Objective To overcome the ill-posedness of the bioluminescence tomography (BLT) reconstruction problem and obtain stable reconstruction results, researchers combined different prior information and regularization techniques to design various reconstruction algorithms. Among them, biological tissue structure information, a permissible source region, multi-spectral measurement information, and light source distribution sparseness are priori information widely used in reconstruction. The reconstruction algorithm based on regularization is divided into convex and non-convex optimization methods according to whether the objective function is non-convex. Although the regularization models of these reconstruction algorithms are different, the regularization parameter play a significant role in the reconstruction process, which directly affects the reconstructed image quality. Thus, the selection of the optimal parameters has always been a challenging problem for research. In this study, we proposed a multi-spectral BLT reconstruction method based on primal dual active set with continuation (PDASC) algorithm. The proposed method combines the primal dual active set (PDAS) algorithm with continuity technology, which can automatically adjust the regularization parameter to obtain a globally optimal solution.

Methods In this study, the iterative algorithm, PDASC, contains inner and outer iterations. The inner iteration part is the PDAS algorithm, which determines the active set based on the primal and dual variables. It then updates the primal and dual variables by solving the least square problem of the active set. The outer iteration combines the continuity technology of the regularization parameter. In the PDASC algorithm, the stopping criterion in the continuity technology directly affects the determination of the regularization parameter. Thus, it is essential to select an appropriate stopping criterion. If the noise level is known, we can choose the deviation principle as the stopping criterion. However, it is not easy to accurately estimate the noise level in actual situations. Thus, we choose the Bayesian information criterion that can adjust the regularization parameter to control the size of the active set and obtain a globally optimal solution.

Results and Discussion To verify the performance of the proposed PDASC algorithm in BLT, we designed multiple sets of simulation experiments compared with PDAS and HTP algorithms on the digital mouse model. The proposed algorithm was further examined with a mouse in vivo experimental data. The simulation results of the non-homogeneous digital mouse model showed that the Dice coefficient based on the PDASC algorithm can reach or exceed 65%, the positioning error is within 0.9 mm, and the contrast noise ratio is greater than 16.52 in single and double light source experiments (Table 2 and Table 3). These quantitative indicators validate that PDASC algorithm has the smallest reconstruction error, the highest quality of the reconstructed image, and the best reconstruction results of the shape and volume of the real light source (Table 2 and Table 3). For the double-source case, the PDASC algorithm has the highest shape fit of the reconstructed image and the best source-resolving ability (Fig. 5). The performance of PDASC algorithm on the three indicators for the in vivo experiment is also consistent with the simulations (Table 4). Above results indicate that the proposed PDASC algorithm is promising in practical tumor detection applications.

Conclusions In this study, we proposed a multi-spectral BLT reconstruction algorithm based on primal dual active set with continuation. The proposed algorithm combines the PDAS with the continuation technology for the regularization parameter, which can automatically adjust the regularization parameter to obtain the global optimal solution. Besides, the use of multi-spectral information reduces the ill-posedness of reconstruction. Multiple sets of simulations on a digital mouse confirm the effectiveness and stability of the proposed algorithm. The in vivo experimental results show the potential of the algorithm in practical applications. Although the proposed algorithm is better than the compared algorithms, it cannot fit the shape or contour of the light source perfectly. With the continuous development of deep learning, deep imaging algorithms have also appeared in the field of optical molecular imaging. Most of these algorithms are currently based on end-to-end neural networks, such as K-nearest neighbor local connection network, 3D deep encoder-decoder network, and stacked auto encoders neural network. By establishing the nonlinear mapping relationships between surface fluorescence and light source distributions, the deviation caused by the simplified linear model is avoided. However, the size of the training dataset, which plays a significant role in the depth imaging algorithm will directly affect the reconstruction performance. Thus, the focus of our future study is to determine how to combine the model with the network to solve the ill-posedness of BLT reconstruction.

Objective Recently, researchers increasingly focused on air quality. The air microorganisms cause severe harm to human health and severe effects on some industrial production. The latest national standard “Public Places Hygiene Indicators and Limits Requirements” stipulates the total number of air bacteria. Microbial detection based on fluorescence technology is widely used in medicine, pharmaceuticals, food, and environmental monitoring. The detection technologies include real-time fluorescent quantitative polymerase chain reaction (PCR), adenosine triphosphate (ATP) fluorescence detection, and microbial particle fluorescence-sensing system. The fluorescent microbial particle counter can directly count microbial particles, which has some advantages of good real-time performance, a high degree of automation, and simple operation. Besides, it is suitable for real-time online monitoring of the concentration of air microorganisms. This study designs a optical system based on the fluorescence detection principle in microbial particle counter to realize the online monitoring of microbial particles.

Methods The optical system is designed based on the fluorescence detection principle. In this study, the fluorescence characteristics of riboflavin, nicotinamide adenine dinucleotide, and other substances contained in microbial particles were tested and analyzed at first. Then, a 405 nm wavelength semiconductor laser was determined as the excitation light source. To reduce the output stray light of the laser, the light source shaping and fluorescence detection optical paths based on the combined diaphragm and lens were designed to obtain a high-quality flat rectangular line spot. Subsequently, consisting of oxidized and blackened aluminum alloy, the optical detection cavity structure were designed in the shape of hexahedron, and the production and assembly of the inspection structure were completed. Finally, the performance of the optical detection system was tested and analyzed using fluorescent microspheres in different particle sizes.

Results and Discussions In this study, the fluorescence detection and analysis of two fluorescent substances, riboflavin and nicotinamide adenine dinucleotide, were first conducted. Under the excitation of blue light of the same wavelength, the fluorescence peak position of riboflavin is 541 nm [Fig. 1(a)]. The peak position of the fluorescence spectrum of adenine dinucleotide is 492 nm [Fig.1(b)]. Then, fluorescent microspheres were used to test the performance of the designed optical detection system. The results showed that the final output noise of the system was is about 20 mV [Fig. 8(c)], and it could achieve graded detection of 10, 5, 2, and 1 μm fluorescent microspheres. The test voltage signal of 10, 5, 2, and 1 μm fluorescent microspheres has a signal amplitude of 350--380 mV (Fig. 9), 250--290 mV (Fig. 10), 130--140 mV (Fig. 11), and 78--90 mV (Fig.12), respectively. The test results showed that the optical detection system can effectively detect the signals of fluorescent microspheres of different particle sizes and has the characteristics of high signal-to-noise ratio and high detection sensitivity, which is of great significance for the further development of aerosol microbial particle counting instruments.

Conclusions In this study, an aerosol microbial particle counting instrument optical system based on fluorescence detection technology was designed. The overall structure of the instrument optical system was proposed. Besides, the design and structure manufacturing of the optical system were completed. By designing optical denoising optical path, optical noise is effectively suppressed, and the system signal-to-noise ratio is improved. Combined with the second-order RC low-pass filter circuit, the final noise of the system is only about 20 mV. The performance of the detection system was preliminarily tested with 10, 5, 2, and 1 μm fluorescent microspheres. The measured pulse signal amplitudes were 350--380 mV, 250--290 mV, 130--140 mV and 78--90 mV; system detection resolution is better. Next, some microbial samples, such as Staphylococcus aureus and Escherichia coil will be tested, and further the structure will be optimized to complete the overall design of the instrument.

Objective Photonic crystal fibers (PCFs) have wide applications in gas sensing, all-optical switching, four-wave mixing, and other fields due to its unique light control characteristics. In recent years, with the reduction of loss and cost, the sensors based on PCF have the characteristics of short absorption path and sensitive detection, which have become the focus of attention of researchers. However, many scholars have only optimized optical parameters such as sensitivity and limiting loss, ignoring the influence of the dispersion effect on the optical signal. When the dispersion is too large, it is very likely that the optical pulse will be broadened, causing the overlap of adjacent pulses. Therefore, the increase of the bit error rate will not be conducive to the propagation of light, so it is a challenge to reduce the dispersion and improve the detection sensitivity. Therefore, we have studied the octagonal PCF structure with multi-slot waveguides, which provides the possibility to achieve accurate detection of harmful gases, and at the same time achieves low-dispersion and flat-bandwidth optical signal transmission in the near-infrared wavelength range.

Methods In the infrared spectrum of various gases, the uniqueness of the absorption band is of great significance for the trace amount of the gas. When a beam of light with an intensity of I₀ passes through the photonic crystal fiber, the intensity of light passing through the gas to be measured changes due to the absorption of the light field by the gas to be measured, and the output light intensity I satisfies the Lambert-Beer law. The optimal structure is obtained through parameter optimization, and two grooves close to the core are filled with optical fluid to study the influence of optical fluid technology on optical properties. In order to ensure that the optical fluid only enters the core and not the cladding pores, the optical fluid can be slowly injected into the fiber through a small tip device such as a hypodermic needle or a cladding layer can be deposited on one end of the fiber to block the entry of the optical fluid. With the advent of optical fluids, manipulating light and fluids on a microscopic scale to change the optical capabilities of the medium has become an important means of manufacturing highly sensitive sensors. We adjust the optical characteristics of the photonic circuit through changing the refractive index n, so that the photonic device has tunability and reconfigurability, which can be used for gas sensing detection. In addition, different fluid materials are used to achieve the control of light on substances, and optical fluid technology is introduced into the pores of the optical fiber to dynamically adjust the mode, which reduces the cost caused by replacing the optical fiber and facilitates the construction of a highly sensitive integrated sensor.

Results and Discussions The larger the numerical aperture (NA), the more advantageous it is for sensing applications. When the refractive index difference between the core and the cladding of the PCF is larger, the NA is closer to 1. In this paper, under the best design parameters, we get the NA of 0.11 (Fig. 5), and most of the previously proposed sensor structures ignore this characteristic of PCF. The incident light in the Y polarization direction has higher sensitivity (Fig. 8), so a polarization controller is added between the light source and the sensor to control the light entering the sensor to be linearly polarized light along the Y direction. Since the optical fluid is filled to increase the effective refractive index (A_eff), the A_effis significantly moved up compared to the unfilled structure, the NA is decreased, but the change of NA is small compared to the unfilled structure (Fig. 10). In practical applications, it is necessary to consider the dispersion. The dispersion range obtained in the range of 1.55--1.64 μm is (0.041±0.023) ps·THz ^-1·cm ^-2 (Fig. 11). Compared to the previously proposed structure (Table 1), the dispersion of the proposed method is very low and the flatness is significantly improved.

Conclusions This paper designs a new type of PCF, uses finite element method to study the optical characteristics in the near infrared range, and analyzes the influence of filling on relative sensitivity, limiting loss, and dispersion parameters of the optimized structure combined with optical fluid technology. The results show that in the wavelength range of 1.55--1.64 μm , it has obvious flat dispersion characteristics close to zero, and the relative sensitivity is above 65%. By filling the optical fluid in a wide near-infrared wavelength range, the optical signal propagation with a low loss of 1.52×10 ^-2-2.8×10 ^-2 dB·m ^-1 and a ultra-low dispersion of 0.018 ps·THz ^-1·cm ^-2 is realized. In addition, due to the flexibility of the structure, it is expected to be applied to gas sensing detection in the THz range by adjusting the structural parameters.

Objective With the continuous development of small satellite technology, a large number of small satellite groups flying in formation have gradually replaced single large satellites and become a research hotspot in the field of aerospace. However, due to the constraints of size, mass, and power consumption of small satellite platforms, traditional RF and laser communication technologies can no longer meet the demand of large-capacity, small-delay, and high-reliability intersatellite communication links. As one of the most promising key technologies for the fifth wireless communication and beyond, visible light communication (VLC) has great potential in improving the spectrum efficiency and reducing the cost of spacecraft with many license-free spectrum resources. In practical applications, the narrow modulation bandwidth of LED seriously limits the system capacity and VLC communication rate. Thus, many high spectral efficiency technologies are used to improve the VLC system's data rate, including adaptive modulation, equalization technology, multiple input multiple output (MIMO), and multiple access technology. Among them, power domain NOMA (PD-NOMA) is suitable for downlink VLC systems to enhance the capacity and communication rate through power multiplexing.

Methods In this study, by combining the intersatellite VLC and NOMA technology, an intersatellite NOMA-VLC system consisting of a three-star formation configuration is constructed. Then, based on the analysis of the line of sight (LOS) link model of intersatellite and noise model at the receiver side, the model of signal transmission with power multiplexing is developed. Aiming at the problem of system communication rate optimization, an optimization model based on sum-rate maximization for the system is established. By transforming the nonconvex objective function into the convex function, an optimal power allocation strategy with low complexity is proposed to exploit the explicit optimal solution to the target problem using convex analysis.

Results and Discussions The performance of the NOMA scheme for the intersatellite VLC system is simulated and analyzed using MATLAB. The simulation results show that the sum-rate increases first, then decreases, and finally increases with the power allocation factors. Combined with the constraint conditions, the sum-rate achieves a maximum value of 124 Mbit·s ^-1 when the power allocation factor is 0.1 Fig. 4). Under the same conditions, the sum-rate will increase with the intersatellite distance ratio. It means that the greater the difference in user channel conditions, the more obvious the performance advantages brought by NOMA (Fig. 5). Besides, the average BER of 8-PPM modulation for the system will decrease with an increase in DC bias power; the BER of each curve decreases to the lowest at its optimal power allocation point. When DC power is 10 W, the average BER of the system can achieve 10 ^-3, while the average BER can achieve 10 ^-6 with 20 W (Fig. 6). Through the comparison of power allocation algorithms, it can be seen that the proposed power allocation algorithm performs better than the GRPA and FPA algorithms with a sum-rate factor of 0.5; its performance is almost the same as that of the LD algorithm. However, a convex problem solving during every iteration exacerbates the computational complexity of the LD algorithm; thus, the comprehensive performance of the proposed algorithm is optimal (Fig. 7).

