ObjectiveOn-chip spectrometers based on photonic integration platforms have gained significant attention owing to their compact size, high reliability, low cost, and ease of integration with photodetector arrays. However, achieving high resolution and broad-wavelength coverage with a limited number of output channels remains a challenge. This study addresses this challenge by proposing a novel high-resolution on-chip spectrometer based on a 3×N arrayed waveguide grating (AWG) fabricated on a quartz planar lightwave circuit (PLC) platform. The proposed spectrometer was designed to achieve high spectral resolution and an expanded channel count through time-division multiplexing (TDM), making it suitable for applications such as fiber Bragg grating (FBG) sensing detection.MethodsThe proposed spectrometer owns a 3×N AWG structure with three input and N output waveguides. The input waveguides are designed with a channel spacing of (4/3)Δλ, whereas the output waveguides have a channel spacing of Δλ. By sequentially exciting the three input waveguides using TDM, the spectral responses from each input are combined to achieve an effective channel spacing of (1/3)Δλ and expanded channel count of 3×(N-2). A prototype spectrometer chip with N=40 output channels and an output channel spacing of 1.2 nm was fabricated on a quartz PLC platform. The chip has a compact size of 16 mm×10.5 mm and incorporates a subwavelength grating-based mode field converter to reduce coupling loss between the waveguides and single-mode fibers. Experimental characterization was performed using a tunable laser source and multi-channel power meter to measure the spectral response, insertion loss, and crosstalk of the fabricated chip.Results and DiscussionsThe fabricated spectrometer chip exhibits excellent performance, with insertion losses ranging from -4 dB to -2.5 dB for all output channels and a spectral noise level better than -30 dB. The resolution of the spectrometer is determined by the 3 dB bandwidth of the single-channel spectral response, achieving a spectral resolution of 0.63 nm. By combining the spectral responses from the three input waveguides, the effective channel count is expanded to 114, with a uniform wavelength spacing of 0.4 nm (Fig. 11). The high spectral overlap between adjacent channels makes the spectrometer suitable for wavelength demodulation of FBG sensors. Using the center of gravity (COG) algorithm, the spectrometer successfully demodulates the wavelength shifts of three FBG sensors over a temperature range of 40 to 120 °C, demonstrating a root mean square error (RMSE) of less than 20 pm compared with a commercial spectrometer (Fig. 14). These results highlight the potential of the proposed spectrometer for high-precision FBG sensing applications.ConclusionsThis paper presents a novel high-resolution on-chip spectrometer based on a 3×N AWG structure fabricated on a quartz PLC platform. By employing TDM, the spectrometer achieves an effective channel spacing of (1/3)Δλ and expanded channel count of 3×(N-2), significantly enhancing its spectral resolution and wavelength coverage. The fabricated chip demonstrates low insertion loss, high spectral resolution, and excellent performance in FBG wavelength demodulation, with an RMSE of less than 20 pm. Future work will focus on further optimizing the AWG structural parameters, such as waveguide length and refractive index distribution, to improve performance and reduce costs. Additionally, the proposed spectrometer can be extended to distributed FBG sensing, environmental monitoring, and biomedical imaging, offering a versatile and cost-effective solution for high-precision spectral analysis.

ObjectiveHigh-power fiber lasers are widely used in national defense and scientific research because of their good beam quality, small size, and excellent thermal management. However, increasing the output power of single fiber lasers is challenging because of the limitations of nonlinear effects, thermal effects, and mode instability. Spectral beam combining (SBC) has emerged as a promising technology to boost the output power while maintaining good beam quality. However, as laser arrays expand, SBC systems become increasingly large, limiting their practical applications. Therefore, miniaturizing SBC systems is crucial for enhancing their applicability. SBC based on conical diffraction offers a viable solution—by directing the incident beam at an oblique angle onto the diffraction grating surface. The diffracted beams are separated in different planes, spatially separating the incident and diffracted beams. This approach facilitates the miniaturization of SBC systems and enables novel optical path designs. This study systematically investigated beam quality degradation in SBC systems based on conical diffraction and experimentally examined the grating diffraction efficiency under conical diffraction conditions. We hope that our investigations and findings will aid in the design and study of SBC systems based on conical diffraction.MethodsBased on the fundamental principles of conical diffraction and the grating equations, we parameterized the diffraction angles using the incident azimuth and polar angles. We established a dispersion model for conical grating diffraction by discretizing a laser beam with a finite linewidth into monochromatic sub-beams and applying the conical diffraction grating equation. Numerical simulations were performed to investigate the diffracted beam characteristics after single-beam conical diffraction through the grating, focusing on the evolution of beam spot patterns and beam quality degradation. For experimental validation, a diffraction efficiency measurement setup was developed using an 1170 line/mm multilayer dielectric diffraction grating and a 1083 nm fiber laser. The grating rotation enabled precise control of the conical diffraction conditions. The experiment examined the variation in the grating diffraction efficiency with the incident polar angle at different azimuth angles and the effect of the incident azimuth angle on the diffraction efficiency under near-Littrow-angle incidence conditions.Results and DiscussionsThe incident azimuth angle affects the diffraction efficiency of the grating. However, high efficiency is maintained within a certain range. The diffraction efficiency begins to decline as the azimuth angle exceeds a specific threshold. When the azimuth angle is maintained within 17.5°, the conical diffraction grating maintains a high efficiency over 95% (Fig. 11), which slightly affects the beam combining system. In contrast, the incident polar angle exhibits a more significant effect on the diffraction efficiency. Under nonconical diffraction conditions, the grating efficiency drops below 90% (Fig. 7) when the incident angle is 42.64° (only 3.33° deviation from the Littrow angle). Numerical simulations reveal that when the azimuth angle is within 20°, the effect on the beam quality is relatively small, resulting in a beam quality degradation factor of less than 1.07 (Fig. 16). For a 5 mm beam waist radius at a 20° azimuth angle, the spectral width must remain below 25 GHz to maintain M2 factor below 1.5 (Fig. 15). When the azimuth angle is less than 20°, the spectral width (10?100 GHz) and beam waist radius (2?30 mm) exhibit a more significant impact on beam quality. Therefore, in conical diffraction based SBC systems, a properly selected azimuth angle does not significantly affect either the combined efficiency or beam quality.ConclusionsIn this study, we systematically examine the impact of conical diffraction on SBC systems, focusing on combining efficiency and beam quality through experimental and theoretical approaches. The experimental results demonstrate that polarization-independent gratings achieve maximum diffraction efficiency near the Littrow angle for conical and nonconical diffraction configurations, exhibiting similar efficiency trends across different polar angles. However, as the azimuth angle increases, the peak efficiency shifts toward angles smaller than Littrow angle. Under conical diffraction conditions, the diffraction efficiency remains above 95% when the azimuth angle remains below 17.5°. In contrast, nonconical diffraction decreases below 90% diffraction efficiency, with a polar angle deviation of only 3.33° from the Littrow angle. This indicates that the azimuth angle variation has less influence on diffraction efficiency than the polar angle deviation from the Littrow angle. The experimental results further demonstrate that conical diffraction configurations achieve a slightly higher maximum diffraction efficiency than nonconical diffraction configurations when the incident angle is near the Littrow angle. To examine this effect, we established a conical diffraction dispersion model by analyzing the rotation of far-field elliptical spots with varying azimuth angles. Through irradiance distribution fitting and systematic simulations, we characterized the beam quality degradation after single-beam diffraction and evaluated the effects of the spectral width, beam radius, and azimuth angle on the beam quality. The results show that azimuth angles within 20° have a minimal effect on beam quality, with a degradation factor below 1.07. In conical-diffraction-based SBC systems, the appropriate selection of the azimuth angle not only avoids significant effects on the combined diffraction efficiency and beam quality but also introduces new degrees-of-freedom for optical path design. These findings help develop compact and lightweight SBC systems.

ObjectiveThe satellite-borne laser communication terminal is a key component for establishing high-speed data transmission in satellite internet communication systems. However, during the initial acquisition and link establishment phase, these terminals often have large initial pointing errors, which seriously affects the initial acquisition time and link interruption recovery ability, resulting in low link establishment efficiency and poor link robustness. Especially in the low earth orbit (LEO) satellite internet system, due to the high-speed motion characteristics of satellites, these challenges become particularly prominent, which seriously affects the service availability and operational efficiency of the system. To address the initial pointing error of a satellite-borne laser communication terminal, a fast acquisition scheme based on pointing error correction of a beacon-free optical system is proposed. The purpose is to significantly reduce the uncertainty of initial direction, improve the ability of link establishment and recovery after link disconnection, optimize the problem of poor practicability of a laser communication terminal, and thus improve the overall performance of the laser communication system of a LEO satellite.MethodsIn this study, an optimization algorithm based on ordinary least squares method is proposed to correct the pointing deviation of a satellite-borne laser communication terminal. First, the main error sources that affect the capture of uncertain areas by a satellite-borne laser communication terminal are systematically analyzed. Second, the capture time model with the scanning-staring capture mode is established, and the statistical characteristics of the capture time of the model are thoroughly analyzed by the Monte Carlo method. The results indicate that the optimization of capture time mainly depends on the improvement of pointing accuracy. On this basis, the terminal coordinate system, the satellite body coordinate system. and the reference coordinate system are established, and the transformation matrix between these coordinate systems is derived. It is emphasized that the correction of an installation error matrix is the core content of this study. Through theoretical calculation, the pointing error model is established, and the hybrid optimization algorithm combining the ordinary least square method and the Fibonacci search algorithm is innovatively adopted to successfully obtain the installation angle correction matrix. Finally, the proposed scheme is implemented and tested on the LEO satellite internet laser communication terminal. The experimental results demonstrate that the system achieves remarkable results in reducing the initial pointing error and improving the link establishment and recovery time. Through on-orbit verification, the effectiveness and reliability of the proposed method in practical application environment are fully confirmed.Results and DiscussionsThe research results show that the performance of the satellite-borne laser communication terminal is significantly improved. By applying the proposed optimization algorithm, the initial pointing error is successfully reduced from the initial 6.7 mrad to approximate 0.5 mrad. Additionally, the link interruption reacquisition time is shortened from the initial 8 min to 30 s. The laser link establishment between satellites in different orbital planes is realized. Link establishment between satellites in the same orbital plane lasts for 69 h, while link establishment between satellites in different orbital planes lasts for 77 h. This significantly addresses the poor practicability of laser communication terminals and is of great importance for achieving rapid laser link establishment and long-term operation. Further analysis indicates that the residual pointing error of the system mainly comes from the attitude error, the orbit error, and the micro-vibration of the satellite platform, among which the orbit error contributes the most, with the range of 5 μrad to 0.44 mrad and the average value of 0.14 mrad. The error caused by micro-vibration ranges from 15 μrad to 50 μrad. These findings provide a clear direction for further research.ConclusionsIn this study, a hybrid optimization algorithm combining the least square method and the Fibonacci search algorithm is innovatively proposed to correct the pointing deviation of satellite-borne laser communication terminals. This algorithm achieves the high-precision correction of the pointing error of the laser terminal line-of-sight through optimization calculation, and is successfully applied to the satellite laser communication system without beacon light system, which provides an effective technical solution to improve the system performance. On-orbit verification results demonstrate that the system has excellent performance metrics under different orbit configurations. The recapture time of broken link is reduced from more than 8 min to less than 30 s, with an average of less than 15 s, which optimizes the problem of poor practicability of laser communication terminals and is of great significance for realizing rapid laser link building.

