG processes to generate THz waves simultaneously. The THz waves can effectively couple two sets of CDFG together to amplify the THz waves, and the amplified THz waves can provide positive feedback to the CCDFG to further drive the pump photon to higher-order Stokes light transfer, which substantially improves the THz wave energy conversion efficiency.