Conclusions Based on the combination of intersatellite VLC and NOMA technology, this study investigates the power allocation of intersatellite NOMA-VLC systems. The simulation results show that the design of an efficient power allocation algorithm effectively improves the sum-rate of intersatellite VLC, which is similar to the NOMA technology in radio frequency communication. It also is shown that changing the DC bias power and power allocation factors of the algorithm will affect the system rate. With the increase in user channel difference, the performance advantage of NOMA will be more obvious, and the intersatellite VLC can increase the channel difference by increasing the intersatellite distance ratio. When the intersatellite distance ratio is too large, to ensure the system rate, the transmission power of one user satellite will be far lower than that of the other, which fails to guarantee fairness between users. Besides, through the comparison of power allocation algorithms, it can be seen that the comprehensive performance of the proposed algorithm is optimal.

Objective In the process of exploiting combustible ice, the temperature in the production string can decrease due to the influence of depressurization and hydrate decomposition. This can produce a temperature and pressure environment conducive to the secondary formation of methane or carbon dioxide hydrate, which results in the risk of string blockage. Therefore, it is very important to monitor the gas concentration in real time during drilling in order to determine from the gas concentration whether a secondary hydrate is starting to form and to select measures flexibly to prevent this from blocking the pipe string. However, due to the sizes and depths of the wells, it is difficult to complete downhole work for long-optical-path gas-absorption pools, such as a White pool or a Herriot pool. For an optical path with limited effective absorption, it is important to ensure the smooth progress of combustible ice mining by using digital-filtering methods to improve the signal-to-noise ratio of the system and reduce the minimum concentration necessary for environmental gas monitoring. Traditional denoising methods, such as the Kalman filter, wavelet transform, and empirical mode decomposition, are of limited utility because of the problems of mode aliasing and endpoint effects. In the present study, we have combined a variational mode-decomposition (VMD) algorithm with the Savitsky-Gorai (S-G) filtering algorithm to produce a VMD-based filtering algorithm that effectively solves the modal-aliasing problem and removes system noise. We expect that our basic strategy and findings will be useful for the constant monitoring of gas concentrations during drilling in combustible ice mining.

Methods This paper proposes a VMD-based filtering algorithm based on the VMD algorithm and the S-G filtering. First, it is necessary to determine the number of decomposed modes. We choose different numbers of modes for decomposing the gas signal using VMD. We then apply the fast Fourier transform (FFT) to the decomposed modes, and we determine the optimal number of decomposed modes according to the amount of mode overlap. By calculating the Pearce correlation coefficient between each decomposition mode and the original signal, it is possible to judge whether the effective signal is a low-frequency mode. After decomposition a low-frequency mode is selected for S-G filtering, and the residual high-frequency noise after VMD filtering and the low-frequency system noise are filtered out. In addition, we calculate the system signal-to-noise ratio, linear correlation coefficient, and minimum detection volume fraction to evaluate the performance of the algorithm.

Results and Discussions In our simulation experiment, the absorption line of CH₄ at 1653.72 nm is taken as an example, and the pure signal and the dye-noise signal are obtained (Fig. 1). The dye-noise signal is processed using the VMD-based filtering algorithm to yield the filtered signal [Fig. 4(b)]. The noise in the contaminated signal is thus effectively filtered out, and the signal-to-noise ratio increases from 7 dB to 20.1 dB. Then we applied the VMD-based filtering algorithm to the actual gas-monitoring instrument used in drilling to mine combustible ice in order to obtain the gas signal before and after noise reduction (Fig. 9). The signal-to-noise ratio of the gas signal increases from 8.5 dB to 21.7 dB. Gases with volume fraction ranging from 200×10 ^-6 to 500×10 ^-6 at intervals of 50×10 ^-6 were selected for detection in order to determine the relationship between the second-harmonic amplitude and the volume fraction (Fig. 10). The linear correlation coefficient of the instrument is increased from 0.9633 to 0.9940 by using the VMD-based filtering algorithm, and the minimum detectable volume fraction decreases from 85.2×10 ^-6 to 6.7×10 ^-6.

Conclusions In this study, we have proposed a VMD-based filtering algorithm to improve the signal-to-noise ratio for gas detection by combining the VMD algorithm with the S-G filtering algorithm. The problem of modal aliasing and end effects in previous gas-noise reduction algorithms is well solved with this approach, and the effective signal is separated from the noise signal. We applied the VMD-based filtering algorithm to the actual gas-monitoring instrument used during drilling to mine combustible ice, and the experimental results show the new algorithm produces substantial improvement. Our research has thus shown that this VMD-based filtering algorithm effectively improves the signal-to-noise ratio and decreases the minimum gas volume fraction detectable with the instrument, making this method an effective tool for the field of spectral signal processing and gas-concentration monitoring.

Objective With the rapid development of the Internet of Things industry, the demand for indoor positioning solutions is increasing. Visible light indoor positioning technology has attracted increasing attention in research and application development. Currently, LED indoor positioning technology is still in its infancy. However, with the development of visible light communication technology, the visible light indoor positioning industry has also developed rapidly in recent years. Visible light indoor positioning is a new positioning technology that combines lighting and communication. Compared with traditional indoor wireless positioning methods, it has the advantages of low cost, no electromagnetic interference, high positioning accuracy, and broad prospects. However, existing visible light positioning technology has difficulty in handling background noise interference and indoor reflection noise, which leads to unstable positioning accuracy. An artificial neural network (ANN) is capable of nonlinear mapping, self-learning, self-adaptation, and generalization. Additionally, ANNs can extract key information from a large amount of data. ANNs have been applied to outdoor positioning based on the Global System for Mobile Communication. To reduce the interference of diffuse reflection of wireless optical channels to RSS-based visible light positioning systems and improve positioning accuracy, this paper proposes a high-precision indoor positioning algorithm based on a multiple reflection channel model and a neural network.

Methods This paper investigates visible light indoor positioning algorithms commonly used at home and internationally. Indoor positioning technology based on high-precision photoelectric sensors and image sensor imaging are compared and analyzed. The visible light indoor location algorithm based on a neural network is summarized and proposed to improve the location accuracy. First, a visible light indoor stereo positioning system is modeled. To avoid the influence of diffuse reflection of the light channel on positioning accuracy, a channel mathematical model that includes a direct line-of-sight link and first-order reflection link is established. Second, to achieve 3D positioning, the optical intensity data should be obtained by decoding different LEDS at different positions on different planes of different heights. These data can be used to create fingerprint databases. After determining the LED light source and channel model, combined with an LED channel diffuse reflection model, grid calibration is carried out on the receiving plane and the illumination intensity of different LEDs at the center point of each grid is collected. After classifying the collected data, the training and test datasets can be created. Third, the localization algorithm based on a BP (Back Propagation) neural network is designed, and data training and prediction is performed. The neural network positioning system designed in this paper is divided into input, hidden, and output layers. The input to the neural network is RSS from different LEDs. A BP neural network is used to fit the parameters of a real indoor wireless channel. The output of the neural network is an m-dimensional space vector used for coarse positioning of the target to be measured. This coarse positioning represents the relative spatial position of the position coordinates of the predicted receiver and the position coordinates of the LED light source. Finally, through the positioning error constraint model based on location variance and Euclidean distance to solve the positioning equation, the predicted position coordinates of the target to be tested is determined.

Results and Discussions To verify the theoretical validity and positioning reliability of the proposed algorithm, a simulated three-dimensional (3D) positioning experiment and an actual positioning experiment are performed. During the simulation positioning test, the 3D space with 4 m×4 m×3 m is taken as the model in this paper, and the simulation experiment is carried out according to the simulation parameters shown in Table 1. In the experiment, a training set with a spacing of 5 cm is divided on each plane, and the area of each rectangle is 5 cm × 5 cm. A reference fingerprint point is selected from each small square, and a total of 6561 points are selected from each plane. According to the results (Fig.4), when the plane with a height of 0.5 m is tested, there is no great deviation between the predicted position and the actual position coordinates. The maximum error is 7.10 cm and the average error is 1.73 cm; 90.1% of the error is within 3 cm (Fig.7). In the test plane with a height of 1.0 m, the maximum positioning error is 5.56 cm and the average error is 1.29 cm (Fig.5); 91.7% of them have positioning errors less than 3 cm (Fig.8). The maximum positioning error is 12.38 cm and the average error is 3.85 cm when the height plane is 1.5 m (Fig.6), and positioning error data within 3 cm accounts for 41.7% (Fig.9). In the measurement and positioning stage, experimental platforms are built in 0.8 m-long, 0.8 m-wide, and 0.8 m-high three-dimensional spaces (Fig.10). After multiple positioning tests are conducted on 81 groups of training data and 16 groups of position data, the average positioning error is 3.65 cm (Fig.12).

Conclusions Traditional visible light indoor positioning systems based on RSS are vulnerable to background noise and indoor reflection noise. In this paper, a visible light indoor positioning model based on a neural network is proposed by combining the neural network with RSS positioning technology. Combined with multiple reflection channel modeling, the model uses an ANN to study the visible light channel parameters to facilitate neural network training and model testing. The positioning error constraint model based on location variance and Euclidean distance is used for effective correction. These can significantly improve the indoor positioning accuracy of a visible light system to achieve accurate positioning.

Objective In this paper, a composite 7-core photonic crystal fiber is designed and investigated theoretically. By combining the step-index structure and the photonic crystal fiber structure, the inter-core crosstalk of the proposed fiber can be effectively reduced and the core density could be greatly improved, which provides a new opportunity for the realization of large-capacity and long-distance optical fiber space division multiplexing technology. The parameters of the fiber structure are analyzed by the theoretical analysis and research. At the wavelength of 1550 nm, the crosstalk between the intermediate core and the peripheral core is lower than -60 dB/km, the effective mode field area is over 90 μm ², and the core spacing is up to 31.7 μm. When increasing the core number to 31, the relative core multiplexing factor can reach 8.78, which effectively improves the core density. This work has a guiding significance for the design of multi-core photonic crystal fiber for space division multiplexing technology and can be used in the network system which demands low crosstalk and large capacity for long distance transmission.

Methods Based on the theory of mode coupling and power coupling, the finite element method is used to calculate the crosstalk characteristics of the fiber. The cross-section and refractive index distribution of the composite multi-core photonic crystal fiber proposed in this paper are shown in Fig. 1. In order to suppress the crosstalk and nonlinear effects in the fiber, analyze the influence of the fiber structure parameters on the crosstalk and the effective mode area of each core, and select a set of initial structure parameters, as shown in Table 1, the theoretical analysis is at the wavelength of 1550 nm, the crosstalk and the effective mode area variation law of L=1 km in fiber propagation. In order to show the advantages of composite multi-core photonic crystal fiber in suppressing XT when the core spacing is small, this paper compares the designed composite 7-core PCF with the traditional step multi-core fiber and trench assisted multi-core fiber with known structural parameters. In order to further increase the transmission capacity of the optical fiber, the composite multi-core photonic crystal fiber has the characteristics of low crosstalk and small core spacing to expand the number of cores in the optical fiber from 7 to 31 cores.

Results and Discussion For the composite 7-core photonic crystal fiber, increasing the effective mode field area of the fiber is very important to increase the transmission capacity and overcome the nonlinear effect. Under the condition of ensuring the fiber single-mode transmission, appropriately increase the core size and reasonably control the core doping concentration, Using the air holes periodically arranged around the core to restrain the beam, by optimizing the design of the air hole structure to suppress crosstalk, a larger effective mode field area can be obtained at a lower doping concentration(Fig. 2). For the composite 7-core photonic crystal fiber designed in this paper, choosing the appropriate air hole parameters can achieve the effect of the smaller the distance between the cores, the smaller the crosstalk, so as to overcome the mutual restriction of low crosstalk and high-density in traditional multi-core fibers (Fig. 4). In the 31-core example presented in this article, the relative core multiplexing factor can reach 8.78, which has great advantages over the reported high-density multi-core fiber (Fig. 7).

Conclusions The composite 7-core photonic crystal fiber proposed in this paper has the characteristics of low crosstalk, high-density, and flexible design. By analyzing the influence of fiber core size, core-cladding relative refractive index difference, air hole spacing, and air hole structure parameters on the optical performance of the 7-core photonic crystal fiber, three sets of balance parameters are obtained, it balances single-mode transmission, larger mode field area, and lower crosstalk. The restriction relationship between the three sets of balance parameters can be obtained, and the crosstalk can be lower than -60 dB/km at the wavelength of 1550 nm, and the effective mode field area can exceed 90 μm ². Comparing the composite 7-core photonic crystal fiber with the conventional step multi-core fiber and trench assisted multi-core fiber that have been reported, the results show that the 7-core photonic crystal fiber has more advantages in reducing crosstalk and distance between cores. It can effectively alleviate the mutual restriction of low crosstalk and high-density. On this basis, the number of fiber cores is expanded to 31-core, the minimum value of outer cladding thickness is calculated to be 42.5 μm, and the relative core multiplexing factor reaches 8.78. The composite 7-core photonic crystal fiber designed in this paper has broad application prospects in the direction of high-density, long-distance, and large-capacity information transmission systems.