ObjectiveSpace laser communication has been widely utilized in deep-space exploration, satellite communications, and other domains due to its high data rate, low power consumption, compact size, and robust security. The narrow divergence angles of laser beams impose stringent requirements on beam alignment and tracking precision, thereby necessitating the deployment of an acquisition, tracking, and pointing (ATP) system to establish stable laser links for high-speed optical communications. Contemporary ATP systems typically utilize a dual-stage (coarse-fine) composite control architecture to reconcile the conflicting demands of wide field-of-view (FOV) and high precision during ATP. This architecture comprises a coarse tracking system and a fine tracking system. The fine tracking system, characterized by high servo bandwidth and precision, critically determines the overall performance of the ATP system, positioning it as one of the core technologies in ATP architectures. Satellite platform vibrations and space background light are primary factors degrading the fine tracking performance in space laser communication. The former necessitates the fine tracking system to exhibit a high disturbance suppression bandwidth, while the latter requires the spot localization method to simultaneously achieve high-precision spot position measurement and robust anti-interference capability. In this study, the effects of satellite platform vibration and space background light interference on the fine tracking performance of space laser communication are considered comprehensively. Through algorithmic enhancements and system optimization, a high-performance fine tracking system is designed. The proposed system demonstrates superior positioning accuracy under degraded spot conditions and exhibits effective suppression capability against disturbances within a 200 Hz bandwidth.MethodsTwo principal factors limiting fine tracking system performance are concurrently addressed. First, a Fourier phase-shift (FPS) algorithm-based spot localization method is developed. The spot position is determined by calculating the optimal symmetry center through analysis of the fundamental frequency phase information in the image. Unlike conventional centroid methods, this method eliminates direct current (DC) offset artifacts, enhances low-frequency noise immunity, and incurs no additional computational latency. Simulation experiments validate its anti-interference capability, and field-programmable gate array (FPGA) based mapping confirms its engineering feasibility. Second, the fine tracking system is implemented using a space-grade complementary metal-oxide-semiconductor (CMOS) sensor. Through integrated hardware-software co-design and algorithmic optimization, all functionalities including high-speed image acquisition/processing, spot localization, and proportion integration differentiation (PID) control are consolidated on a single FPGA. This approach reduces system latency while maintaining application-specific requirements, thereby achieving an enhanced disturbance suppression bandwidth. Finally, a comprehensive test environment is established, utilizing a signal generator to drive a fast-steering mirror (FSM) with multi-frequency excitation signals for simulating vibrational disturbance. Systematic validation is conducted through static-condition evaluations and dynamic disturbance suppression tests to assess the system actual performance.Results and DiscussionsThe fine tracking system designed in this study achieves a positioning accuracy of 0.001 pixel under degraded spot conditions and attains a disturbance suppression bandwidth exceeding 200 Hz, effectively mitigating the impacts of satellite platform vibrations and space background light interference on space laser communication performance, thereby enhancing the capability of the overall ATP system. Spot localization experiments are conducted using simulated spot images under noise-contaminated conditions. The results demonstrate that the FPS method achieves superior positioning accuracy under noise interference compared to conventional approaches (Table 1). Static-environment testing results reveal that the proposed fine tracking system attains 0.001 pixel accuracy under suboptimal spot conditions (Fig. 10), outperforming the traditional centroid-method-based fine tracking systems by nearly threefold. Disturbance suppression tests demonstrate a 56.4% suppression ratio against 418 μrad perturbations at 170 Hz and 51.3% against 391 μrad perturbations at 200 Hz (Fig. 11), with the system achieving a validated suppression bandwidth of 200 Hz (Fig. 12).ConclusionsTracking accuracy and disturbance suppression bandwidth constitute critical performance metrics for fine tracking systems in space laser communication. To address the impacts of satellite platform vibrations and space background light interference on the performance of fine tracking systems, an optimized fine tracking system is developed through algorithmic refinement and system co-design, which is validated through rigorous testing. The system employs a Fourier phase-shift-based spot localization method that eliminates DC offset interference, demonstrates enhanced robustness against low-frequency noise compared to the conventional centroid methods, and introduces no additional computational latency. A positioning accuracy of 0.001 pixel is achieved under degraded spot conditions, demonstrating a threefold improvement over that of the conventional centroid method. Furthermore, the integrated hardware design reduces system latency, enabling a closed-loop control frequency of 4 kHz and a disturbance suppression bandwidth exceeding 200 Hz. The proposed fine tracking system synergizes high-precision spot localization with low-latency operation, effectively counteracting satellite platform vibrations and space background light interference, thereby achieving system-level performance enhancement.

ObjectiveThe fiber optic gyroscope (FOG) is a high-precision angular velocity sensor that serves as a key sensing component in modern high-accuracy inertial measurement technology. Currently, achieving high precision, miniaturization, and high environmental stability are the major challenges that hinder the development of FOGs for application in aerospace, satellite, strategic missile, and other inertial navigation systems. Fine-diameter polarization-maintaining photonic crystal fibers offer an opportunity for FOGs to break through the bottleneck of achieving high precision, miniaturization, and high environmental stability. Oriented to the urgent demand of high-precision miniaturized FOG, a fine-diameter polarization-maintaining photonic crystal fiber, with an 80 μm cladding diameter, is designed and successfully manufactured.MethodsThe performance of dual-large-hole polarization-maintaining photonic crystal fibers (PM PCFs), with a cladding outer diameter of 80 μm, was optimized using the finite-element method combined with a perfectly matched layer. Based on the optimal result, an optimal fine-diameter dual-large-hole PM PCF was designed. Then, a stack-and-draw method was employed to manufacture two types of working samples of dual-large-hole PM PCFs with imported and domestic pure silica tubes. The cut-back method and Sagnac interferometry were employed to test the loss and birefringence characteristics of the fiber sample. To validate its application in miniaturized FOG, the sample's bending characteristic was measured by bending it around cylinders with diameters of 5 mm and 16 mm. The temperature stability of birefringence, shown by the fiber sample, was evaluated within the temperature range from -40 ℃ to 60 ℃ by placing the test fiber in a temperature chamber. Finally, the performances of the two types of dual-large-hole PM PCFs, fabricated with imported and domestic pure silica tubes, were compared.Results and DiscussionsExperimental results demonstrate that the fiber exhibits a low loss of 1.13 dB/km and high birefringence of 5.5×10-4 at 1550 nm (Fig. 4 and 5). Its birefringence temperature coefficient reaches 5×10-8 ℃-1 from -40 ℃ to 60 ℃, and the low loss of 1.2 dB/km can be maintained at a bending radius of 16 mm (Fig. 6 and 8). This result demonstrates that the fabricated fiber can be utilized to develop high-precision miniaturized FOG owing to its small diameter, high birefringence, excellent temperature stability, and high bending performance. To promote the domestic development of high-precision FOG, a comparative study of optical fibers manufactured using imported and domestic pure silica tubes is performed. Fig. 9 demonstrates significant performance difference between the fibers fabricated with imported and domestic pure silica tubes. At a wavelength of 1550 nm, the fiber fabricated using imported tubes exhibits a transmission loss of 1.13 dB/km, whereas the domestic fiber shows a markedly high transmission loss of 7.36 dB/km. In addition, while both fibers display pronounced hydroxyl (OH?) absorption peaks at 1390 nm, the domestical fiber undergoes extreme degradation with a loss of 206.06 dB/km, which is 6.3 times higher than that of the imported fiber. Furthermore, in the wavelength range of 1400?1700 nm, the birefringence shown by the domestic fiber is relatively lower than that exhibited by the imported fiber. However, both fibers maintain birefringence magnitudes of the order of 10-4, thus showing a good polarization-maintaining performance.ConclusionsIn this study, fine-diameter PM PCFs, exhibiting low losses, high birefringence, excellent temperature stability, and high bending performances, have been designed and successfully fabricated. These good optical performances confirm the feasibility of applying the fabricated fibers in high-precision miniaturized FOG. Simultaneously, the loss of the fiber prepared using the domestic pure silica tube at a wavelength of 1550 nm is higher than that of the fiber manufactured using the imported pure silica tube. This result is mainly attributed to the influence of the purity and geometrical accuracy of the domestic pure silica tubes, highlighting the manufacturing process of domestic pure silica tubes as a possible direction for improvement.