Objective In digital holography, CCD or CMOS photodetectors are used to record holograms instead of the traditional recording plate in optical holography. The holograms are reproduced through digital simulation. However, array size and the total number of pixels of CCD or CMOS photodetectors restrict the imaging field of view and quality of reconstructed images, limiting the widespread application of digital holography. The main methods to obtain a large field of view images include hologram splicing and phase splicing. The hologram-splicing method is affected by the clarity and noise of the hologram. However, phase stitching provides a method to increase the size of the detection field and improve the quality of three-dimensional (3D) images without increasing the difficulty of the experimental optical system for digital holography. In the field of digital holographic phase stitching, the conventional block-matching algorithm has the disadvantage that the splicing efficiency of block matching is significantly reduced with the increase in the size of the subaperture phase map after the phase image is stitched many times. Block matching is prone to mismatching in similar regions of the phase map. The conventional corner-detection algorithm extracts corners from the entire image with unnecessary corner detection and extraction, leading to excessive registration time consumption and affecting registration accuracy. To solve the problem of efficiency and accuracy of phase stitching of subaperture phase diagram in digital holography, a phase-stitching method based on multi-algorithm fusion optimization is proposed to realize two-way phase stitching in digital holography.

Methods In phase stitching, the phase correlation method is used to determine the overlapping area to limit the detection and extraction range of feature points, thus improving the feature point detection speed and the proportion of effective feature point detection. Harris corner detection is conducted for the overlapping area, and the pseudocorners caused by flat area, noise point, and edges are eliminated according to the phase information of the corner neighborhood. Then, the normalized cross-correlation function is applied for corner matching. Guided complementary matching and voting filtering methods are used to simultaneously eliminate mismatched corner-matching point pairs, and the corresponding best matching point pair is obtained. The search range of the small block matching algorithm is reduced according to the best corner-matching point pair. Finally, the full matching search algorithm is used to accurately match the best corner-matching point pair, and weighted fusion is adopted to realize the reconstruction and phase splicing of 3D topography.

The sub-aperture holograms of four parts of the letter “a” of glass sample plate are collected using the reflection off-axis digital holography experiment system; at least 50% overlapping area should be reserved in the adjacent holograms. Next, the diffraction of a light wave is simulated using a computer. The reconstructed image phase is analyzed using the Fresnel integral formula. The reconstructed image phase distribution is obtained using the least square phase unwrapping. Finally, Harris algorithm, scale-invariant feature transform (SIFT) algorithm, Susan algorithm, full search method, and the proposed algorithm are used to splice the phase map of each subaperture of the letter “a” of the glass template to obtain the intensity map and phase distribution map of the letter “a” of the glass template. The splicing experiment is conducted hierarchically, i.e., the transverse adjacent subaperture phase map (85 pixel×85 pixel) is horizontally spliced, and then the resultant image (115 pixel×85 pixel) is longitudinally spliced. Finally, the overall splicing phase distribution map (115 pixel×125 pixel) is obtained.

Results and Discussions The experimental results showed that there are obvious errors in the phase stitching based on the Harris algorithm; moreover, the phase splicing results based on Susan algorithm are greatly misplaced. However, the results of SIFT algorithm, full search method, and proposed algorithm are better (Fig. 7). To compare the splicing accuracy of each algorithm in Fig. 7, the phase distribution map of each algorithm is selected for contour comparison and analysis with the image measured using the image measuring instrument. The matching accuracy of the proposed algorithm is the highest (Table 1). The experimental matching results showed that the efficiency of phase stitching based on SIFT algorithm and Susan algorithm is low; Harris algorithm has high antirobustness and high matching efficiency, but it is easily affected by noise, resulting in false corners and corner clusters, and there are certain errors in matching. SIFT algorithm has high matching accuracy; however, its matching efficiency is low, and the hierarchical splicing introduces new errors. This further reduces the matching success rate of SIFT algorithm. Susan algorithm cannot guarantee the matching success rate for hierarchical splicing because of the need to manually adjust the threshold. The full search method algorithm has the lowest matching success rate due to the mismatch problem of similar regions, and the block matching selection is full of uncertainty. The proposed algorithm has the matching success rate, matching time, and robustness. It can improve the matching efficiency and ensure matching accuracy (Table 2). In addition, the algorithm reduces the influence of the size of the subaperture phase map on its matching efficiency (Table 3).

Conclusions Phase stitching is an effective method to enlarge the field of view in digital holography. The phase-matching stitching technique of the Harris corner detection algorithm for each subaperture is simple. However, the splicing result has a certain error due to error accumulation. The full search method has the advantages of simple operation and high search accuracy, but it has a large calculation quantity and is prone to mismatching in similar regions. In this study, the phase splicing method based on multi-algorithm fusion optimization in digital holography is proposed by combining the Harris algorithm and full search method points, which can improve the matching efficiency and accuracy. Moreover, it provides full play to the high robustness of the Harris algorithm and does not require objects to have strong edges. It has a wide application prospect in high-resolution mosaic measurement.

Objective In general, a single-mode polarization-maintaining fiber can serve as the stretcher and the Treacy-type grating pairs can serve as the compressor in the fiber chirped pulse amplification (FCPA) system. Although the positive group delay dispersion (GDD) introduced by the fiber stretcher can be compensated by the negative GDD introduced by the compressor, but the signs of the third-order dispersion (TOD) introduced by the stretcher and the compressor are the same, resulting in the deterioration of pulse quality due to the accumulation of TOD during the pulse amplification process. To solve the above problem, a segment of negative TOD fiber, high-order mode dispersion fiber or chirped fiber Bragg grating (CFBG) is usually introduced into the fiber stretcher to compensate the TOD in the system. However, the residual TOD in the system cannot be accurately measured, and the length of the dispersion fiber introduced in the stretcher can only be estimated. Therefore, several experiments have attempted to obtain the best dispersion compensation effect. However, these dispersion compensation methods are complicated and time-consuming. Here, we report an FCPA system that is composed of a mode-locked fiber oscillator, a pulse stretcher, a pulse picker, a pulse delay unit, an Yb-doped fiber preamplifier, a rod-shaped photonic-crystal fiber main amplifier, and a grating compressor. Among them, the pulse stretcher and compressor are based on block gratings. By finely adjusting the position and incidence angle of the gratings in the stretcher and compressor, a real-time dispersion compensation in the system is realized and a high-quality pulse is obtained. Compared with the other methods, it is a more convenient dispersion compensation method. However, in previous studies, the single-pulse energy of the CPA system with a rod-shaped photonic-crystal fiber served as the gain medium was generally lower than 100 μJ, and the pulse width was limited to 400 fs. To further reduce the pulse width and simultaneously obtain the hundred-microjoule chirped pulse-amplification laser system with high pulse-quality, further research works are done. Subsequently, a nonlinear frequency-doubled experiment is carried out with a BBO crystal.

Methods First, a set of home-made passive mode-locked fiber oscillator based on the nonlinear polarization evolution (NPE) principle was constructed. The output of the oscillator was directed to a Martinez-type pulse stretcher. The stretched pulse duration was measured to be approximately 1 ns. Then, the stretched pulse from the stretcher was amplified step by step through four ytterbium doped fiber preamplifier stages with the forward pumping scheme. Meanwhile, a fiber coupled acoustic optical modulator (AOM) was used to reduce the pulse repetition rate of the system from 62.8 MHz to 1 MHz@500 kHz. The output laser at the fourth fiber preamplifier stage was coupled to that at the main amplifier stage with the backward pumping scheme by means of space coupling. Then, to compress the laser pulse to the femtosecond level, the laser beam was directed to a Treacy-type pulse compressor. High pulse quality and stability femtosecond laser pulses were obtained by controlling the dispersion, which was optimized by finely adjusting the position and incidence angle of the gratings in the stretcher and compressor in the system. At the same time, the second harmonic generation frequency resolution optical gate (SHG-FROG) was used to observe the pulse duration and phase information online. In addition, a nonlinear frequency-doubled experiment was carried out with a BBO crystal. A half wavelength plate (HWP) placed before the BBO crystal was used to adjust the polarization state of the fundamental laser beam. Simultaneously, the phase-matching condition between the fundamental and the frequency-doubled lasers was optimized to obtain a high average power of green laser.

Results and Discussions The mode-locked ytterbium (Yb)-doped fiber oscillator that was designed to have a repetition rate of 62.8 MHz delivered pulses with an average output power of 12 mW, the central wavelength of 1031 nm, and a bandwidth of 15.8 nm (Fig. 2). The output of the oscillator was directed to a Martinez-type pulse stretcher. The stretched pulse duration was measured to be approximately 1 ns (Fig. 4). Owing to the losses from diffraction gratings and multiple reflections on the mirrors, the average power and spectral bandwidth of the stretcher decreased to 2.87 mW and 13.5 nm, respectively (Fig. 2). Then, to ensure the spectral quality, the average power of the stretcher was enhanced step by step through four ytterbium-doped fiber preamplifier stages with the forward pumping scheme and a main amplifier with the backward pumping scheme (Fig. 2). Device parameters for different stages in the system were listed in detail (Table 1). To avoid excessive gain narrowing, the average power of the fourth fiber preamplifier stage was limited to 0.86 W at a pulse repetition rate of 500 kHz and 2.0 W at a pulse repetition rate of 1 MHz, respectively. The optical spectra were recorded after different amplification stages. Only minor gain narrowing effect was visible (Fig. 2). This could be attributed to the distribution of the amplification gain over multiple stages of the amplifiers. With the increase of pumping power, the average powers of the main amplification and compressor were recorded (Fig. 5). The stability of the system was studied to meet the long-term test requirements of some special experiments. During the process of the 2.5 h continuous test, the laser operated normally, the output average power maintained high stability, and the root mean square(RMS) of the power is 0.31%(61.23 W@1 MHz) or 0.21%(50.4 W@500 kHz) (Fig. 6). The beam quality was measured at the average power of 50 W and a pulse repetition rate of 1 MHz in the system, showing a Gaussian distribution of near-field with M²=1.22 (Fig. 6). The pulse duration was characterized by SHG-FROG. At a repetition rate of 1 MHz in the system, a high-quality femtosecond laser pulse with an average power of 61.5 W and pulse duration of 273 fs was obtained (Fig. 7). A nonlinear frequency-doubled experiment was carried out with a BBO crystal, and more than 20 W average green light power at 517 nm was obtained (Fig. 8).

Conclusions The FCPA laser system based on transmission diffraction gratings serving as stretcher and compressor, was experimentally studied. By controlling and optimizing the spectral shape of the seed source, the stretcher and all stages of fiber pre-amplifiers without distortion are used to ensure that the spectral shape of the main amplifier was smooth and the distortion of spectral shape after de-chirped was avoided. To obtain a high-quality pulse, real-time compensation of the dispersion of the system was conducted by finely adjusting the position and incidence angle of the gratings in the stretcher and compressor. Finally, the high pulse quality and stability femtosecond laser with pulse duration of 251.7 fs, average power of 51.5 W, and 103 μJ of energy per pulse at repetition rate of 500 kHz was obtained. At a repetition rate of 1 MHz in the system, a high quality femtosecond laser pulse with average power of 61.5 W and pulse duration of 273 fs was obtained. By carrying out the nonlinear frequency-doubled experiment with a BBO crystal, a green laser with average power of over 20 W at 517 nm was generated. The CPA device will be applied in femtosecond laser processing, medical treatment, national defense, and other fields. The UV light source prepared by this system can be used in photoelectron spectroscopy experiments and has important practical value in the field of material surface science research.

Objective Optically-pumped vertical-external-cavity surface-emitting lasers (OP-VECSELs) combine advantages of vertical-cavity surface-emitting lasers (VCSELs) and solid-state disk lasers. In addition, OP-VECSELs can produce high output power and good beam quality simultaneously. VECSELs are of interest in many fields due to the tailorability and tunability of emitting wavelengths. In addition, pulsed VECSELs with high-energy and high peak power are of considerable demand in applications such as frequency conversion, fluorescence excitation, and laser medicine. Q-switched VECSEL has been reported once, but it has not been investigated specifically and extensively, and there is no published experimental or theoretical work on a Q-switched VECSEL so far. This study introduced passively Q-switched VECSELs with a Cr ⁴⁺∶YAG crystal and a semiconductor saturable absorb mirror (SESAM), respectively. Based on the time characteristics of the quantum wells in the active region of the VECSELs and the time behaviors of the saturable absorbers (the Cr ⁴⁺∶YAG crystal and the SESAM), the experimental results were analyzed, and the formation mechanisms of the microsecond pulses were proposed.

Methods The gain chip used in the VECSELs is epitaxially grown on a GaAs substrate in reverse sequences as following: an etch stop layer of AlGaAs with high Al composition, a protective layer of GaAs, an AlGaAs layer with a high barrier, an active region comprising 12 InGaAs/GaAsP quantum wells (designed to meet a target laser wavelength of 980 nm), and a distributed Bragg reflector (DBR, which is composed of 30 pairs alternate AlGaAs layers with high and low Al composition). When the grown wafer is split into small chips with 4 mm×4 mm dimension, the epitaxial end face of the chips are sequentially metalized with titanium-platinum-aurum; then, the chips are bonded to a copper heatsink, and the substrate is removed using a chemical etching. The passively Q-switched VECSEL with Cr ⁴⁺∶YAG crystal uses a linear cavity, and the Q-switching crystal is placed to the gain chip as near as possible during the experiment, while the passively Q-switched VECSEL with SESAM uses a folded cavity, and the length of the arm containing the gain chip is longer than that of the arm with SESAM to produce a tighter focusing of the light on SESAM, to satisfy the need of SESAM saturation and start the Q-switching process.

Results and Discussions When a Cr ⁴⁺∶YAG crystal is placed into the resonant cavity, a stable pulse train is obtained. Under room temperature and 4.5 W pump power, the pulse width and period are 10 and 38 μs, respectively, corresponding to a repetition rate of 26.3 kHz (Fig. 5). As SESAM is inserted into the folded cavity, a steady pulse train is produced, and the pulse width and period are 8 and 38 μs, respectibvely (Fig. 6), corresponding to a repetition rate of 26.3 kHz (the same as that in the Cr ⁴⁺∶YAG Q-switched VECSEL) under room temperature and 4.5 W pump power. The maximum average output power of the SESAM Q-switched VECSEL is 33 mW, the repetition rate is 58.1 kHz, and the single-pulse energy is 0.57 μJ when the pump power is 7.2 W (Fig. 8). The relationship between pulse periods and pump powers of the Q-switched VECSELs is different from a typical Q-switched solid-state laser. In a passively Q-switched solid-state laser, the pulse period decreases reciprocally with the increase in pumping power; however, for the passively Q-switched VECSELs, the pulse period decreases approximately exponentially (Fig. 7), and we believe this is due to the short life of the nanosecond magnitude of carriers in the active region of the VECSELs.

Conclusions We have demonstrated passively Q-switched VECSELs with Cr ⁴⁺∶YAG crystal and SESAM, respectively. The pulse widths of the Cr ⁴⁺∶YAG and SESAM Q-switched VECSEL are 10 and 8 μs, respectively, with the same repetition rate of 26.3 kHz when the pump power is 4.5 W. A maximum average output power of 33 mW is obtained from the SESAM Q-switched VECSEL with 7.2 W pump power, and the pulse repetition rate is 58.1 kHz, corresponding to a single-pulse energy of 0.57 μJ. With the increase in pump power, the pulse period decreases approximately exponentially in the Q-switched VECSELs instead of reciprocally in a typical Q-switched solid-state laser. The time characteristic of quantum wells in active region, i.e., the short life time of nanosecond magnitude of carriers, is the reason the pulse duration is of microsecond magnitude. Since the VECSELs can produce high output power and good beam quality simultaneously, these compact and wavelength tailorable passively Q-switched VECSELs have potential application in many fields when the average output power is improved and the pulse peak power is upgraded.

Objective At present,distributed Bragg reflector (DBR), distributed feedback (DFB) laser, or external cavity diode laser (ECDL) is usually used to realize a tunable single-frequency laser output in 1.3 μm. However, the output power of these diode lasers is as low as several mW. Some studies used a 1.3-μm laser for an effective selective atom stimulation; hence, a higher output power of the lasers was needed. This work presents an injection-locked Nd∶YVO₄ ring laser that can effectively improve the power of a CW single-frequency 1342-nm laser with wavelength tuning. The amplified 1342-nm laser retains most of the spectral characteristics of the seed laser. This injection-locked Nd∶YVO₄ ring laser has the advantages of high gain and high beam quality and is very easy to realize. As a consequence of the high power, the doubling frequency of 1342 nm (671-nm red light) and the quadruple frequency (336-nm UV light) can be obtained more easily for some other works.

Methods An injection-locked Nd∶YVO₄ ring laser was studied herein. Three modules were considered, namely the seed laser, the laser amplifier, and the Pound-Drever-Hall (PDH) frequency locking system. The seed laser provides the injection source. While the PDH system is being unlocked, the seed laser is reflected away from the cavity because it does not match the resonant conditions of the power cavity. Conversely, while the PDH system is locked, the seed light can be injected into the amplifier cavity and effectively amplified. In this work, a seed laser with output power of the order of mW, good beam quality, and good stability was used. After the injection-locked amplification, the laser retained the spectral characteristics of the seed light, including the single longitudinal mode and the adjustable wavelength. Meanwhile, the laser energy and the beam quality were improved. In this study, a tunable 1.0 W CW single-frequency 1342-mm laser was used as the seed light, and an 8-type ring resonator was used as the amplifier cavity. The injection-locked Nd∶YVO₄ ring laser was realized, based on the frequency locking technology of the PDH. The seed laser was amplified by the amplifier cavity, and the output power was significantly increased.

Results and Discussions A 1.3-μm seed laser is successfully injected into the amplifier cavity, and an effective laser amplification with the PDH frequency locked is realized (Fig. 2). At the same time, the frequency characteristics of the 1342-nm output laser are measured by an F-P scanning interferometer. The 1342-nm laser is operated at a single frequency. The spectral line-width is approximately 240 MHz (Fig. 3). We inject 1.0 W of seed light into the amplifier cavity and perform experiments on the input coupling mirror with different transmittances. We achieve a good experimental result with 7% transmittance of the coupling mirror (Table 1). We also perform an optimization experiment of the laser output power with different seed light powers using 7% transmittance of the input mirror. With the increase of the seed light power, the amplified laser power gradually increases, and the frequency locking becomes more stable. The total amplified output power of the 1342-nm laser reaches 8.3 W, when the power of the seed laser is 1 W. Therefore, increasing the seed light power seems to be an effective method of increasing the amplification efficiency and stability (Fig. 4). The maximum output power is 8.3 W with the 35-W pump laser (Fig. 5). Following the increase of the pump power (>35 W), the amplified laser output power decreases with the pump power because of the noise in the laser system. We also investigate the laser tunability. The tuning range is 1342.05--1342.25 nm when the power of the seed laser is 1 W, with 4.8 W as the highest output power. The tuning range of the output laser is 1342.09--1342.21 nm, which is smaller than 4.8 W (Fig. 6), when the power of the seed laser is 1.0 W, with 7.8 W as the highest output power. The experiment result demonstrates that the tuning range of the amplified laser decreases with the increase of the output laser. Increasing the energy of the injected seed laser is likely to be an effective method of increasing the tuning range. The innovative result obtained in this work is the demonstration of an easy and effective method of constructing a tunable CW single-frequency 1342-nm injection-locked Nd∶YVO₄ ring laser with the maximum power output of 8.3 W. Some experiment results are also presented in this paper.

Conclusions An injection-locked Nd∶YVO₄ring laser is studied herein. The influence of the amplification parameters, including the different transmittances of the input mirrors and the different powers of the injected seed light of the injection-locked ring laser, is analyzed. The maximum output power of the CW single-frequency 1342-nm laser is 8.3 W, which is obtained with the 8-type ring cavity at the power of the seed laser of 1.0 W. Characteristics such as high power, high beam quality, and continuous wavelength tunability are observed. The structure of the amplifier cavity will be optimized in subsequent experiments. We expect to acquire a wider tuning range with higher power and more stability of the CW single-frequency 1342-nm laser by increasing the frequency locking accuracy, reducing the system noise, and improving the seed light power.

Objective Spectral beam combining (SBC) is an effective method to achieve a high-power, high beam quality fiber laser. In the SBC system, multi-channel incident lasers are arranged spatially and are combined into a single laser beam via an optical element. The transmitted laser power density in the SBC system is very high due to the high power and small beam diameter. In this case, the thermal blooming effect becomes a nonnegligible factor that influences the far-field beam quality. In addition, a narrow linewidth is required in SBC to eliminate the dispersion effect. As a result, nonlinear effects are easy to stimulate, e.g., stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS), which generates a new wavelength laser. The new wavelength laser may cause enhanced atmospheric absorption and degrade the far-field beam quality. Atmospheric thermal blooming of high-power laser propagation has been studied extensively in the outer path (optical path in atmosphere) and inner path (optical path in the launching system). However, relevant studies of the inside optical path of a high-power laser have not been sufficiently thorough. Therefore, in this paper, the influence of thermal blooming on far-field beam quality in a high-power spectral beam combining system is studied. SRS in the incident narrow linewidth fiber amplifier is verified to be the dominant factor that induces thermal blooming in the beam combining system. In addition, N₂ injection into the combining system essentially eliminates the influence of thermal blooming on far-field beam quality, which can be considered an efficient suppression method.

Methods A three-channel spectral beam combining system is constructed with central wavelengths of 1064, 1072, and 1084 nm, respectively. Each incident laser can deliver 2 kW power. Taking the SRS effect into consideration, we employ 1400 W and 1800 W laser power in this experiment. First, the far-field beam patterns of each incident laser at 1400 W and 1800 W are tested. Then, the far-field beam patterns of the three-channel combined beam at different power are measured. By analyzing the measured results, the causing factor of thermal blooming in SBS system is confirmed. Then, the relationship between the optical path length and thermal blooming effect is investigated by adjusting the beam splitter position of a 1084 nm laser. Finally, suppression of the thermal blooming effect by N₂ injection is verified.

Results and Discussions When the power of each incident laser increases from 1400 W to 1800 W, apparent degradation is observed in the far-field beam pattern [Fig. 5(a)--(c)]. The peak intensity degrades severely, and the beam distribution disperses badly, which reduces the laser’s focusing property. For the combined beam, when the power reaches 2000 W to 3800 W, no obvious beam quality degradation is observed [Fig.5(d)]. The results demonstrate that the 1 μm signal laser does not cause obvious thermal blooming effect in the SBC system. The thermal blooming effect of the incident laser at 1800 W can be attributed to the SRS light. When the incident laser power is 1800 W, the SRS is measured as 100 W. In addition, the SRS wavelength covers from 1.1 μm to 1.3 μm for the 1 μm signal laser, which is in the strong absorption band of the H₂O molecule in atmosphere. Thus, air in the beam propagation path is heated to cause the thermal blooming effect. We found that optical path length has direct influence on the thermal blooming effect. When the optical path length increases from 100 mm to 450 mm, the thermal blooming effect becomes increasingly significant (Fig. 6). The far-field beam patterns of the 1084 nm laser at 1400 W and 1800 W after N₂ injection are measured (Fig. 7). The peak intensity increases significantly from 1400 W to 1800 W, and no beam quality degradation is observed, which means that the thermal blooming effect did not occur. This result demonstrates that N₂ injection can be an effective method to eliminate the thermal blooming effect in the SBC system.

Conclusions In this paper, we investigate the thermal blooming effect in an SBC system. By comparing the far-field beam patterns of a sub-beam and combined beam with identical power density, stimulated Raman scattering in the incident narrow linewidth fiber amplifier is verified as the dominant factor that induces thermal blooming in the SBC system. When the power density of Raman light reaches 180 W/cm ², the peak intensity of the far-field beam is reduced significantly, and the energy spreads. The influence of optical path length on thermal blooming is investigated. The focusing property of the far-field beam degrades gradually and finally spreads as the length increases from 100 mm to 450 mm. By injecting N₂ into the combining system to reduce H₂O content, the thermal blooming effect is effectively suppressed. The results presented in this paper are expected to facilitate optimization of the beam quality of high-power spectral beam combining.

Objective Diode-pumped alkali-vapor lasers (DPALs) represent a research hotspot in the field of high-power lasers owing to their advantageous properties, such as high efficiency, excellent beam quality, and scalability. However, DPALs are also affected by several issues: (1) alkali-metals are very active and react easily with coating materials of windows, sealant materials, etc., especially at high temperature; therefore, it is very challenging to prepare the sample cell; (2) alkali-metals also react with relaxing gas (methane or ethane) and produce carbon that contaminates windows, thus seriously reducing the windows lifetime of the sample cell. As a consequence, researchers are putting enormous efforts into the exploration of substitutes for alkali-metals. Among these, metastable rare gases are considered to be the most promising candidates. Metastable rare gases have an electronic structure similar to that of alkali-metals. Therefore, optically-pumped metastable rare-gas lasers (OPRGLs) are expected to have similar properties to DPALs, without any of the disadvantages mentioned above. However, metastable rare gases do not readily exist; they are normally prepared trough high-voltage discharge. The density, homogeneity, and stability of metastable rare gases are key factors for OPRGLs.

Methods The discharge system was composed of a simple circuit with a ~100 ns pulsed high-voltage power supply and a pair of parallel plate Cu electrodes (Fig. 2). The flat electrode discharge technique was used to produce a metastable state (5s[3/2]₂) for Kr (here denoted as Kr ^*). The discharge voltage is 15 kV, the distance between electrodes is 1.5 cm, and the electrodes dimensions are 120 mm×10 mm. In order to improve the homogeneity and stability of the discharge, a UV light pre-ionization technique was applied. A stainless-steel structure with three windows was used to contain the ultrahigh purity Kr (99.999%). The front and back windows were made of CaF₂ to ensure that the infrared laser could pass through the cell, whereas the side window was made of polymethyl methacrylate. A tunable continuous infrared laser, based on the Cr∶LiSAF crystal, was used as the probe laser, offering a tunability from 800 nm to 850 nm with a linewidth of 70 MHz. The output power is above 20 mW at 811 nm, with a pump power of 450 mW. Therefore, the absorption profile could be recorded through scanning the laser frequency with a step of 3--5 pm. After the probe laser passed through the cell, the residual light was collected using an integrating sphere, then detected via an avalanche photodiode (APD 120A). An oscilloscope was used to visualize the absorption curve. In order to evaluate the Kr ^* density uniformity, the absorption curves along different paths were recorded separately. Moreover, an Ocean optics HR4000 spectrometer was used to measure the optical emission spectra of the high-voltage DC discharge plasma along the back window.

By means of the Beer theorem, the Kr^* density could be calculated from the residual rate, which is defined as the ratio of the residual probe laser power I_L to its initial value I₀. The value of ln[I₀/I_L(v)] is proportional to the absorption profile g(v). g(v) represents the convolution function of the Doppler broadening profile with the pressure broadening profile. The Doppler broadening profile was obtained by analyzing the optical emission spectra, whereas the pressure broadening profile was derived from the fitting process.