ObjectiveThe rapid growth of the metaverse and advancements in virtual reality technology have significantly heightened the demand for immersive experiences. Near-eye displays serve as a crucial interface between users and virtual environments, providing high-quality visual experiences. Among these, digitally driven organic light-emitting diode-on-silicon (OLEDoS) microdisplays stand out for their high brightness, low power consumption, and long operational lifespan. However, the accelerating data volume driven by increasing resolution and refresh rates has surpassed device bandwidth, whereas the large frame buffer requirements in timing control chips have increased design costs, limiting scalability and widespread adoption. Consequently, developing efficient data compression technologies to reduce transmission bandwidth and frame buffer demands has become essential for advancing near-eye display systems.MethodsThis study combined the cruciate-block compression foveated just noticeable difference (CB-FJND) model with the centralized 25-subfield (CSF-25) scanning algorithm to examine bit-plane data characteristics and propose an adaptive pixel block sequence encoding method. To assess and optimize sequence length, experiments were conducted to analyze compression rates, total buffer data, and subspace row counts. In addition, optimization experiments were performed to determine the optimal parameter combinations for pixel block sequences with different characteristics. Based on this encoding method, a comprehensive bit-plane compression strategy was developed. First, a compression rate prediction model was introduced to dynamically adjust the CB-FJND threshold, minimizing data loss. Then, a subspace buffer structure was designed and validated through simulation experiments. Finally, the effectiveness of the proposed bit-plane compression strategy was demonstrated by implementing a timing control circuit on a field-programmable gate array (FPGA) validation platform.Results and DiscussionsTable 4 shows that the proposed bit-plane compression strategy achieves an average compression ratio of approximately 25% for the test video sequences, with the worst-case compression ratio for the smallest unit remaining below 40%. As Table 5 indicates, this strategy maintains the frame buffer capacity required for displaying the test video sequences in the range of 28.595?43.611 MB, with no data loss and a buffer resource utilization rate that exceeds 65%. In addition, Table 6 demonstrates that when the frame buffer capacity exceeds the target by 20%, the losses in peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) remain negligible, thereby preserving high-quality display performance.ConclusionsThis study presents a pixel block sequence encoding method based on the CB-FJND model and CSF-25 scanning algorithm. By optimizing the sequence length and parameter combinations, this method adapts to bit-plane data with varying characteristics, effectively minimizing statistical redundancy. Alongside this encoding technique, a comprehensive bit-plane data compression strategy is developed, which includes a compression rate prediction model and an overflow prevention mechanism to dynamically adjust the CB-FJND threshold, thereby ensuring data integrity. In addition, a subspace buffer structure is designed to significantly reduce the requirements for frame buffer capacity. The proposed strategy is validated on an FPGA testing platform, yielding an average data compression ratio of approximately 25% compared to the original data. Furthermore, with the frame buffer capacity set to 40% of the original requirement, the CB-FJND-processed data remains lossless. Experimental results show that this strategy effectively reduces bandwidth pressure and buffer requirements, offering a practical and cost-effective solution for silicon-based OLED microdisplay systems.

ObjectiveMultispectral images are obtained by capturing data across multiple spectral bands, with each band corresponding to a different spectral range. These images provide rich spectral information, which facilitates a detailed analysis of the spectral characteristics of materials, and play a crucial role in various fields, such as remote sensing, medical imaging, and environmental monitoring. However, multispectral images require a high storage capacity or bandwidth for transmission, which limits their applicability. Existing compression methods cannot achieve high compression ratios and preserve both the spectral and spatial characteristics of images, particularly for high-dimensional data such as multispectral images. Consequently, advanced compression algorithms that reduce storage requirements and maintain the image quality necessary for subsequent analysis tasks are required. The network addresses issues such as spectral redundancy, feature extraction, and compression efficiency, while maintaining the quality of the reconstructed images. This approach aims to enhance the compression performance while ensuring a high reconstruction accuracy.MethodsThis paper introduces a deep-learning-based framework consisting of three key modules: spectral mix, feature fusion, and global attention modules. The spectral mix module employs 3D convolutions combined with the SwiGLU activation function to reduce spectral redundancy and extract meaningful prior information from image bands. This module reduces spectral redundancy by extracting interband features as prior information and blending them into the original image. The module improves the compression efficiency by reducing spectral redundancy without sacrificing crucial spectral information. The feature fusion module consists of a multiscale feature fusion layer that employs depth-wise separable convolutions, a channel attention mechanism, and an feedforward neural network (FFN) layer with an inverted bottleneck structure. This module fuses both spatial and spectral features, enabling more precise feature extraction and enhancing the quality of the compressed images. The global-attention module introduces a hybrid architecture that combines spatial attention and channel feature transformation by dynamically weighting each region in an image based on its significance. This adaptive attention mechanism enables the network to concentrate on the most informative regions while suppressing less relevant areas, thus ultimately enhancing the compression performance. The model consists of a symmetrical encoder?decoder network and space-channel-scale (SCS) context model. In this study, the proposed feature fusion and global attention modules were used in both the encoder and decoder, whereas the spectral mixing module was applied before encoding. The entire model was trained end-to-end with a custom compression loss function, which optimized the tradeoff between the compression ratio and image fidelity, and ensured high-quality reconstructed images, even at high compression rates.Results and DiscussionsThe proposed model has been evaluated using three open-source multispectral image datasets, viz. high-resolution remote sensing images from Landsat-8, Sentinel-2, and WorldView-3. The performance of the proposed multispectral image fusion compression network (MIFCN) is compared with that of two classical traditional image compression algorithms (JPEG2000 and 3D-SPHIT), five mainstream deep-learning-based image compression methods (Scale-only, Mean-Scale, Joint, Cheng2020, and ELIC), and two multispectral image compression methods (LBDRN and SSPC) across three datasets. Peak signal-to-noise ratio (PSNR), multiscale structural similarity index measurement (MS-SSIM), and mean spectral angle (MSA) have been used as evaluation metrics to assess the compression performance of the model for multispectral images. The experiments show that the proposed MIFCN outperforms the other methods on three datasets across the three metrics, particularly when compared with traditional methods (Figs. 6?8). Specifically, on an eight-band dataset, the proposed method outperforms methods (such as ELIC, Scale-only, Cheng2020, Joint, Mean-Scale, and SSPC) in terms of PSNR by an average of 0.35 dB, 1.08 dB, 1.93 dB, 1.25 dB, 1.14 dB, and 0.89 dB, respectively. The average MS-SSIM values are higher than the aforementioned methods by 0.85 dB, 0.99 dB, 1.64 dB, 1.18 dB, 1.21 dB, and 1.15 dB, respectively, and the MSA loss is on average 7.5%, 8.4%, 13.8%, 9.6%, 9.1%, and 5.4% lower than the aforementioned methods, respectively. In the subjective comparison experiments on the compressed output of the same image, the proposed method effectively reconstructs the original image, thereby preserving the textures and edge details with the highest accuracy and providing the best visual quality (Figs. 9?11). In addition, a complexity analysis of partial methods has been performed using a seven-band dataset (Table 1), and a quantitative ablation study has been performed on the proposed method to demonstrate its effectiveness (Fig. 12). In general, the compression performance of the proposed method is superior to that of the existing compression methods.ConclusionsThis paper introduces an end-to-end image compression network based on multi-scale and multi-feature fusion. The network, designed for multispectral images, leverages spectral mixing, feature fusion, and global attention modules, which effectively reduce spatial redundancy and interspectral redundancy, thus enhancing the compression performance. The experimental results show that the proposed method outperforms traditional and existing deep-learning-based image compression methods across multiple metrics on multispectral image datasets. These results indicate that combining multi-scale and multi-feature fusion is an effective strategy for realizing efficient multispectral image compression. This approach significantly improves the compression efficiency and optimizes the compression quality.

ObjectiveThe rapid development of high-power thin-disk lasers has revolutionized applications in ultrafast optics, precision machining, and extreme ultraviolet (EUV) light generation. However, domestic research has faced challenges due to technical barriers in disk crystal packaging and multi-pass pump module design. This study addresses the critical need for localized innovation by developing a high-performance, fully domestically produced Yb∶YAG thin-disk laser system. The primary objectives include: 1) demonstrating the feasibility of a self-developed 32-pass pump module and Yb∶YAG disk bonding technology; 2) investigating the laser performance under both continuous-wave (CW) and pulsed pumping schemes using zero-phonon line (ZPL) pumping at 969 nm; and 3) achieving output power and efficiency to lay the groundwork for kilowatt-class laser systems. By comparing pulsed and CW operations, this work also explores thermal management and efficiency limitations which are critical for industrial scalability.MethodsThe experimental setup (Fig. 3) centers on a custom-designed Yb∶YAG thin-disk module featuring a 215-μm-thick, 10%-doped Yb∶YAG crystal bonded to a diamond heat sink. The large aspect ratio (17 mm diameter) of the disk and direct water cooling (6.7 L/min flow rate) ensure efficient heat dissipation. A 32-pass pump configuration (Fig.1) with relay imaging optics homogenizes the pump spot (7.2 mm diameter) to achieve >98% absorption. ZPL pumping is implemented using 969 nm diode lasers stabilized by volume Bragg gratings (VBGs), with spectral widths of 0.32 nm (CW) and 0.19 nm (pulsed) (Fig. 4). The laser resonator comprises a short linear cavity (150 mm length) with a planar output coupler. Two pump sources are tested: a pulsed diode (450 μs pulse width, 1 kHz repetition rate, 30% duty cycle) and a CW diode. Output power, efficiency, temperature dynamics, and beam quality are systematically characterized. Thermal imaging is used to monitor disk temperatures (Fig.7). The spectral analysis (Fig. 8) and beam profiling (Figs. 9 and 10) provide insights into mode competition and thermal lensing effects.Results and DiscussionsUnder the pulsed pumping mode, at 1 kHz repetition rate, the system delivers a maximum output power of 583 W with an optical-to-optical (O-O) efficiency of 59.2% (Fig. 5). Relaxation oscillations during the initial 100 μs of each pump pulse (Fig. 6) introduce additional losses, limiting efficiency at higher powers. Peak pump intensity reaches 6.62 kW/cm2, inducing partial bleaching of the Yb∶YAG crystal. The disk temperature peaks at 65 ℃ under pulsed operation (Fig. 7), demonstrating effective thermal management. Under continuous-wave pumping mode, the system achieves 809 W output power at 65.8% O-O efficiency. Because of the absence of transient effects, the power increases approximately linearly, corresponding to a maximum average power density of 3.16 kW/cm2. However, higher average power leads to increased disk temperatures (89 ℃) and pronounced thermal lensing, degrading beam quality to Mx2=21.2, My2=16.6 (Fig. 10). The central peaks of the output spectra of both modes are located at 1030.5 nm, but CW operation exhibits a broader spectrum (Fig. 8), suggesting multi-mode competition. Pulsed output shows a dominant central peak, favoring preferential gain buildup. Pulsed pumping reduces thermal load compared to CW pumping, validating its advantage for heat-sensitive applications. Thermal distortions under CW pumping mode promote higher-order transverse modes, which is evident in beam profile evolution (Fig. 9).ConclusionsThis study employs a self-developed high-power disk module based on Yb∶YAG crystal to construct a multimode short-cavity disk experimental setup. The system utilizes both pulsed and continuous-wave 969 nm wavelength-locked semiconductor lasers as pump sources for comprehensive characterization of the disk module. In pulsed pumping mode, the system achieves a maximum output power of 583 W with an optical-to-optical efficiency of 59.2% and a slope efficiency of 67.6%. Under continuous-wave operation, the output power reaches 809 W, corresponding to a peak O-O efficiency of 65.8% and a slope efficiency of 76.1%. The experimental results reveal that relaxation oscillations induced by pulsed pumping lead to additional population inversion losses, thereby limiting the O-O efficiency. Notably, the disk crystal temperature remains significantly lower under pulsed pumping compared to that under CW pumping. Spectral analysis further demonstrates distinct differences in output characteristics between the two pumping regimes. Comparative testing confirms the superior performance of the self-developed disk module, which establishes a critical foundation for achieving kilowatt-class high-power laser output.