Results and Discussions The absorption curve shape (Fig. 3) could be altered upon tuning the frequency of the probe laser. The shape of the absorption curves indicates that the Kr^* density is firstly increased and then decreased. The maximum Kr^* density occurs 15.8 μs after triggering the discharge. It is noticed that the absorptivity saturates as the frequency of the probe laser approaches the resonant frequency of the transition 5s[3/2]₂→5p[5/2]₃, which could result in a fitting error. The saturation of all curves disappears 23.8 μs after triggering the discharge. Hence, g(υ) could be obtained by fitting the ln[I₀/I_L(v)] curve starting from 23.8 μs, whereas the maximum Kr^* density was calculated using the experimental data at 15.8 μs (Fig. 5). This new fitting technology is here referred to as complex fitting method. Compared with the results obtained from the traditional fitting method (Fig. 4), the proposed complex fitting method has clear advantages.

The results show that under a discharge voltage of 15 kV, the Kr^* density can reach a magnitude of 1.3×10¹² cm^-3 and last for 3 μs (Fig. 6). The results also indicate that the full width at half maximum of the Kr energy profile is 5 GHz, being equally affected by the Doppler and pressure broadening.

Conclusions In this work, a nanosecond high-voltage pulsed power device was fabricated to generate metastable-state rare gases with high density. The time-resolved density of metastable Kr^* was characterized via tunable continuous laser absorption spectroscopy. The results show that under a discharge voltage of 15 kV, Kr^* can reach a magnitude of 1.3×10¹² cm^-3 and last for 3 μs. These results fully meet the requirements for optically-pumped metastable rare gas lasers. In future experiments, the electrodes shape and discharge mode will be explored to further improve the density of metastable Kr.

In addition, it was shown that a complex fitting method can be used to solve the fitting error caused by the saturated absorption. This method can not only improve the calculation accuracy of metastable Kr, but also provides information on the broadening, which can be used in the rate equations for the Kr metastable laser system.

Objective Er ³⁺/Yb ³⁺ co-doped fiber laser has attracted significant attention. It is widely applied in communication, military, medical, and scientific research fields. Er ³⁺/Yb ³⁺ co-doped fiber laser operates at 1.5 μm, which is located in the low-loss transmission window of silica fiber and considered as an eye-safe wavelength band. In Er ³⁺/Yb ³⁺ co-doped fiber, Yb ³⁺ ions, which act as an excellent sensitizer, have wide absorption bands of 800--1000 nm and high absorption intensity. When Yb ³⁺ and Er ³⁺ are sufficiently close, resonance energy transfer occurs between them, which improve the luminescence efficiency at 1.5 μm. The introduction of Yb ³⁺ also increases the distance between Er ³⁺ and prevents Er ³⁺ from forming clusters. However, the amplified spontaneous emission (ASE) at 1 μm emitted by Yb ³⁺ is inclined to give rise to the bottleneck effect of Er ³⁺/Yb ³⁺ co-doped fiber lasers. The output power of 1.5-μm laser and the slope efficiency will be strongly diminished by the ASE of Yb ³⁺. In this study, a series of technical solutions to alleviate ASE is proposed to achieve high efficiency Er ³⁺/Yb ³⁺ co-doped fiber lasers. Most of the proposed methods focus on changing the structure of fiber lasers. However, optimizing the composition of the fiber core and fabricating high-performance Er ³⁺/Yb ³⁺ co-doped fiber seems to be a more fundamental approach to suppress ASE. Thus, the Er ³⁺/Yb ³⁺ co-doped fiber is prepared by modified chemical vapor deposition (MCVD) process combined with solution doping technology, and the Er ³⁺/Yb ³⁺co-doped fiber laser system is constructed. Finally, the output power and ASE spectra at different pump powers are investigated.

Methods The MCVD and solution doping technologies are used to prepare fibers by introducing a large amount of phosphorus into the core. The refractive index profile (RIP) of the fiber is also analyzed by P104. Moreover, PK2500 is utilized to test the background loss and absorption coefficient of the fiber. The ASE test structure, as shown in Fig. 4, is established to observe a 1-μm ASE spectrum, which varies with pump power. The linear relationship between the output power of the 1550-nm laser and the pump power is also observed. The laser test configuration, as shown in Fig. 6, is established to further verify the fiber laser performance. By optimizing the fiber, the slope efficiency and output power are 35.5% and 2.5 W, respectively.

Results and Discussions Fig. 2 shows the RIP of the optical fiber preform. The numerical aperture (NA) attains 0.216, and the RIP center depression is caused by the volatilization of the core phosphorus element during the collapsing process. Fig. 3 shows related optical fiber performance parameters. The background loss is about 42.15 dB/km at 1190 nm. The cladding absorption coefficient at 940 nm and the core absorption coefficient at 1535 nm are 3.58 dB/mand 34.5 dB/m, respectively. The backward 1-μm ASE spectrum changes with the pump source power, as shown in Fig. 5. The inset shows that the 1.5-μm laser power increases in synchronization. When the Yb ³⁺ pumping rate is faster than the energy transfer rate of Yb ³⁺→Er ³⁺, the ²F_5/2 energy level of Yb ³⁺ will accumulate a large number of the excited state particles, and the 1-μm signal will gradually be amplified in the laser system due to the unsaturated gain. Thus, it reduces the system pump conversion efficiency and produces parasitic lasers or even giant pulses, which can burn the fiber output end face. For this fiber, along with the 1-μm ASE power continuing to increase, the peak power is below -45 dBm from beginning to end. The 1-μm ASE does not accumulate rapidly with the increase of pump light power. The reason may be attributed to the enhancement of Yb ³⁺→Er ³⁺energy transfer efficiency by phosphorus doping. A two-level laser test platform, as shown in Fig. 6, is developed to further verify the laser performance of the homemade Er ³⁺/Yb ³⁺ co-doped fiber. Furthermore, the laser output power under each pump power of the second stage is tested, and a linear fit is made to the obtained data. Fig. 7 shows the test result with a slope efficiency of 35.5% and coefficient of association of 0.99805. When the output power reaches 2.5 W, there is still no over-rolling phenomenon, suggesting that the 1-μm ASE has no significant adverse impact on the 1.5-μm laser output.

Conclusions The Er ³⁺/Yb ³⁺co-doped double-clad fiber is successfully fabricated by MCVD and solution doping. The diameter of the core and cladding are 10 μm and 130 μm, respectively. The cladding absorption coefficient reaches 3.4 dB/m at 940 nm. The core absorption coefficient is 35 dB/m at 1535 nm. The laser test results show that the maximum slope efficiency of 1550 nm laser is 35.5%, and the output power is greater than 2.5 W. This indicates that phosphorus doping has a significant effect on the optical performance of Er ³⁺/Yb ³⁺ co-doped fiber. The fiber rapid development lays a solid foundation for further research on a 1.5-μm high-power fiber laser.

Objective Because of the important applications of Rb atoms in precision measurement, the linearly polarized, narrow-linewidth, and frequency-stable 780 nm laser source which matches the D2 transition line of Rb atoms has recently begun to attract more attention. The linewidth of the 780 nm laser diode and the 1560 nm laser diode used for the frequency doubling of periodically-poled Lithium Niobate (PPLN) crystal both are in the order of MHz. Although the linewidth of the Ti∶Sapphire laser is as narrow as kHz, it presents its own problems, such as large size, high cost, and difficulty of maintenance and transport, which greatly limit the practical use of high-precision atom interferometers. The 780 nm laser source-realized by the combination of techniques including power amplification of the narrow linewidth 1560 nm fiber by the erbium doped fiber amplifier (EDFA), frequency doubling by the PPLN crystal, and sideband locking, is currently the most promising candidate; however, its maximum power is only 1.2 W, presenting difficulty in meeting the requirements of the above applications. In this paper, a high-power 780 nm laser source prototype of our own design and development, with stable frequency, narrow linewidth, and high linear polarization, is presented. In addition, the cooling, repumping, and atomic interference coherent operation lasers can be simultaneously obtained by this prototype, which is convenient for precise measurement based on super-cold Rb atoms.

Methods The 780 nm laser source uses a single 1560 nm fiber laser with linear polarization, narrow linewidth, and broadband tunable frequency as its seed source. After the 1560 nm laser's power is boosted by the EDFA, the polarization-maintaining fiber coupler divides it into two parts. One part is frequency doubled by the waveguide-type PPLN crystal to stabilize the 1560 nm laser's frequency via saturation absorption spectroscopy; by using sideband-locking technology, the sideband frequency of the 780 nm laser is locked to the hyperfine transition of the ⁸⁵Rb atoms, and a wide range of frequency tuning can therefore be obtained. The other part is used as the signal light of the cladding-pumped erbium-ytterbium co-doped double-clad fiber (EY-DCF) amplifier used for power boost. The ytterbium band amplified spontaneous emission(Yb-ASE)during the amplification process can be effectively suppressed by dual-wavelength auxiliary signal injection technology, which subsequently increases the 1560 nm laser output power of the fiber amplifier. Finally, a high-power 780 nm laser output can be obtained due to the relatively high fundamental frequency optical power.

Results The saturation absorption spectroscopy of the Rb atom (Fig. 2) can be scanned by precisely adjusting the control temperature and PZT voltage of the seed laser. When the +1 order modulation sideband of the 780 nm laser is locked to the ⁸⁵Rb saturated absorption cross-resonant peak F=3→F'=CO3-4, the frequency of the 780 nm laser can be stabilized within 150 kHz (Fig. 3(a)) for a long time. By using sideband-locking technology, the frequency of the 780 nm laser can also be precisely tuned in a tuning range of 1.2 GHz (Fig. 4(b)). The 780 nm laser power generated by the PPLN crystal is as high as 2.25 W, benefiting from the improvement of the fundamental frequency light power. The signal-to-noise ratio of the 780 nm laser is as high as 60 dB (Fig. 3(b)), the linewidth is expected to be less than 80 kHz, and the measured linear polarization degree is as high as 23 dB.

Conclusions A sideband-locked high-power 780 nm laser source prototype designed and developed for Rb atom precision measurement applications is reported. The seed laser is a homemade single 1560 nm linearly polarized DBR fiber laser. Dual-wavelength auxiliary signal injection technology is used to suppress the influence of the Yb-ASE, effectively improving the amplification effect of the cladding-pumped EY-DCF amplifier on the 1560 nm laser and making the 780 nm laser power up to 2.25 W after the 1560 nm laser has its frequency doubled by the PPLN crystal. By locking the sideband of the 780 nm laser to the saturated absorption cross-resonant peak of the ⁸⁵Rb atom, the frequency fluctuation of the 780 nm laser reaches about 150 kHz within 15 minutes, with linewidth less than 80 kHz and linear polarization degree as high as 23 dB. In addition, the frequency of the high-power 780 nm laser can be precisely tuned in a tuning range of 1.2 GHz, so the cooling, repumping, and atomic interference coherent operation lasers can be obtained simultaneously by a single laser source. The 780 nm high-power laser source has been integrated in a 4U standard box, which is convenient for handle and transportation, thus it is highly suitable for precise measurement based on super-cold rubidium atoms.

Objective With the rapid development of 5G communications, global cloud computing, ultrahigh-definition videos, and internet of things, the demand for data communications has increased exponentially. Moreover, the traditional communication systems are unable to meet the current data transmission requirements. The communication capacity of a single channel is close to Shannon's limit and is challenging to increase. Therefore, expanding the transmission bandwidth, particularly for the L-band, is currently an effective solution based on the existing transmission systems.

Methods A modified chemical vapor deposition (MCVD) technology was used to fabricate the extended L-band erbium-doped fibers. To extend the L-band gain bandwidth, P/Al was introduced into the fiber core to suppress the excited state absorption (ESA) of Er ³⁺. In addition, the optical parameters of the fibers were measured and analyzed, and the L-band amplification performance was investigated based on the two-stage amplification structure.

Results and Discussions The erbium-doped fiber has the core and cladding diameters of 5.4 μm and 125 μm, respectively. The fiber's numerical aperture is approximately 0.2, the absorption coefficients at 980 nm and 1535 nm are 11.04 dB/m and 38.8 dB/m, respectively, and the background loss at 1200 nm is 15 dB/km. Figure 2 shows the absorption and emission cross-sections of the extended L-band erbium-doped fiber. The difference between emission and absorption in the L-band region reflects the gain capability of the fiber in the L-band. Ostensibly, when the wavelength is longer than 1622 nm, the difference between emission and absorption is negligible, indicating that the ESA of the erbium-doped fiber is well suppressed and it has a strong gain ability in the extended L-band region. Based on the two-stage amplification structure in Fig. 3, the input signal power is -1 dBm, the 20 dB gain output is extended to 1622 nm, the maximum noise figure is 5.3 dB, and the saturated output power is 24.5 dBm.

Conclusions We demonstrated an extended L-band erbium-doped fiber fabricated via the MCVD technology. Based on the two-stage amplification structure for the first and second stages with lengths of 11 m and 25 m , respectively, the long-wavelength of the 20 dB gain output was extended to 1622 nm under a 980 nm excitation. The maximum noise figure was 5.3 dB, and the saturated output power was 24.5 dBm.

Objective Fluorozirconate optical glasses are widely used as fibers because of their excellent optical properties, such as their transparency in the mid-infrared wavelength range around 8 μm. These glass fibers show a wide range of military and industrial applications, such as in the ultra-low loss, long, and repeaterless optical communication links. They are typically fabricated from the fluorozirconate glass preform by the rod-in-tube method that allows for precise control of fiber dimension and geometry. To a large degree, the fiber quality depends on the quality of the preform. Before fabrication of the fluorozirconate glass fiber, the preform must undergo optical cold processing, including grinding and polishing. After shown in the structure model of the glass surface in Fig.1, defects, such as impurities, scratches and microcracks, are introduced on the surface and subsurface of the fiber preform during this processing. During the fiber fabrication process, the defects end up at the core/cladding interface, decrease the strength of the fiber, and increase the optical losses. An acid treatment is an effective method to enhance the mechanical strength of the optical glass surface and eliminate the surface and subsurface defects. In general, the preform surface of the fluorozirconate glass fiber is treated with an aqueous acid solution, such as hydrochloric acid or boracic acid. However, the fluorozirconate glass surface degrades rapidly upon exposure to aqueous media or humid atmospheric environments because of its poor chemical stability. Therefore, the conventional surface treatment of fluorozirconate glass fiber preform by etching with an aqueous acid solution increases the surface roughness and creates a hydrated surface layer. It also causes precipitation of crystalline dissolution products on the surface, which increases the optical losses, decreases the tensile strength of the fiber, and increases the risk of devitrification during fabrication of the fiber. Therefore, it is more optimal to treat the fluorozirconate glass surface using an nonaqueous solution.

Methods An nonaqueous organic solution composed of organic solvent, mixed acid, and additives (Table 1) was formulated to treat the surface of an fluorozirconate glass fiber preform. The organic solvent was composed of ethyl alcohol and amyl alcohol, which cannot corrode the fluorozirconate glass surface. Therefore, a corrosion layer cannot be created. The mixed acid component was a mixture of hydrochloric acid and oxalic acid with a small amount of water, which was further diluted with an organic solvent. The amount of water used did not cause chemical etching of the surface. The additives used were zirconyl chloride and ethylene diamine tetraacetic acid, which are metal complexing agents that increase the solubility of the etching products and prevent their precipitation on the surface. The nonaqueous organic solution could more effectively remove the surface and subsurface defects caused by optical cold processing, without creating a corrosion layer.

Results and Discussions To compare the two different surface treatments (using an aqueous acid solution and an nonaqueous organic solution, respectively), we have studied the surface compositions of the fluorozirconate glass using X-ray photoelectron spectroscopy (XPS). The composition variation of the fluorozirconate glass surfaces treated by these two surface treatments is shown in Fig. 2. It is evident that the compositions of the fluorozirconate glass surface etched by the nonaqueous organic solution were closer to those of bulk glass for the elements, Zr, Na, and Ba. Furthermore, it is clear that dissolution of the surface compositions etched by the aqueous acid solution was quicker than that by the nonaqueous organic solution, and the chemical etching by the nonaqueous organic solution was more uniform and did not create a corrosion layer or precipitation leading to opaque crystalline surface deposits. By using atomic force microscopy (AFM), we have studied the surface morphology of the fluorozirconate glass surface treated with these two methods. The surface root-mean-square (RMS) roughness of the fluorozirconate glass surfaces was 0.925 nm after polishing with nano-CeO₂ (Fig.3), 8.971 nm after etching with the aqueous acid solution (Fig.4), and 2.152 nm after etching with the nonaqueous organic solution. The surface roughness after etching with the nonaqueous organic solution was lower than that after etching with the aqueous acid solution. Furthermore, the morphology of the surface etched by the nonaqueous organic solution was better than that etched by the aqueous acid solution. This means that the chemical reaction between the nonaqueous organic solution and the fluorozirconate glass surface was more stable, and with the lack of precipitation of the reaction products on the surface to affect the etching, the surface was smoother. Etching of the fluorozirconate glass fiber preform surface with the nonaqueous organic solution results in a higher surface quality, which is useful for subsequent fiber fabrication. Figure 6 shows the optical losses of the fluorozirconate optical glass fibers fabricated from preforms with the different surface treatments. The optical losses of the fluorozirconate optical glass fiber fabricated from the preform etched by the nonaqueous organic solution were lower at different wavelengths than those fabricated from the preform etched by the aqueous acid solution. It is evident that the fluorozirconate glass surface treatment with the nonaqueous organic solution was more effective at eliminating surface and subsurface defects and removing impurities, which increases the scattering and absorption losses compared to the traditional surface treatment using aqueous acid solution. The weibull failure probabilities of the fluorozirconate glass fibers fabricated from preforms with the two surface treatments are displayed in Fig.7. The median tensile stress at failure is about 300 MPa for the fiber fabricated from the preform etched by aqueous acid solution and about 450 MPa for the fiber fabricated from the preform etched by nonaqueous organic solution. Therefore, it is shown that fluorozirconate glass preform surface treatment with nonaqueous organic solution was more effective in removing failure-producing defects than that with aqueous acid solution.

Conclusions In order to decrease optical losses at the fluorozirconate glass fiber core/cladding interface, the method to treat the preform surface using nonaqueous organic solvents is investigated. When comparing the surface quality of the preform and the performance of the resulted fiber after treatment with nonaqueous organic solvents or traditional aqueous acid solution, it is evident that the treatment with the former allows for the fabrication of an fluorozirconate glass fiber with lower optical losses and higher strengths than that with the latter.

Objective Richtmyer-Meshkov instability arises when a shock wave encounters an interface between two materials of different densities. As instability develops through linear regime to nonlinear regime, mixing between two materials occurs and grows. The study of interface instability and mixing is relevant and of significant interest due to its promising application in many studies and engineering fields, such as phase transformations, multi-phase flow, and dynamic damage. Generally, hydrodynamic instabilities are studied under liquid conditions in which the materials have been shocked to liquid. Meanwhile, instability in solids is governed by their elastic and plastic properties (strength), and this area is attracting much interest presently due to its promising applications in investigating the constitutive properties of matter. Usually, a laser pulse ablation produces an unsupported shock in a material, and Rayleigh-Taylor instability (RTI) is induced due to the interface deceleration after the shock transit. In this study, we investigate the instability and mixing between the tin and polymer foam under unsupported shock loading via nanosecond laser ablation. The loading pressure is changed to evaluate the influence of strength on the instability growth and mixing characteristic via high-energy radiography. We hope the experimental results can improve the understanding of the issue and provide help for further studies.

Methods Tin and polymer foam with initial single-mode sinusoidal interface perturbation (Atwood number A=-0.87, kAη₀=0.82) are employed in this study. A nanosecond laser pulse after the continuum phase plate of 2 mm diameter is focused on the tin surface, and an unsupported shock is produced at the tin-polymer foam interface. Another picosecond laser ablates the golden wire and produces several high-energy X-ray images, which are used to diagnose the instability and mixing via side-on radiography. The radiographs are recorded by the image plate fixed on the rear side of the high-energy X-ray camera. The evolution images of interface instability and mixing are obtained by changing the radiography time related to the nanosecond laser.

Results and Discussions Since the Atwood number, A, is negative, the interface experiences a phase inversion at the beginning. As instability comes into a nonlinear regime, the radiographs of interface instability and mixing under different loading pressure become quite different. When the tin is shocked into liquid, the spike evolves into a mushroom tip, just like wearing a thin “hat”, which has a sharp crest and two long braids around two sides (Fig. 4). Afterward, secondary spikes emerge at the center of the original spikes due to the second shock loading within the tin. However, when the loading pressure is lower, the tin has not melted or only melted partially upon release. In this case, the growth of the spike and bubble is suppressed by the strength and the spike evolves into a different appearance (Fig. 6). The spikes consist of one thin tip and one thick root. Later, the tip becomes thicker and the it is different from the root shrinks. In the end, the mixing between the tin and polymer foam becomes acute, leading to curve and fragmentation of spike tip. Besides, the spike root has totally deviated from the initial interface and broken up into debris. Assuming that the spikes have achieved their maximum height before fragmentation, then the yield strength of tin can be determined. Moreover, the contribution of RTI is evaluated according to the interface deceleration process (Fig. 8).

Conclusions In this study, the interface instability and mixing between the tin and polymer foam with initial single-mode sinusoidal interface perturbation driven by unsupported shock is studied via high-energy side-on X-ray radiography for the SG-Ⅱ upgraded laser facility. Radiographs of instability and mixing at different delay times are obtained at two typical loading pressures. One is at the shock melting point and the other is around the melting point upon release. When the tin is shocked into liquid, the spikes evolve into a mushroom tip. However, when the loading pressure is lower, the tin has not melted or only melted partially upon release, the growth of spike and bubble is suppressed by residual strength of the tin, and the interface evolves into another pattern. The spikes consist of one thin tip and one thick root. In the end, severe mixing between tin and polymer foam results in the curve and fragmentation of spike tip. Besides, the spike root has totally deviated from the initial interface and broken up into debris. Assuming that the spikes have achieved their maximum height before fragmentation, the yield strength of tin is determined, which is consistent with the reported value. Moreover, the contribution of RTI is evaluated due to interface deceleration and the results show that its contribution is negligible. Overall, this study improves the understanding of the interface instability and mixing driven by unsupported shock; in addition, it will serve as a useful reference for future studies.

Objective Composite materials have the advantages of high specific strength, specific modulus, and fatigue resistance and have been widely used in aerospace, ships, vehicles, and other fields. However, the properties of composites are easily influenced by their internal defects. Shearography has the advantages of full field, high sensitivity, anti-environmental-interference, and no special requirements of material types. Compared with temporal-phase-shift-based shearography, spatial-phase-shift-based shearography has a fast detection speed and is suitable for real-time detection. Spatial carrier frequency introduction is the most commonly used spatial-phase-shift method. However, in the Michelson-based spatial-phase-shift system, the shear amount and spatial phase shift are both controlled by a rotating mirror. To obtain a separated spectral diagram, a large amount of shear is required, but the effective measurement area is reduced, which leads to excessive sensitivity. In the Mach-Zehnder-based spatial-phase-shift double-imaging system proposed by Gao et al., the shear amount and spatial phase shift can be controlled independently. The imaging lens is placed after the Mach-Zehnder shear part, and the detection area of the system is limited by the size of the first beam-splitter prism in the shear part. When the distance between the shearography system and the detected material is fixed, the field of view of the system is usually small and fixed. Because of the small field of view, the detection efficiency is low. To solve this problem, this paper introduces an improved Mach-Zehnder-based spatial-phase-shift double-imaging system. The advantage of the independent adjustment of shear amount and spatial carrier frequency is retained, the field of view is enlarged, and the detection efficiency is improved.

Methods The solid state laser with a wavelength of 532 nm is expanded by the beam expander and irradiates on the surface of a rough material. The speckle produced by the rough surface of the material is reflected and imaged by an imaging lens on its focal plane. The focal point of lens 1 coincides with that of the imaging lens, so after passing through lens 1, the light reflected by the rough surface becomes parallel light. After passing beam-splitter 1, the two light beams are reflected by mirror 1 and mirror 2, respectively, where mirror 2 is used to introduce shear. The spatial carrier frequency is introduced in the two beams and is generated after passing through apertures 1 and 2. The two beams converge via lens 2' and lens 2″, and after passing through beam-splitter 2, the two light beams interfere with each other on the CCD target; thus, the speckle pattern is obtained. The spatial carrier frequency is introduced by the dislocation of apertures 1 and 2 in the spatial position. When the beam is passing through the aperture, the spatial carrier frequency is introduced into the beam. In a certain system in which the wavelength of laser and the distance between the aperture and CCD camera are fixed, the spatial carrier frequency is influenced only by the spatial positions of the two apertures. After the Fourier transform of the image obtained by the CCD camera, the spectrum with phase information can be separated. The inverse Fourier transform is applied to the spectrum containing the phase information, and the deformation distribution can be obtained by subtracting the phase information before and after the deformation.

Results and Discussions Two specimens were analyzed in this work: a defect-free aluminum plate and a composite plate with internal defects. The Mach-Zehnder-based spatial-phase-shift double-imaging system with a large field of view uses an imaging lens with a focal length of 35 mm to analyze the two specimens. The first derivative of the out-of-plane deformation distribution is shown in Fig. 6(a) and the internal defect distribution can be seen in Fig. 6(b). The result shown in Fig. 6 proves the suitability of the system for surface deformation and defect detection. The same specimen was analyzed using the traditional and Mach-Zehnder-based spatial-phase-shift double-imaging system with a large field of view including two imaging lens with different focal lengths, and Fig. 7 shows the contrast experimental results. From Fig. 7, the double-imaging system has a large field of view compared with the traditional double-imaging system. The use of imaging lenses with different focal lengths can change the field of view. When the camera is unchanged, the enlarged field of view causes the image resolution to decrease. In the actual detection process, according to the field of view and the quality requirements, a camera with higher resolution and a larger target surface and matching short-focal-length imaging lens can be used.

Conclusions This paper introduces a Mach-Zehnder-based spatial-phase-shift double-imaging system with a large field of view that can be used to detect deformation and internal defects. The spatial carrier frequency can be adjusted by changing the relative position of the two apertures placed in front of the lens. The advantage of adjusting spatial carrier frequency and shear amount independently is retained. The experimental results reveal that the field of view in double-imaging shearography can be enlarged by changing the focal length of the imaging lens. According to the actual situation, the field of view is adjustable by changing the focal length of the imaging lens, which leads to an improvement in efficiency.

Objective Ultrashort laser pulses have become an important tool for studying the interaction between lasers and matter and have important application values in the fields of biomedicine, high-energy physics research, and communications. The pulse width is an important parameter of the time characteristics of ultrashort laser pulses. For picosecond and femtosecond laser pulses, the pulse width is often measured by an autocorrelator. The time resolution of the autocorrelator must be accurately calibrated before the measurement. For traditional calibration schemes such as the mobile optical path retarder, although their calibration results are accurate, it cannot be calibrated in a single time. On the contrary, the discriminant rate board method can be calibrated in a single time; however, the accuracy of the calibration result is poor, and the accuracy is not high. This study proposes a new method for calibrating the time resolution of the autocorrelator. A flat crystal that can produce a specific time delay is designed, manufactured, and placed in the optical path during calibration. The time resolution can be obtained through a single calibration. Moreover, the measurement results are accurate and reliable.