ObjectiveLithography machine is widely regarded as the most precise equipment in the manufacture of integrated circuits, with the illumination system being a core system of the lithography machine. One of the primary functions of the illumination system is to generate a specific distribution and uniform illumination field in the mask plane. In general, the illumination-integrated nonuniformity is used to assess the illumination intensity nonuniformity in the non-scanning direction. The increase of the illumination-integrated nonuniformity will cause the width of the exposure line to be difficult to control, which will impact the efficacy of the exposure process. So, the illumination field uniformity technology is applied to the illumination system in order to improve its uniformity. As lithography process nodes advance, it is difficult for many illumination field uniformity technologies to directly meet the uniformity requirements of lithography illumination systems, such as integrating rods and microlens arrays. Additionally, the aging and usage loss of optical components also lead to uniformity degradation. Therefore, this paper proposes a design and optimization method for the uniformity compensation corrector of a lithography illumination system. The proposed method takes the illumination-integrated nonuniformity and the energy loss as evaluation indexes, and uses genetic algorithm to design and obtain the uniformity compensation corrector.MethodsThe lithography illumination system uniformity compensation corrector designed in this paper can be used to correct the nonuniformity of the illumination field in the x-direction. It is placed at the defocus distance above the mask plane. The design method is outline as follows: first, the intensity distribution of the illumination field in the wafer plane of the lithography machine is actually measured, and the resulting data is fitted to calculate the illumination field intensity distribution of the mask plane. Then, the illumination field distribution of the correction plane is obtained by convolution calculation. Taking the illumination-integrated nonuniformity and the energy loss as the evaluation indexes in the correction plane, the genetic algorithm is used to optimize the calculation and obtain the transmittance function of the uniformity compensation corrector, so as to realize the uniformity of the illumination field intensity distribution of the single illumination mode. On this basis, the adaptability function is improved by integrating the indexes of multiple illumination modes, and the uniformity compensation corrector compatible with multiple illumination modes is designed to correct the illumination field intensity distribution of six illumination modes at the same time. The optimized design of the uniformity compensation corrector is carried out according to the illumination field distribution under different illumination modes of an actual lithography machine, and the optimized calculation results are obtained and verified by simulation using the optical software LightTools. The nonuniformity results obtained through simulation verification are calculated both before and after correction. These results are finally analyzed in comparison with the nonuniformity results obtained from design calculations.Results and DiscussionsBased on the measured illumination field intensity distribution data of six illumination modes, the optimized design of the uniformity compensation corrector is carried out. The optimization results show that, when the six illumination modes are optimized separately, the six uniformity compensation correctors designed by the proposed method can correct the illumination-integrated nonuniformity to less than 0.23%, and the error between the simulation verification result and the design calculation result via LightTools is within 0.015% (Table 4). When the six illumination modes are optimized simultaneously, the illumination-integrated nonuniformity can be corrected to less than 0.39%, and the error between the simulation verification result and the design calculation result via LightTools is within 0.014% (Table 5). This validates the correctness of the design method of the uniformity compensation corrector.ConclusionsThis paper proposes a design and optimization method of a uniformity compensation corrector based on the static gray scale filtering method. The purpose of this method is to improve the uniformity of the illumination field intensity distribution of lithography machines. For the illumination intensity distributions of six illumination modes, the design and optimization of the uniformity compensation corrector are carried out separately. On this basis, the synergistic optimization of multiple illumination modes is realized by modifying the adaptability function through the evaluation indexes of multiple illumination modes. This refinement enhances the applicability of the uniformity compensation corrector. The simulation results show that the designed uniformity compensation corrector for single illumination mode and compatible with multiple illumination modes can effectively improve the illumination uniformity of six illumination modes. The proposed method has important theoretical significance and application value for correcting the nonuniformity of the lithography illumination system and improving the exposure quality of the lithography machines.

SignificanceWith the development of the semiconductor pump source, the rare-earth doped fiber, and the fiber device manufacturing techniques, the ytterbium-doped all-fiber nanosecond-pulsed lasers have developed unprecedentedly, playing an increasingly important role in scientific research, industrial production, and national defense. The all-fiber nanosecond-pulsed amplifier based on the master oscillator power amplifier (MOPA) structure is currently the mainstream strategy to boost the nanosecond pulse energy, and 100 mJ level pulse energy is now available with the single module nanosecond fiber laser. However, for nanosecond fiber laser systems producing 10 mJ level output pulse energy, which require at least 50 μm level core diameter as the fundamental support, the laser beam quality typically degrades significantly, far from the high beam quality criterion of M2<2. These low beam quality fiber lasers are not applicable to high brightness applications, and will be an obstacle to the promotion of laser practical performance. In addition to nonlinear effects such as stimulated Raman scattering (SRS), the excess high-order mode components in large core diameter fibers are the most critical issue to improve the beam quality at high pulse energy output. This paper summarizes the progress of research on all-fiber nanosecond-pulsed lasers based on uniform core diameter fibers and tapered fibers. Furthermore, the technical scheme to realize the all-fiber nanosecond-pulsed laser with synergistic development of pulse energy and beam quality is primarily investigated, in the terms of fiber design and laser system global optimization.ProgressWith continuous and thorough research on nanosecond-pulsed fiber amplifiers, differentiated by the longitudinal core diameter variability, the gain medium of the MOPA system can be roughly classified into two categories. One is the fiber with a uniform core diameter (hereinafter referred to as uniform fibers), and the other is the fiber with a variable core diameter, that is, the recently proposed tapered fibers. According to their internal structure, uniform fibers include photonic crystal fiber (PCF), chirally-coupled-core (3C) fiber, and large mode area double-clad fiber (LMA-DCF), etc. For PCFs, the unique core diameter-independent and endless single-mode property allows near-diffraction-limited and high pulse energy laser output within PCFs with large core diameters. In 2012, Stutzki et al. reported a 26 mJ, M2=1.3 nanosecond fiber laser system based on a 135 μm large-pitch PCF (Fig. 1). Similarly, by properly arranging spirally distributed side cores around the main core, high-performance laser output can also be obtained from 3C fiber-based nanosecond fiber amplifiers. For example, Zhu et al. demonstrated a near single-mode, three-stage MOPA system with a pulse energy of 9.1 mJ by incorporating a 55 μm 3C fiber as the power amplifier medium (Fig. 2). However, for some objective reasons, such as the difficulty in PCF fusion, 3C fiber fabrication, and applicable fiber pump combiner, all-fiber nanosecond-pulsed lasers based on 3C fibers and PCFs have seldom been reported. In high-energy all-fiber applications, LMA-DCF remains the most commonly used gain medium, and the core diameter is one of the most critical parameters, as it largely determines the laser beam quality and extractable pulse energy. For a MOPA system built with LMA-DCF with a relatively small core diameter at the 30 μm level, a near single-mode, mJ-level pulsed result can typically be obtained. When the core diameter increases to the 50 μm level, the theoretical extractable energy reaches the 10 mJ level, but the beam quality degrades correspondingly. In 2013, Malinowski et al. successfully amplified the seed pulse to 10.6 mJ within a 50 μm step-index gain fiber, resulting in a measured beam quality of M2=7.3 due to the increased number of supported high-order modes. Moreover, LMA-DCF with larger core diameters will produce higher pulse energies but more degraded beam quality. Pulse energies in the tens of mJ and hundreds of mJ levels have been reported in all-fiber and spatially coupled nanosecond MOPA systems, respectively. Regarding tapered fibers, their longitudinal geometry profiles determine their superior suppression effect on nonlinear effects and stimulated Brillouin scattering (SBS) in particular. This has promoted tapered fiber-based systems focusing mainly on single-frequency, narrow linewidth nanosecond fiber lasers. In these studies, limited by the gain bandwidth, only sub-mJ to mJ-level, near single-mode pulsed lasers can be achieved. For wide-spectrum and high pulse energy research, in 2021, Huang et al. demonstrated an all-fiber nanosecond MOPA system as depicted in Fig. 13, in which the power amplifier medium is a tapered fiber with a tapering ratio of 2 and a large-end core diameter of 62 μm. A high-performance pulse output with 8.3 mJ pulse energy and beam quality of M2=3.5 is recorded, which is the highest reported pulse energy in laser systems configured with tapered fibers.Conclusions and ProspectsIn this paper, we review the current progress in research on high pulse energy all-fiber nanosecond-pulsed amplifiers based on uniform fibers and tapered fibers. The degradation of beam quality at high pulse energy indeed restricts the application expansion of nanosecond lasers. Consequently, the development of all-fiber lasers to synergistically enhance beam quality and pulse energy is of high priority. Based on this, we propose a number of reasonable optimization strategies covering gain fiber design and system configuration. The key issue is to suppress high-order modes in large core diameter gain fibers. In this regard, tapered fibers can effectively reduce interference between modes, which has been proven to be a promising method for future performance improvement of pulsed lasers. In addition, the combination of tapered fiber and the newly emerging oscillating-amplifying integrated configuration contributes to efficient and stable pulsed output. Although the rapid growth of all-fiber nanosecond amplifiers also exposes the challenges ahead, the latest progress in theoretical and technical solutions will further optimize the comprehensive performance of nanosecond lasers. In the future, we believe that all-fiber nanosecond-pulsed lasers will provide more possibilities for widespread applications.