Methods The designed and manufactured flat crystal with a specific time delay generates double pulse with a fixed time interval T (ignoring high-order reflections), when the pulse to be measured passes through the flat crystal. When the double pulses met in the autocorrelation crystal, the generated autocorrelation signal was a three-peak structure, i.e., a weaker secondary peak signal appeared at equal distances on the left and right sides of the primary peak signal. The time interval between the main peak and the secondary peak signal was denoted as T. The time resolution of the autocorrelator could be obtained by calculating the number of pixels between the primary and secondary peaks. The influence of the thickness, refractive index, and angle of the flat crystal on the calibration result was then analyzed. The time resolution and the relative expanded uncertainty of the autocorrelator were calculated. Finally, the autocorrelator was calibrated using two other calibration methods. The measurement results of the time resolution and the relative expanded uncertainty were given. Moreover, the advantages and the disadvantages of the three schemes were compared.

Results and Discussions After the flat crystal is placed in the optical path, the placement angle, thickness, and refractive index will affect the calibration accuracy of the time resolution. Figure 4 shows the deviation caused by the placement angle of the flat crystal. The deflection angle deviation only slightly affects the time resolution. A resolution error of 2% requires a deflection angle of 16.6°. The measurement error primarily comes from the deviation in the thickness h of the flat crystal and the reading. Figure 5(a) depicts the autocorrelation signal collected on the CCD. Obvious secondary peak signals can be found at both ends of the main peak signal, which is consistent with the theoretical analysis results. In this experiment, the thickness h=1.02 mm and refractive index n=1.450 of the plane flat crystal were maintained. The time interval between the primary and secondary peaks is 9.86 ps. The time resolution of the autocorrelator is 217.88 fs/pixel. The relatively extended uncertainty is 1.50%. Table 3 shows the results of the time resolution and the expanded uncertainty obtained by the three calibration methods. The results of the time resolution calibration using a flat crystal are accurate and reliable.

Conclusions This study proposes a new method for calibrating the time resolution of an ultrashort pulse measuring device based on a flat crystal. By placing a special flat crystal in front of the ultrashort pulse measuring device, double pulse with a time interval T is generated after the pulse to be measured passes through. The generated autocorrelation signal exhibits weaker sub-peaks on both sides of the primary peak. As shown in Fig. 2, the time interval of the sub-peak 2T can be obtained from the refractive index and the thickness of the flat crystal. The pixel value between the sub-peaks can ascertain the time resolution of a single picosecond autocorrelator and calculate the pulse width at the same time. Subsequently, experiments are performed on a femtosecond laser with a pulse width of 180 fs. Figure 5 illustrates the autocorrelation signal collected by the CCD in the experiment, which is consistent with the theoretical prediction. Using this method to calibrate the time resolution of the autocorrelator yields 217.88 fs/pixel. Compared with the calibration result of 214.27 fs/pixel obtained by the moving optical path retarder method, the relative error is only 1.68%. Compared with the discrimination rate board method, the relative expanded uncertainty of the calibration result using this method is 1.50%, which is far better than the discrimination rate board method of 6.96%. A single calibration of the autocorrelator is realized. In conclusion, the calibration result is accurate and reliable.

Objective A laser Doppler velocimeter (LDV) obtains the moving velocities of carriers by gauging the interference signal when the signal light is mixed with a reference. As a novel speed sensor, LDV possesses several advantages: non-contact measurement, no interference with the target, and high speed-measurement accuracy. However, when measuring the velocity of a solid surface, an LDV can scale the speed only within a limited range. When the moving surface is beyond the measurable range of the LDV, the intensity of the scattered light decreases, and the quality factor of the Doppler signal reduces. A Doppler signal is validated by the quality factor Q, which directly determines the working distance and measurable range of the LDV. When the quality factor is below the threshold, the carrier velocity cannot be determined from the Doppler signal. To meet the requirements of the measurable range, the quality factor is traditionally enhanced by two lenses with fixed focal length, which change the position of the waist spot of the outgoing Gaussian beam. However, this method increases the distance between the lenses and excessively expands the LDV volume. Meanwhile, the measurement scope remains limited and non-adaptable to actual situations. To change the measurable range of the LDV, one must either change the distance between the lenses or reform the lens combination. Mechanically transforming the lens distance will increase the volume and the system complexity, largely restricting the operating range of the speedometer. In addition, the lens combination cannot be changed at any time in practical engineering applications. No other reasonable method can expand the measuring range. Herein we present a beam transformation system based on a liquid lens. The waist-spot position of the Gaussian beam is controlled by changing the driving current, enhancing the quality factor above the threshold over a considerable range. Our design greatly improves the working distance and measurable range of the LDV. We hope that our basic strategy and findings will benefit the speed measurement and navigation ability of the carrier.

Methods This paper combines a theoretical analysis and simulation with experimental verification. In the theoretical analysis, we first evaluated the feasibility of transforming the LDV's Gaussian beam through a liquid lens. Based on Gaussian optics, the positions and size of the waist spot were simulated under different driving currents of an electrically tunable lens (ETL). We then constructed an LDV with the ETL and changed the position of its waist spot by changing the driving current without increasing the displacement mechanism. Throughout the experiment, we determined the relationship between the quality factor of a single point and the driving current, and the working distance and measuring range of the LDV for different offset lenses.

Results and Discussions The presented method improved the working distance and measurable range of the LDV. Owing to the sharp response time of the liquid lens (in order of milliseconds) (Table 1), the driving current can be controlled by a feedback signal, achieving real-time adjustment of the liquid lens (Fig. 5). In the new LDV structure, the maximum quality factor of a single measuring point reaches 3482, 22.9 times that of a traditional speedometer (Fig. 9). When the F_offset=-25.4 mm offset lens was selected, the working distance of the LDV was changed to the maximum extent, with a measuring range of 0.7--3.3 m. The system volume was reduced at the same time (Fig. 10, Table 2).

Conclusions This paper proposes a novel LDV scheme based on a liquid lens. Within this design, the waist spot position of the Gaussian beam can move and the working distance of the LDV can be changed simply by controlling the driving current, without increasing the displacement mechanism. Therefore, the quality factor of the Doppler signal is greatly improved. The quality factor of a single measuring point is maximized at 3482, 22.9 times that of a traditional speedometer. The new structure improves the measuring range of the LDV to 0.7--3.3 m, 4.3 times that of the traditional structure (1.2--1.8 m), while reducing the volume of the speed measurement system. These improvements will greatly expand the engineering applications of LDVs.

Objective The research on the electric field of ultrashort laser pulse has a wide application prospect. The ultrashort femtosecond laser pulse is used in many scientific and engineering domains, such as ultrashort spectroscopy, quantum coherent modulation, and ultra-intense laser physics. A typical method of measuring ultrashort laser pulse is the frequency-resolved optical gating (FROG). Using FROG, we first split the pulse into two replicas and then apply a time-delay to one of them. Next, we allow them to interact in a nonlinear process to generate a signal, in which we use spectroscopy to measure the spectral intensity. Finally, we tune the time delays to obtain the spectral intensities of a set of nonlinear signals, which constitute a spectrogram named FROG trace. A phase retrieval algorithm is always required to reconstruct the original laser pulse because only the intensities are recorded in FROG trace. As an efficient phase retrieval algorithm, the prominent component general projecting algorithm (PCGPA) is widely used for ultrashort pulse measurement. However, PCGA brings several practical problems for the FROG measuring process because PCGPA requires that the trace be a square one and that its frequency axis and delay axis coordinates are coupled by fast Fourier transform. According to the different applications of the nonlinear process, FROG can also be realized in different geometrical schemes, for example, second harmonic generation (SHG), polarization gate (PG), and cross-phase modulation (XPM). In this study, we aim to (i) build a non-square FROG trace by taking the features of the measuring devices into fully account to realize successful pulse reconstruction and avoid the drawbacks accompanied by PCGPA and (ii) compare the retrieving results in different geometries to select a more efficient and practical one.

Methods First, we build the non-square trace by applying the following three transformations on the 256×256 square FROG trace (Fig. 1): (i) low-pass filtering in the frequency axis (F_LPF), (ii) up-sampling in the frequency axis (F_US), and (iii) down-sampling in the delay axis (D_DS). To identify the relevant non-square traces, we also use the three aforementioned transformations. Then, we numerically generate 200 pulses, whose envelopes are the superposition of 2--6 Gaussian functions and phases are composed of chirps, quadratic chirps, and self-phase modulations. We also obtain few-cyclic experimental pulses for comparison. Next, we use the ptychography algorithm, originally developed in coherent diffraction imaging, to retrieve the FROG trace phase and the corresponding pulse field. Ptychography algorithm is accustomed to non-square traces without further adjustment because it uses only one column of a trace in its single iteration. To evaluate the results, we use the intersection angle θ between the original and the reconstructed pulses in multi-dimensional space, which is considered eligible when less than 0.1. Finally, we realize the pulse reconstruction from non-square FROG traces in different geometric schemes (i.e., SHG, PG, and XMP schemes) and compared the results.

Results and Discussions For SHG FROG (Table 1), pulse reconstruction can be realized from trace after F-LPF, which should be regarded as super-resolution one because of the absence of high-frequency information, and F_US application can improve the reconstruction. Although the results will be slightly worse for applying D_DS, it is still less than 0.1 when only 14-delay data are left. For PG and XPM FROG traces (Table 2 and Table 3, respectively), the effects of these three transformations on the retrieval result are similar to the SHG FROG trace; however, the minimum amount of delays for successful reconstruction is only 12 and 8, respectively. Ptychography algorithm from non-square FROG traces (Fig. 2 and Fig. 3) can restructure both the numerally generated pulse and the few-cyclic experimental pulse. For different geometries, XPM FROG can be deemed the most practical because it requires the least delays. SHG FROG trace is symmetrical; thus, only half of the delays in a trace are effective, leading to the requirement of more delay steps to make the algorithm be converged. The nonlinear signal in PG FROG is proportional to the product of the original pulse field and the delayed pulse field, so it vanishes and is useless when the time-delay is longer than the pulse duration. The nonlinear signal in XPM geometry is the original pulse under the same conditions because the delayed pulse replica only modulates the original pulse phase. In short, XPM FROG trace contains more effective information than the other two types of trace; therefore, few time delays are needed for efficient pulse reconstruction.

Conclusions In this study, we build non-square traces by applying three transformations on the corresponding square one: (i) F_LPF to reduce the requirement of large phase-matching bandwidth, (ii) F_US to utilize the high resolution of spectrometer, and (iii) D_DS to reduce the measuring time. Ptychograpy algorithm can reconstruct simulated and few-cyclic experimental pulses from the non-square traces in SHG, PG, and XPM FROG. After applying F_LPF and F_US for the XPM FROG trace, only eight delays are sufficient to retrieve the pulses successfully. Changing the delay is the most time-consuming step in FROG; hence, reducing delays will benefit FROG to realize the real-time measurement of ultrashort pulses.

Objective In recent years, III-V semiconductor materials have been widely used in optoelectronic devices, such as lasers, detectors, and LEDs, and have attracted widespread attention of researchers. Among these materials, the band gap of the InGaAsSb/AlGaAsSb quantum well structure is between that of GaSb and InAs. Therefore, the InGaAsSb/AlGaAsSb quantum well structure is the preferred material for the preparation of antimonide semiconductor lasers with a wavelength range of 1.8--3 μm. In molecular beam epitaxial (MBE) growth of antimony alloy semiconductor materials, defects and molecular clusters are introduced. These defects reduce the light-emitting characteristics of the materials, affecting the threshold current, output power, and spectral line width of the laser. In order to further improve the optical properties of InGaAsSb/AlGaAsSb quantum well materials, a rapid thermal annealing method is used to treat the quantum well structure. The effects of rapid thermal annealing on the performance of quantum wells are studied here using photoluminescence spectroscopy.

Methods An InGaAsSb/AlGaAsSb quantum well structure is grown using a DCA-P600 MBE system. A GaSb buffer layer with a thickness of 500 nm is first grown on an n-type GaAs substrate. Then, three periods of In_0.1Ga_0.9As_0.08Sb_0.92/Al_0.3Ga_0.7As_0.13Sb_0.87 are grown on the buffer layer. The thickness of the In_0.1Ga_0.9As_0.08Sb_0.92 well layer is 20 nm and the thickness of the Al_0.3Ga_0.7As_0.13Sb_0.87 barrier layer is 30 nm. The as-grown sample is cleaved into four pieces of equal size. One of the samples is designated as the as-grown sample and does not undergo rapid thermal annealing. The other three samples are subjected to rapid thermal annealing for 30 s in a nitrogen atmosphere at either 500 ℃, 550 ℃, or 600 ℃. A laser with a wavelength of 655 nm and spot area of 0.4 cm ² is used to measure the photoluminescence spectrum of the samples. A HORIBA iHR550 spectrometer, with an InGaAs detector kept at -30 ℃, is used to detect photoluminescence signals. The line density of the selected spectrometer grating is 600 line/mm and the wavelength of filter is selected 1000 nm. All tests are carried out in a closed-circulation liquid helium cryostat with a CaF₂ window. The laser power density is changed from 1 mW/cm ² to 300 mW/cm ² during the power-dependent photoluminescence measurement and the temperature is changed from 10 K to 300 K during the temperature-dependent photoluminescence measurement.