ObjectiveThe 1.5 μm laser is widely used in modern fiber-optic communication systems due to its low propagation loss in optical fibers, which effectively supports long-distance transmission. Additionally, the 1.5 μm laser plays a crucial role in gas analysis, environmental monitoring, and remote sensing. Furthermore, a high-performance 1.5 μm frequency-stabilized laser can serve as a reliable wavelength reference source for dense wavelength division multiplexing (DWDM), precision fiber-optic sensing, and other high-accuracy measurement applications. However, the conventional 1.5 μm acetylene gas absorption frequency stabilization systems are often complex and bulky. To address this issue, this study develops a low-cost and structurally simple 1.5 μm distributed feedback semiconductor laser diode (DFB-LD) frequency stabilization system, integrating acetylene gas absorption characteristics with current modulation techniques. By employing a self-developed digital control circuit and the modulation-demodulation algorithm, the laser wavelength is accurately locked.MethodsA self-developed digital control system is used to regulate the laser output frequency via current feedback, achieving precise and stable laser frequency control. The system transmits the real-time laser status to a host computer through a serial communication protocol, enabling monitoring and adjustments. By combining acetylene gas absorption characteristics with current modulation techniques, the system utilizes a microcontroller unit (MCU) to perform laser wavelength tuning and demodulation of the modulation signal. The laser undergoes 2.5 kHz modulation, generating a 60 MHz modulation depth, and is split into two parts by a 1∶9 optical coupler, where 90% of the output light is fed into the optical heterodyne detection system and the remaining 10% is used for frequency stabilization. The stabilization beam passes through an acetylene gas cell and is subsequently converted into an electrical signal by a photodetector. This signal is processed by a bandpass filter and sent to an analog-to-digital converter (ADC) chip for high-precision sampling before being transmitted to the MCU for further processing. The MCU applies a cross-correlation algorithm to analyze the collected signal, extracting the error signal, which represents the deviation of the laser frequency from the reference absorption peak. This error signal is fed into a proportion-integration-differentiation (PID) control circuit, which calculates the required current correction value based on the error signal. The correction current is subsequently injected into the semiconductor laser, forming a current control signal, thereby stabilizing the laser output frequency and ensuring precise frequency locking at the acetylene gas absorption peak. This process forms a closed-loop control system, ensuring long-term frequency stability and high-precision locking. By optimizing a few PID and pre-divider parameters, the system enables flexible frequency tuning. Additionally, the high signal-to-noise ratio (SNR) harmonic demodulation allows for accurate identification of the absorption peak and rapid frequency locking.Results and DiscussionsThe heterodyne beat signal of the semiconductor laser is measured and compared under free-running and feedback-controlled conditions. By comparing the heterodyne results with those from an optical wavelength reference device, it is confirmed that the proposed frequency stabilization system effectively enhances laser frequency stability. With current feedback and temperature control, the 1 s frequency stability is optimized from 8.8×10-9 to 3.2×10-9, while the long-term 1000 s stability is optimized from 7.1×10-8 to 9.7×10-11, achieving an optimization of nearly three orders of magnitude. The system also demonstrates a reproducibility of 1.1×10-8, fully validating the effectiveness of the feedback control system in frequency stabilization. By optimizing the laser structural layout and the digital control strategy, the system achieves miniaturization and integration while maintaining high precision. This meets the requirements of precision measurement, gas analysis, LIDAR, and other applications for a high-accuracy laser wavelength reference source.ConclusionsThis study investigates a digital frequency stabilization control method for a 1.5 μm distributed feedback semiconductor laser, achieving laser frequency stabilization through a self-developed digital control system with current feedback regulation. The digital stabilization system transmits the real-time laser status to a host computer via a serial communication protocol, enabling real-time monitoring of the scanning or locking state of the laser, thereby enhancing system interactivity and monitoring capabilities. The digital frequency stabilization technology proposed in this study successfully overcomes the limitations of traditional analog control methods, such as tedious tuning and low intelligence levels. It significantly improves system accuracy and stability while optimizing operational procedures. This method aligns with the trend of digital and intelligent transformation in metrology and exhibits broad application prospects in precision gas analysis, LIDAR, remote sensing, and other high-precision measurement fields. It provides an efficient, accurate, and intelligent solution for modern metrology and high-precision measurements.

ObjectiveEnhancing the randomness of true random numbers using optical chaos signal as physical entropy source is a key research focus. On one hand, efforts are devoted to eliminating the time-delay signature of chaos signal to avoid introducing periodicity into the random numbers. On the other hand, the amplitude distribution of chaos signal needs to be improved to approach a Gaussian distribution, thereby achieving a balanced bit “0” and bit “1” distribution in the generated random numbers. However, most current studies on improving the amplitude distribution of chaos signal face the challenge of electronic bottlenecks due to the use of electronic components. For addressing this issue, this study integrates theoretical analysis and experimental validation to propose an amplitude distribution optimization method for chaos signal based on optical-domain differentiation, and the effects of differential input optical power and time delay on the skewness of the amplitude distribution of chaos signals, along with the corresponding optimization conditions, are investigated. Experimental results demonstrate that this method significantly improves the amplitude distribution of chaotic signal. Furthermore, random numbers generated using the optimized chaos signal exhibit excellent balanced bit “0” and bit “1” sequences and successfully pass the NIST randomness test. These findings provide an ideal chaotic optical source for high-speed random number generation.MethodsIn this study, a semiconductor laser is driven into chaos through optical feedback. The chaos signal is split into two beams: one beam is directly fed into a 90° optical mixer, while the other is first passed through a time-delay fiber before being input into the same 90° optical mixer. This configuration enables optical-domain differential processing of these two chaos signal beams, generating an output signal with an optimized uniform amplitude distribution. To investigate the optimal conditions for optimization of chaos signal, we utilize the optical transmission to construct the simulation system,and the effects of differential input optical power and time delay on the skewness of chaos signal are investigated. Next, we conduct experimental verification of the amplitude optimization of chaos signal. Furthermore, we evaluate the randomness of random numbers generated from both the original and optimized chaos signals using the NIST test suite.Results and DiscussionsFirst, typical theoretical results of the amplitude distribution optimization of chaos signal are presented, demonstrating a reduction in skewness from 0.4414 to 0.0021 (Fig. 2). Next, the effects of differential input power and time delay on the skewness of chaos signal are investigated theoretically. The skewness reaches its minimum when the input optical powers are equal, and increases monotonically with growing power difference (Fig. 3). For time delay selection, the optimal delay should avoid both the relaxation oscillation period and the external cavity feedback period, where the autocorrelation function of chaos signal exhibits peaks (Figs. 4 and 5). Furthermore, experimental validation is performed (Fig. 6), achieving a reduction in skewness from 0.4939 to 0.0349. Finally, random number generation tests are conducted using both original and optimized chaos signals (Figs. 7?9). The results confirm that the optimized chaos signal generates random numbers with superior randomness properties, passing all 15 NIST tests compared to the original signals.ConclusionsThis paper proposes an optical-domain differentiation method for optimizing the amplitude distribution of chaos signal. Compared with the electrical-domain and offline optimization approaches, this method effectively overcomes the electronic bottleneck limitation and enables real-time random number generation. Theoretical investigations reveal the influence of differential input optical power and time delay on the skewness of the amplitude distribution of chaos signal and optimization conditions. Experimentally, we achieve the optimized chaos signal with a skewness of 0.0349, representing an order-of-magnitude reduction compared to the original signal. The optimized chaos signal generates well-balanced bit “0” and bit “1” sequences and successfully passes all NIST randomness tests. The proposed method provides a viable solution for high-performance physical random number generation in secure optical communication systems.

ObjectiveLaser chaos, characterized by its sensitivity to initial values and broad spectrum, has garnered significant attention across numerous research domains. In applications such as high-capacity optical communications, multi-channel high-speed physical random number generation, and 3D chaotic lidar detection, there exists a critical demand for chaotic sources capable of parallel generation of multi-channel broadband chaotic signals. Current multi-channel chaotic sources primarily fall into three categories: laser arrays, micro-ring resonators, and Fabry-Pérot (FP) lasers. While distributed feedback laser arrays enable a simultaneous multi-channel chaotic output, their single longitudinal mode operation imposes limitations on channel scalability. Chaotic optical frequency comb solutions based on high-quality-factor micro-ring resonators offer multi-channel chaotic generation but require external high-power optical pumping. In contrast, FP lasers, with their mature manufacturing process, can achieve multi-channel chaos generation through wavelength division multiplexing. Although traditional FP lasers can generate multi-channel chaos through optical feedback, their bandwidth is only a few GHz. Our research group has previously developed a long cavity FP (LC-FP) semiconductor laser with an active resonator length of 1500 μm. Using the beat frequency effect of an FP longitudinal mode, a multi-channel wideband chaotic laser is generated under the feedback of the external cavity of the fiber. Integrated chaotic sources demonstrate superior potential for practical engineering applications in secure optical communications, random number generators, and distributed fiber sensing systems due to their compact footprint, operational stability, and cost-effectiveness, establishing integration as an essential developmental pathway for chaotic semiconductor lasers. However, integration imposes constraints on feedback cavity dimensions, with short external cavities typically inducing pulse envelope oscillations rather than chaotic states. Consequently, fundamental questions remain regarding the dynamical behavior of LC-FP lasers under short external cavity feedback conditions and their chaotic generation capability in integrated configurations, necessitating a further systematic investigation.MethodsWe construct a free-space short external cavity optical feedback experimental setup utilizing an LC-FP laser chip. A planar mirror with a reflectivity-to-transmissivity ratio of 9∶1 is employed between the collimating and focusing lenses to introduce an optical feedback. By systematically translating the planar mirror within the short external cavity range, the influence of external cavity length on the operational states of the laser is investigated. Spectral, frequency-domain, and temporal characteristics of each state are analyzed, with particular focus on the ratio between the longitudinal mode spacing (Δνin) of the laser chip and the mode spacing (ΔνCCM) of the compound cavity (formed by the feedback external cavity and the laser active cavity). This ratio (Δνin/ΔνCCM) is used to analyze the physical causes of each state.Results and DiscussionsThe experiment initially measures the spectral characteristics, frequency spectrum, and temporal characteristics of the free-running laser (Fig. 2). Under short external cavity feedback conditions, the LC-FP laser exhibits four distinct operational states during external cavity length variation: mode-locking, linewidth-broadened single-period oscillation, multi-period oscillation, and chaos. The mode-locking state emerges when Δνin/ΔνCCM equals a positive integer, during which the laser linewidth is narrowed. A particular case occurs when Δνin/ΔνCCM equals n/2 (n is an odd number greater than 2), where specific longitudinal modes are suppressed due to compound cavity mode effects, resulting in a doubled longitudinal mode spacing (Fig. 3). In unlocked states, most operational conditions manifest as linewidth-broadened single-period oscillations with external cavity length variations (Fig. 4). Periodic modulation envelopes emerge in the laser spectrum under compound cavity mode influences, accompanied by altered mode spacing. When the compound cavity mode spacing approaches the relaxation oscillation frequency, the system transitions into a multi-periodic state (Fig. 5). Spectral analysis reveals symmetrical side peaks adjacent to longitudinal modes, where either relaxation oscillation peaks or compound cavity modes can be exclusively observed. When Δνin/ΔνCCM is near an integer and the deviation from the integer is less than 0.01, the compound cavity mode is out of lock with the longitudinal mode of the laser. Under the combined action of longitudinal mode, compound cavity mode, and relaxation oscillation, the laser generates chaos (Fig. 6). Notably, a 17.5 GHz chaotic signal is generated at an external cavity length of 21.33 mm.ConclusionsThe study reveals that LC-FP lasers under a short external cavity feedback exhibit diverse dynamical behaviors with variations in the feedback time delay. Experimental results demonstrate that during integrated packaging of LC-FP chaotic lasers, the external cavity length should be selected near integer multiples of the internal cavity optical path. Under such conditions, the compound cavity mode is more likely to lose lock with the longitudinal mode of the laser, and the laser is more likely to produce chaos. The integrated laser can be used in the field of large capacity chaotic secure communication and high-speed random number generator by using the characteristics of multi-longitudinal mode and large chaotic bandwidth through wavelength division multiplexing. Additionally, leveraging the narrowed linewidth in mode-locked states, these devices show potential for implementation in high-speed optoelectronic oscillators. These findings provide critical theoretical guidance and practical references for the integrated packaging design of optical feedback-based LC-FP lasers, bridging fundamental research with engineering applications.

ObjectiveLaser diodes in the 800 nm band hold significant application value in laser power transmission, laser lighting, and solid-state laser pumping. However, the poor beam quality and low brightness of laser diodes fail to meet the demand for high-power, high-brightness light sources required for long-distance laser power transmission. Grating external cavity spectral beam combining (SBC) technology has been demonstrated as an effective approach to enhance the output power and brightness of laser diodes. Nevertheless, achieving stable frequency locking across the full operating current range in external cavity SBC systems presents considerable challenges, particularly in multi-channel combining where “lose of lock” phenomena frequently occur. In this study, we design a transmission grating-based external cavity spectral tuning experiment for 800 nm-band laser diode single emitters. The spectral characteristics, frequency-locking tuning behavior, linewidth narrowing, and locking efficiency under various driving currents are systematically investigated. Additionally, we analyze the lockable spectral range, the maximum combinable channel count, and the efficiency variation of the SBC system under full operating current conditions.MethodsBased on a transmissive diffraction grating, this study designs an external cavity spectral tuning experiment. First, the optical parameters of the laser in the frequency locking system are determined by leveraging grating diffraction and external cavity frequency locking principles. This includes the design of the transformation lens parameters (focal length of 700 mm), grating specifications (grating density of 1851 line/mm, Littrow angle θlittrow=50.08°@828.781 nm), and cavity mirror configurations. Figure 6 illustrates the schematic diagram of the grating external cavity tunable laser diode. The designed structure enables convenient spectral tuning by rotating the output mirror to adjust the locked wavelength of the emitted laser, while simultaneously achieving significant linewidth narrowing. Subsequently, a single-emitter laser diode operating at 800 nm is employed for structural packaging and beam collimation. The divergence angle and beam width are measured to finalize the experimental device. Spectral tuning experiments are conducted to investigate fundamental spectral characteristics, tuning range, locking efficiency, and the numbers of beam-combining channels. Finally, a comprehensive analysis is performed to evaluate critical parameters of the grating external cavity laser diode system under full operating current conditions, including frequency locking range, bandwidth, and beam-combining channel count.Results and DiscussionsThrough structural packaging, the laser diode single emitter demonstrates stable room-temperature operation with a threshold current of 0.65 A, a slope efficiency of 1.53 W/A, and an electro-optic conversion efficiency of 61.32%. Under 9.5 A continuous current driving, it achieves a 11.32 W output power [Fig. 3(a)], exhibiting strong gain in the 820?840 nm spectral range [Fig. 3(b)], with feasibility for spectral frequency stabilization and tuning. Fast-axis and slow-axis collimating lenses respectively collimate the beam dimensions to 0.408 mm [Fig. 5(a)] and reduce the fast-axis divergence to 2.95 mrad [Fig. 5(b)]. Without frequency stabilization, the central wavelength shifts from 829.972 nm at 1.5 A to 831.794 nm at 9.5 A, showing a current-dependent wavelength drift coefficient of 0.227 nm/A [Fig. 7(a)]. Grating-stabilized operation reduces this drift to 1.75 pm/A while maintaining 0.083 nm spectral linewidth (full width at half-maximum,FWHM) [Fig. 7(b)], achieving a stable narrow-linewidth output across current variations. Frequency-locked tuning ranges span 821.974?833.853 nm at 1.5 A and 826.768?834.141 nm at 9.5 A (Fig. 8). High-current operation shows a reduced tuning range due to intensified competition between intracavity lasing modes and grating feedback modes. Full operational current conditions yield an 826.768?833.084 nm tuning range, with an 828.348 nm demonstrating peak output power [Fig. 12(a)] corresponding to the central wavelength of 828.781 nm of the gain spectrum, where mode loss minimization enhances power output. Maximum electro-optic efficiency of 54.82% occurs at 828.348 nm [Fig. 12(b)]. At 9.5 A driving current, the system achieves a 9.92 W output [Fig. 13(a)] with 828.348 nm stabilized wavelength and 0.083 nm linewidth [FWHM, Fig. 13(b)]. The 0.007 nm discrepancy between measured and theoretical linewidths originates from energy attenuation artifacts in charge coupled device (CCD)-based beam width measurements used for simulations.ConclusionsThis study focuses on investigating the spectral tuning characteristics and linewidth properties of a grating external cavity laser diode under varying driving currents, aiming to determine its full operational current-dependent tuning range and experimentally quantify its specific linewidth and tunable bandwidth parameters. Based on a single-emitter 800 nm-band laser diode, we design and conduct a series of frequency-locking and tuning experiments using the grating external cavity configuration. Experimental results demonstrate that the spectral beam combining system employing this grating-external-cavity laser diode achieves a frequency-lockable spectral range spanning 826.768 nm to 833.084 nm under comprehensive operating current conditions (1.5?9.5 A), corresponding to an effective bandwidth of 6.316 nm. The system currently supports up to 32 beam-combining channels through precise wavelength control. However, challenges persist regarding the limited tunable bandwidth and relatively low channel count in the 800 nm-band laser diode devices. Future researches will prioritize overcoming these limitations by optimizing the external cavity grating configuration, enhancing the thermal management strategies, and improving the wavelength stabilization mechanisms. Key objectives include expanding the spectral coverage while maintaining narrow linewidth characteristics, increasing the numbers of combinable channels without compromising output stability, and achieving robust full-current-range operation for the grating-based SBC laser source. These advancements aim to establish a high-power, spectrally stable laser system with extended tunability for applications demanding precise wavelength control and multi-channel beam combining in industrial and scientific domains.