Results and Discussions The photoluminescence results show that rapid thermal annealing causes atoms to interdiffuse throughout the quantum well layer and the barrier layer interface in the quantum well structure. This can improve the crystal quality of the quantum well material and reduce structural strain, thereby improving the optical properties of the quantum well material. At room temperature, the photoluminescence spectrum shows a gradual blue-shift with increasing annealing temperature. When the annealing temperature is 500 ℃, 550 ℃, and 600 ℃, the photoluminescence shift is 7 meV, 8 meV, and 9 meV, respectively (Fig. 2). From the temperature-dependent and power-dependent photoluminescence spectra, it can be seen that the emission peak at 0.687 eV is the result of local carrier recombination and the emission peak at 0.701 eV is the result of free exciton recombination (Fig. 4). The experimental results show that increasing the annealing temperature can reduce the proportion of local carrier recombination. When the temperature is 600°C, the intensity ratio of local carriers to free excitons is reduced to 22.6% of that of the sample annealed at 500 ℃ (Fig. 5). The experimental results show that the photoluminescence performance of the quantum well material can be effectively improved with the appropriate rapid thermal annealing temperature.

Conclusions An InGaAsSb/AlGaAsSb quantum well structure was grown on a GaAs substrate using a MBE system and the effects of rapid thermal annealing on luminescence properties of the quantum well material are systematically discussed. The experimental results show that rapid thermal annealing causes interdiffusion of elements on the heterogeneous interface between the quantum barrier layer and the well layer. This interdiffusion increases the energy of the ground state transition of the quantum well material and thus causes a blue-shift of the room temperature photoluminescence peak of the quantum well material. The emission of the quantum well samples is determined by excitation power-dependent photoluminescence spectrum and temperature-dependent photoluminescence spectrum. There is recombination of localized state carriers and recombination of free excitons at the low energy and high energy end of the photoluminescence peak, respectively. The localized carrier emission of the material is reduced with the increase of rapid thermal annealing temperature. These results show that rapid thermal annealing is beneficial for uniform distribution of atomic clusters produced by diffusion and that it can also promote healing of resulting holes. The rapid thermal annealing process can optimize emission in the quantum well structure when the appropriate annealing temperature is selected, thereby effectively improving the performance of laser materials and laser devices.

Objective The measurement of key parameters of combustion flow field can effectively evaluate combustion efficiency, control pollution emission, and improve energy efficiency. Because of its obvious superior features such as high precision, noncontact measurement, and low cost, tunable diode laser absorption spectroscopy (TDLAS) is an effective way to measure temperature, concentration, velocity, and pressure in combustion flow field. Combined with computerized tomography (CT), TDLAS can achieve two-dimensional(2D) or three-dimensional (3D) tomography. In the 1980s, Emmerman et al. used the direct absorption spectroscopy (DAS) for combustion diagnosis in reactive flows, which verified the feasibility of the method to realize 2D combustion diagnosis. With the development of the laser and reconstruction algorithms, the DAS-based 2D reconstruction technology has begun to be applied to engineering practice. This technology has been successfully used in the Hypersonic International Flight Research Experiment (HIFiRE) conducted by the US Air Force Laboratory and NASA. Although the DAS exhibits many advantages, it is difficult to apply this method under low signal-to-noise ratio (SNR) conditions. The wavelength modulation spectroscopy developed on the basis of the DAS can significantly improve the SNR under weak absorption conditions, thus improving the detection accuracy and detection limit of the absorption spectroscopy. In line-of-sight measurement, the wavelength modulation spectroscopy (WMS) shows good noise resistance and is therefore suitable for the flow field measurement under weak absorption or high-pressure conditions. Calibration-free WMS (CF-WMS) proposed by Hanson's group from Stanford University is one of the widely used WMS methods. As far as we know, the literature mainly focused on numerical simulation analysis for the difference in 2D reconstruction between the DAS and WMS. It is necessary to verify the difference between the two methods by experiment.

Methods Combined with the algebraic reconstruction technique (ART), we introduced the principle of two-dimensional temperature reconstruction based on WMS, and analyzed the difference between DAS and WMS in the two-dimensional reconstruction under the influence of various noises through numerical simulation. Next, the combustion flow field generated by the McKenna flat flame furnace was used as the measurement object. The two-dimensional temperature measurement experimental system was built around the flat flame furnace. DAS- and WMS-based two-dimensional temperature reconstructions of methane-air premixed flame with an equivalent ratio of 1 were carried out, and the reconstruction results were analyzed.

Results and Discussions In numerical simulation, the temperature reconstruction results of the simulated flow field with two reconstruction methods under various noise intensities are provided (Table 2). The maximum deviation and mean square relative error of WMS are 0.0186 and 40.3 K, respectively, and those of DAS reconstruction are 0.0192 and 42.5 K, respectively. Under the condition of no noise, these values are relatively consistent. With the increase in noise intensity, the reconstruction error based on DAS gradually increases, while that of WMS does not change significantly. The maximum deviation and mean square relative error of WMS based reconstruction are 0.0206 and 49.8 K, respectively, and those of DAS based reconstruction are 0.0795 and 353.6 K, respectively (Fig. 3). Under the condition of noise intensity I_RIN=-140 dB/Hz, these values are greatly different. This result shows that the reconstruction accuracy of the WMS based method is higher than that of the DAS based method in the presence of measurement noise, and the suppression effect of the WMS based method on noise is still effective in a two-dimensional reconstruction. Under the condition of a weak-absorption flow field, the two-dimensional reconstruction method based on the WMS can effectively suppress the influence of noise in measurement with higher measurement accuracy.

In experimental verification, the maximum deviation between the reconstructed temperature field obtained by the DAS-based method and the thermocouple measurement result appeared in the range of 50 mm in diameter is about 56.6 K (8.5%), and the relative error of the mean square of the reconstructed temperature field is 0.0469 (Fig. 9). Although the reconstruction results based on DAS reflect the temperature distribution characteristics of the combustion flow field, the overall error is relatively large. This error mainly comes from the baseline fitting error and the Voigt fitting error caused by noise, while the influence of the baseline fitting error is more serious in a weak absorption environment. For a 2D reconstruction, the Voigt fitting error will affect the accuracy of ART 2D reconstruction, and it will eventually show up as a temperature reconstruction error. Selecting absorption spectral lines with stronger absorption will help reduce the error of the DAS based method in a two-dimensional reconstruction. The maximum deviation of the reconstructed temperature field obtained by the WMS-based method is 39.2 K (5.9%), which also occurred in the range of 50 mm in diameter (Fig. 9). The relative error of mean square is 0.0268. In general, the reconstruction result based on WMS is consistent with the thermocouple measurement result, and the measurement error is smaller than that of the DAS-based method. In one-dimensional TDLAS, WMS is not affected by the baseline and has significant inhibition effect on the noise at absorption peak, which is also reflected in 2D reconstruction. As the 2f/1f signal has a better suppression effect on the environmental noise, the signal of each ray has a higher SNR, which is helpful to a more accurate 2D reconstruction.

Conclusions In this paper, WMS combined with ART is applied to the two-dimensional reconstruction of the combustion flow field. The reconstruction speed is large, and the number of spectral lines required is small, which has great advantages in practical applications. From the numerical simulation and experimental verification, the difference between DAS- and WMS-based 2D reconstruction is analyzed. It is proved that WMS has a better suppression effect on noise than DAS in a 2D TDLAS. In a numerical simulation, the difference in the reconstruction result between the two methods under different noise levels is analyzed. The result shows that with the increase in the noise level, a WMS-based 2D reconstruction has better robustness while a DAS-based 2D reconstruction varies significantly. In the case of a high noise level, a DAS-based 2D reconstruction cannot accurately reflect the characteristics of a simulated flow field environment. In an experimental verification, by comparing with the result measured by the thermocouple, we find that the maximum deviations of the DAS-based 2D reconstruction and WMS-based 2D reconstruction are 8.5% and 5.9%, respectively, and the mean square relative errors are 0.0469 and 0.0268, respectively. The results show that the WMS-based 2D reconstruction has higher anti-noise capability than DAS-based 2D reconstruction and the accuracy of a WMS-based 2D reconstruction is higher than that of the DAS-based 2D reconstruction under weak absorption. It is advised that a WMS-based two-dimensional reconstruction method is suitable for engineering applications where noise has a great impact, such as 2D reconstruction of flow field in a scramjet combustion chamber and the wind tunnel flow field quality assessment.

Objective Optical frequency comb (OFC) is a coherent light source with excellent time-frequency stability. In frequency domain, an OFC is a set of frequency comb teeth with narrow linewidth and equidistant distribution. Because of this characteristic, the OFC has revolutionized the approach to molecular spectroscopy, making it possible to simultaneously and rapidly measure hundreds of molecular spectral lines with high resolution. The OFC spectroscopy technology has become a hot spot in the field of spectral technology, and has promoted the technological changes in the fields of optical coherence tomography, trace analysis and optical remote sensing. However, due to the limitation of the light source gain bandwidth, the comb spectrum is still unable to compare with the traditional Fourier transform spectroscopy technology in ultra-wideband spectrum measurement, which limits its applications in, such as chemical analysis and atmospheric environment monitoring. At present, supercontinuum (SC) generation technology is the main way to expand the spectral width of light sources. However, the strong nonlinear effect and phase modulation instability inside nonlinear fibers will not only cause strong amplitude oscillation and jitter of SC spectrum, but also introduce additional phase (frequency) noise, resulting in obvious decoherence. These problems seriously limit the application of SC generation technology in comb and spectrum measurement. Here, the generation of near infrared SC comb with high coherence and flat spectrum is investigated. The coherence is confirmed by beat note measurements and nonlinear Schr?dinger equation (NLSE) based numerical simulation. The source could be useful for broadband gas sensing in monitoring of electrical installations.

Methods First, an erbium-doped fiber comb is harnessed for producing a flat SC with spectral coverage of 1250--1900 nm in a high nonlinear dispersion shifted fiber(HNL-DSF). A home-made nonlinear-polarization-rotation (NPR) mode-locked fiber laser comb delivered a train of 650 fs pulses at a repetition rate of 54.5 MHz with 10 mW of average output power (Fig. 1). The output pulses are temporally chirped with a 2 m-long single mode fiber (SMF) and then amplified by a bidirectional pumped erbium-doped fiber amplifier (EDFA) with an output power up to ~100 mW. The EDFA also behaves as a fiber compressor, producing pulses of sub-100 fs which is directly injected into a 200 m-long HNL-DSF (Yofc) for SC generation with a flat spectral profile. The HNL-DSF had a zero dispersion wavelength around 1550 nm (dispersion slope of 0.03 ps/(nm ²·km); loss coefficient <1.5 dB/km; nonlinear coefficient >10 W ^-1·km ^-1). Second, beat note measurements between the original spectrum (and SC) and two stable continuous-wave (CW) lasers at 1550.5 nm or 1535.4 nm are performed for confirming the coherence of the SC. For investigating the coherence beyond the CW laser wavelengths, numerical simulation is performed, revealing pulse propagation inside the fiber, by solving NLSE using split step Fourier method. Wide-band first-order spectral coherence is confirmed. Finally, the SC is launched for spectral measurements of a mixed gas sample, containing HF (6666.1 Pa), ¹²CO (19998.3 Pa), ¹²C₂H₂ (6666.1 Pa), and the natural water vapor in the laboratory. The measurements are carried out with a home-made Fourier-transform spectrometer at a spectral resolution of 0.1 cm ^-1. The temperature is 297 K.

Results and Discussions In the experiment, a broadband SC comb, spectrally spanning from 1250--1900 nm (Fig. 2) with good flatness around 1400 nm and 1800 nm, is achieved in a piece of DSF. The high coherence of SC is verified by theoretical simulation and experimental measurements. Simulation results show that the SC comb had a high coherence, g(ω)~1, and low phase noise (<10 mrad) over a wide spectral range (Fig. 3). Experimentally, the beat notes between the 1550.5 nm/1535.4 nm laser and the comb and SC show linewidths at -3 dB of (2.7±1.0) kHz/(2.0±1.0) kHz and (2.6±1.0) kHz/(1.8±1.0) kHz, respectively (Fig. 4). No obvious linewidth broadening is found, indicating the coherence remain unchanged in the nonlinear spectral broadening process. The absorption peak of water vapor in the near infrared region is measured around 1365 nm (Fig. 5). Meanwhile, the transition lines for HF (around 1300 nm), ¹²CO (1580 nm), ¹²C₂H₂ (1560 nm) are measured simultaneously. For spectroscopic validation, the results of HF are compared with the simulation based on the parameters given by the HITRAN2012 database. The experimental results are consistent with the simulation results (deviation less than 1.6%, as shown in Fig. 6), indicating that the SC comb could be an excellent light source for multi-gas sensing as required by monitoring of electrical power equipment.

Conclusions In conclusion, ultra-broadband near-infrared SC generation is performed using a dispersion shifted high nonlinear fiber, pumped by 1.55 μm comb pulses. The excellent flatness and coherence of SC are investigated by numerical simulation and experimental beat-note measurements. As a result, high spectral coherence and low phase noise (<10 mrad) are demonstrated for a wide spectral coverage. Particularly, the beat note linewidths between the initial comb and SC with two CW lasers confirm that the phase noise induced by the DSF, to a certain extent, is negligible, comparing to the comb line spacing (54.5 MHz). Furthermore, based on the SC comb source, Fourier transformed frequency comb spectroscopy is carried out for measuring ultra-broadband and high-resolution molecular spectra of mixed gases (HF、 ¹²C₂H₂、 ¹²CO、H₂O). The experiment data are consistent with that simulated in HITRAN2012 database with standard deviation of less than 1.6%. We believe that flat SC based frequency comb spectroscopy will provide a promising approach for multi-gas sensing with high precision and high resolution.