ObjectiveHigh-brightness solid-state lasers are critical for scientific, industrial, and defense applications. Yb∶YAG crystals, with superior quantum efficiency and thermal properties over Nd∶YAG, are ideal for high-power lasers. Traditional fiber lasers suffer from nonlinear effects at peak power, while bulk/rod lasers face thermal limitations. Crystal waveguides offer advantages like low threshold, high gain, and brightness. Single-clad waveguides improve beam quality but limit pump absorption, whereas double-clad designs enhance efficiency by confining both pump and signal light. However, small core double-clad waveguides restrict power scaling, while large-core ones induce higher-order modes, degrading beam quality. In 2019, a 400 μm×320 μm single-clad Yb∶YAG waveguide achieved a 26 W output with beam quality factor M2 of ~1.1 but low efficiency (25.2%). Addressing this, we design a 65 mm long double-clad circular waveguide with a 1%Yb∶YAG core with size of 400 μm × 400 μm and 0.5%Er∶YAG cladding with diameter of 1.2 mm. This structure balances the large mode volume and fundamental-mode operation. Cavity optimization mitigates thermal lensing, enabling a 110 W continuous-wave output at 1030 nm with x direction beam quality factor Mx2 of 1.07 , y direction beam quality factor My2 of 1.05, 54% optical efficiency, and 67% slope efficiency. This breakthrough demonstrates that large core double-clad waveguides effectively reconcile high power, efficiency, and beam quality, advancing high-brightness laser development.MethodsIn this study, 1%Yb∶YAG crystals are used as the core layer material to reduce the reabsorption effect and the risk of concentration quenching by low doping, while 0.5%Er∶YAG with matched refractive index is selected as the cladding material to form a double-clad circular waveguide structure (size of 400 μm×400 μm for the core layer, 1.2 mm in the diameter of the cladding layer, and 65 mm in the length). Finite element software is used to simulate the effects of cladding shape, size, and numerical aperture (NA) of pump light on absorption efficiency and temperature to determine the optimal structure and size of the circular cladding. The waveguides are prepared by the diffusion bonding technique combined with precision polishing and high-temperature treatment, and the surface is sputtered with low-refractive index SiO? coating and plated with anti-reflective film. A water-cooling system (20 ℃) and indium foil thermal deposition are used for low heat accumulation. To address the thermal lensing effect, a thermal focal length model is developed and the resonant cavity design is optimized. The concave-convex cavity structure (50 mm radius of curvature for the front mirror and 100 mm for the rear mirror) is selected through the ABCD transmission matrix analysis to compensate for the thermal lensing effect and to enlarge the mode volume. The effect of the NA of pump light on the absorption efficiency is tested experimentally, the focal length of the lens is optimized (F2 focal length of 60 mm, NA of 0.147), and the cavity length (L1=20 mm) and the radius of curvature of the cavity mirror (R1=52 mm, R2=-115 mm) are adjusted to achieve high efficiency of mode matching. Output power, spot quality, and stability are finally measured.Results and DiscussionsBy varying the NA of pump light via lenses (focal lengths of 40, 60, 80 mm), the absorption efficiency at low power is measured as 77.6% (NA of 0.22), 76.2% (NA of 0.147), and 74.8% (NA of 0.11), with F2 focal length of 60 mm (NA of 0.147) selected to balance efficiency and thermal load (Fig. 7). Thermal lensing compensation is addressed by optimizing the cavity parameters of the front cavity mirror (M1) distance L1 and curvature radius R1. At L1=20 mm, the output power peaks at 95.2 W with a symmetric mode distribution, while L1 of 10 mm or 30 mm causes power loss or overcompensation (Fig. 8). Further tuning R1 (107, 52, 43 mm) reveals that R1 of 52 mm delivers a maximum 100 W output (Fig. 9). Combining with output mirror with R2=-115 mm, the optimized concave-convex cavity achieves a 110 W average power, 67% slope efficiency, 54% optical-to-optical efficiency, Mx2 of 1.07 , and My2 of 1.05. The output remains stable (<3% fluctuation over 2 h) under a 203 W pump power (Fig. 10 and Fig. 11).ConclusionsIn this paper, a large core diameter double-clad circular waveguide Yb∶YAG laser with high efficiency and high beam quality is presented. First, through the design and preparation of the crystal waveguide, the obtained crystal waveguide is 65 mm long, the rectangular core layer is a 1%Yb∶YAG crystal with size of 400 μm×400 μm, and the circular cladding layer is a 0.5%Er∶YAG crystal whose diameter is 1.2 mm. The experimental parameters are designed in order to compensate the influence of the thermal lens effect on the output performance of the crystal waveguide. By optimizing the concave-convex cavities, a 1030 nm laser output with an average output power of 110 W, slope efficiency of 67%, optical-optical efficiency of 54%, Mx2 of 1.07 ,and My2 of 1.05 is finally achieved. This large core diameter double-clad crystal waveguide laser provides a new approach to realize high-efficiency and high-brightness solid-state lasers.

ObjectiveSemiconductor lasers with proper external perturbation usually exhibit rich nonlinear dynamics, especially a chaotic state. The phenomenon of laser chaos has captured considerable interest, particularly due to its extensive utility across various domains. It plays a pivotal role in establishing secure communication systems, chaotic light detection and ranging, high-speed random number generation and key distribution. It merits emphasis that the majority of existing research on laser chaos has concentrated on the near-infrared band. However, the near-infrared laser is susceptible to environmental disturbances in free-space optical (FSO) links. Compared with near-infrared FSO links, mid-infrared FSO links exhibit lower attenuation and scintillation indices. Owing to its structural simplicity, optical feedback has been widely adopted for generating laser chaos. Quantum cascade laser (QCL) and interband cascade laser (ICL) are typical mid-infrared semiconductor lasers. Laser chaos generated by optical feedback QCLs has been reported for applications in chaotic secure communications. However, due to their ultrafast gain recovery dynamics, conventional QCLs exhibit a chaos bandwidth limited to only a few MHz, resulting in a secure communication rate as low as 0.5 Mbit/s. In contrast, ICLs possess a gain recovery rate comparable to that of conventional semiconductor lasers, making them significantly more suitable for mid-infrared laser chaos generation. Filtered optical feedback has shown more complex dynamic characteristics in near-infrared laser chaos generation compared to conventional optical feedback. In this work, to produce high quality mid-infrared laser chaos, we employ a blazed grating as a feedback device.MethodsFigure 1 shows the experimental setup of a grating feedback ICL. A Fabry-Perot ICL collimated by an aspherical lens serves as a light source and a blazed grating serves as a feedback device. The laser is driven by a low-noise current source under temperature-controlled conditions (25 ℃). Output dynamics are analyzed via Fourier-transform infrared spectroscopy and a mercury cadmium telluride photodetector. Nonlinear dynamics under varying bias currents (200?360 mA) are characterized through optical spectra, time series, and power spectra (Fig. 3). Chaos complexity is quantified using the Wolf algorithm to calculate the maximum Lyapunov exponent. In the experiments, the grating feedback not only perturbs the ICL into a chaotic state but also exhibits a mode-selection effect, thereby enabling wavelength tuning of the chaotic laser through rotational adjustment of the blazed grating. Wavelength tuning is achieved by rotating the grating angle (0°–0.6°) at a fixed bias current (380 mA).Results and DiscussionsAt low bias currents (200 mA and 240 mA), the system exhibits high-amplitude low-frequency fluctuations with distinct relaxation oscillation peaks [Figs.3(c1) and (c2)]. As the bias current increases, both the frequency and amplitude of these oscillations intensify. Increasing the current (280?360 mA) induces chaotic dynamics, evidenced by irregular time series and flattened power spectra [Figs.3(b3)?(b5) and (c3)?(c5)]. The maximum Lyapunov exponent peaks at 3.76/ns under 310 mA, confirming high chaos complexity (Fig. 4). By rotating the grating, the central wavelength is tuned over 45.8 nm (3325.7?3371.5 nm) while maintaining chaos, with the maximum Lyapunov exponent reaching 4.84/ns at 0.4° (Fig.5).ConclusionsThis work demonstrates that a grating feedback ICL can generate high quality mid-infrared laser chaos with high complexity and tunable wavelength. With the increase of the bias current, the average frequency of the low frequency fluctuation increases until the laser enters a complete chaotic state. The chaotic signal generated by the laser under grating feedback always maintains high complexity and the maximum is up to 3.76/ns. Via rotating the grating, the center wavelength of the ICL can achieve a tuning coverage of 45.8 nm, and the maximum Lyapunov exponent can reach 4.84/ns during tuning. The high complexity and the broad tuning range make this system ideal for mid-infrared wavelength division multiplexing. Further optimization of laser parameters can enable continuous single-mode chaotic outputs.

ObjectiveHigh-power fiber lasers with near-diffraction-limited beam quality are critical for applications in fields such as precision industrial machining, aerospace manufacturing, and directed energy systems. However, the power scaling of these lasers is primarily limited by nonlinear effects such as transverse mode instability (TMI) and stimulated Raman scattering (SRS). Although tandem pumping configurations are effective in mitigating these challenges, their reliance on complex cascade architectures and high-cost 1018 nm pump sources limits their widespread application. We proposed a novel and cost-effective approach based on partially ytterbium-doped fiber (YDF) to scale the output power of high-power fiber lasers. The main objectives are twofold: (1) to increase the TMI threshold by redistributing the thermal load through partially doped profiles and selectively amplifying the fundamental mode and (2) to suppress the SRS by broadening the spectrum of the seed laser. By achieving these objectives, this study can demonstrate that 976 nm laser diodes (LDs) with direct pumping can deliver a laser output power of over 5 kW while maintaining high beam quality, thereby providing a viable alternative to conventional high-cost systems.MethodsTwo types of double-clad YDFs were designed and fabricated with core/inner cladding diameters of 25/500 μm: Fiber-A (100% doping ratio in core) and Fiber-B (~80% doping ratio in core). Both fibers were drawn from the same 20/400 preform to ensure consistent fiber properties. A counter-pumped fiber amplifier system was constructed to evaluate laser performance. The system consists of 18 high-power 976 nm LDs (total pump power: 5.4 kW) and a 1080 nm seed laser (approximately 100 W) comprised of a pair of fiber Bragg gratings (high-reflectivity grating: 3 nm bandwidth, 99% reflectivity; low-reflectivity grating: 1 nm bandwidth, 10% reflectivity). The output power, spectral characteristics, temporal stability, and beam quality factor (M2) were measured using a 15 kW power meter (OPhir), a high-resolution spectrometer (Yokogawa AQ6370), and a beam quality analyzer (BeamSquared). Two main modifications were made to optimize Fiber-B, as follows:(1) Coiling pattern improvement: replacing the initial “racetrack” coiling (minimum bending diameter: 14 cm) with a “peanut-shaped” configuration (minimum bending diameter: 11 cm). This modification increases the higher-order mode (LP11) bending-induced losses while maintaining minimal impact on the fundamental mode (LP01).(2) Spectral broadening of the seed laser: the bandwidth of the low-reflectivity grating was doubled (1 nm→2 nm), broadening the longitudinal mode of the seed laser and disrupting the phase-matching condition for SRS.Results and DiscussionsThe TMI threshold of Fiber-B (3.250 kW) improves by over 60% compared to that of Fiber-A (2.004 kW). This improvement is attributed to the partial doping strategy (~80% doping ratio in core), which reduces the thermal load within the fiber by positioning the Yb ions in the central region of the core. This design selectively enhances the gain overlap of the fundamental modes (LP01) while suppressing higher-order modes (e.g., LP11) owing to their weaker interaction with the doping region. To further explore the power scalability of Fiber-B, we performed two key optimizations. First, the coiling pattern was improved by replacing the initial “racetrack” configuration (minimum bending diameter: 14 cm) with a “peanut-shaped” design (minimum bending diameter: 11 cm). This adjustment increases the bending-induced higher-order mode loss and effectively suppresses the TMI (Fig. 4). Second, the spectral bandwidth of the seed laser was doubled (from 1 to 2 nm) by replacing the low-reflectivity fiber Bragg grating. This improvement broadens the longitudinal mode of the seed laser, disrupts the phase-matching conditions required for SRS, and improves temporal stability. These optimizations enable Fiber-B to reach an output power of 5.030 kW with high beam quality (M2 ~1.77). At this power level, the 3 dB spectral width is broadened to 4.44 nm, but no Raman Stokes component is observed (signal-to-noise ratio >43 dB), confirming SRS suppression (Fig. 5). The temporal stability remains consistent throughout the power-scaling process, and the photodetector signal does not fluctuate significantly. Mechanistic analysis shows that the partially doped profile redistributes the modal gain to favor the fundamental mode, whereas the reduced bending diameter (~11 cm) amplifies the higher-order mode losses. In addition, the wider seed spectrum mitigates the SRS by reducing the coherence between the longitudinal modes, thereby reducing the risk of nonlinear interactions.ConclusionsThis work demonstrates the advantages of partially doped YDFs in achieving high-power, high-beam-quality fiber lasers. By reducing the core doping ratio to ~80% and optimizing the fiber coiling, a 5 kW level output is realized without compromising the beam quality or inducing nonlinear degradation. These results provide a cost-effective approach for advancing high-performance fiber laser systems, with implications for industrial and defense applications that require high precision and reliability.

ObjectiveMarine lidar is widely adopted for applications such as seawater optical-parameter profile detection, coastal-zone mapping, marine-resource surveys, and marine-environment monitoring. It offers high detection accuracy, wide measurement coverage, and high measurement efficiency and flexibility. The blue-green spectral band (420?580 nm) exhibits the lowest attenuation in seawater, thus establishing it as the optimal emission source for marine lidar systems. In the coastal seawater region, the optimal light-transmission wavelength of seawater is 520?580 nm. In clear oceanic water, the optimal wavelength for laser detection is 420?510 nm. Owing to advancements in light-source technology, the current wavelength of marine lidar light sources is typically 532 nm, which is not optimal for applications in ocean waters. Additionally, the Fraunhofer dark line (H-β line) of the solar radiation spectrum is located in the seawater optical window, with a central wavelength of 486.13 nm and a spectral linewidth of approximately 0.14 nm. Therefore, the 486.13 nm wavelength of blue light is suitable for application in clear oceanic water. By restricting both the transmitting-laser linewidth and receiver optical-filter bandwidth to ≤0.1 nm (smaller than the H-β dark line bandwidth), solar background noise can be effectively suppressed during signal acquisition, thereby enabling a high signal to noise ratio (SNR). Additionally, the 486.13 nm blue laser radar shows significant advantages in improving the depth (range) of ocean detection and in enhancing the SNR of echoes.MethodsThe 532 nm green laser radar enables hyperspectral resolution detection, with the frequency stability of its 1064 nm seed light source maintained below 10 MHz during long-term operation. To extend such hyperspectral detection capabilities to 486.13 nm blue laser lidar for oceanic applications, the laser source must exhibit a high peak power output, a single-frequency narrow linewidth, and high frequency stability. The most widely adopted approach to achieve these characteristics is optical parametric oscillation/parametric amplification (OPO/OPA) techniques based on single-frequency seed injection, which has been verified to be applicable to oceanic detection lidar systems. This implies that the stabilization of the single-frequency seed laser is a critical performance metric for the overall laser system. Thus, this study proposes a compact frequency stabilization system for seed lasers using the Pound?Drever?Hall (PDH) technique. The system is designed to lock a 972.26 nm laser with high stability within a Fabry-Perot (F-P) cavity and operates reliably at room temperature. By employing this method, the system does not need to identify atomic transition spectral lines corresponding to the laser wavelength for stabilization. Consequently, a stable 486.13 nm blue laser can be achieved through frequency doubling, which fulfills the spectral linewidth and stability criteria for the hyperspectral detection marine-radar blue laser source.Results and DiscussionsThe frequency stabilization system based on PDH technique proposed in this study utilizes the resonant frequency of the F-P cavity as the reference standard (Fig. 1). The distributed feedback single-frequency laser diode (DFB-LD) with an output wavelength of 972.26 nm is segregated into two beams using a fiber beam splitter. One beam serves as the seed light output, whereas the other undergoes phase modulation via an electro-optic modulator (EOM), thus yielding a symmetrical double-sideband spectrum (Fig. 2). The EOM is driven by a 20 MHz radio frequency (RF) signal from the circuit system to modulate the laser phase. The laser output from the modulator is injected into the resonant cavity through the coupling lens (lens 1) to achieve mode matching. The radius of curvature of the F-P cavity is R=50 mm, the free spectral range of the F-P cavity is 1.5 GHz, and the fineness is 1500. The laser oscillates repeatedly within the F-P cavity to form a stable resonance signal. The resonance signal emitted from the resonant cavity is detected by the high-speed photodetector (PD). Subsequently, the frequency error signal is acquired using heterodyne spectrum-detection technology. Using this error signal, the feedback control system swiftly adjusts the laser drive-current parameters and locks the output wavelength of the DFB-LD at the resonant frequency of the F-P cavity, which is precisely maintained at 972.26 nm. This procedure ensures the high-frequency stabilization of the laser system.ConclusionsBased on the specific requirements of hyperspectral detection marine lidar systems for seed laser performance, this paper presents a highly robust frequency-stabilized and frequency-locked laser operating at 972.26 nm. This system utilizes PDH frequency-stabilization technology with a fiber connector to achieve precise control. A notable feature of its design is its compact architecture: while preserving critical components such as the optical fiber collimator, coupling lens, and resonator, all other components employ fiber-based input/output configurations. This design approach significantly simplifies the optical path, reduces system volume, and facilitates integration and alignment. The system utilizes the resonant frequency of the confocal cavity as the frequency reference standard. At room temperature, the root-mean-square value of the 30-min frequency jitter of the laser output is less than 25 MHz, and the corresponding Allen variance exceeds 4×10-8, thus fully satisfying the requirements of the seed light source for hyperspectral lidar. The frequency stability and frequency-locking output of a 486.13 nm blue laser can be achieved using a periodic polarization lithium niobate (PPLN) frequency-doubling crystal. Consequently, the frequency stability of the blue laser surpasses several tens of megahertz. The 972.26 nm frequency-stabilized and frequency-locked laser developed in this study establishes a robust technical foundation for the advancement of hyperspectral detection marine blue-laser radar.

ObjectiveThe 633-nm frequency-stabilized helium?neon (He-Ne) laser has been extensively employed in diverse fields. In nanoscale-length metrology, laser interferometric displacement measurement systems, which serve as traceable instruments for precise length determination, exhibit high measurement accuracies. When the refractive-index fluctuations are negligible, the ultimate precision of the long-range length measurements is fundamentally constrained by the relative frequency stability and absolute accuracy of the laser source. Contemporary ultra-precision measurement systems, requiring multi-axis and multi-channel capabilities, impose stringent demands on light sources, necessitating simultaneous realization of exceptional frequency stability (10-11), absolute frequency accuracy, and a high output power (e.g., total dual-beam power ≥800 μW for interferometric applications). Nevertheless, conventional 633-nm frequency-stabilized He-Ne lasers exhibit performance limitations. Power-balanced thermal frequency-stabilized configurations provide adequate output power (>500 μW) but insufficient frequency stability (10-8?10-9). In contrast, iodine-stabilized lasers achieve metrological-grade frequency stability (10-11) and accuracy at the cost of reduced power (~200 μW) as well as residual frequency modulation unsuitable for high-speed interferometry. To address these constraints, in this study, we have implemented an optical phase-locked loop (OPLL) architecture to lock the frequency of a fully intracavity, thermally stabilized He-Ne laser to both an iodine-stabilized frequency standard and external-cavity diode laser (ECDL). This hybrid approach synergistically combines the high-power capability of thermal stabilization (>600 μW) with the exceptional frequency stability of reference sources (<10-11), thereby fulfilling the dual requirements of modern ultra-precision measurement systems while reducing the density of modulation artifacts inherent in direct iodine-stabilized outputs.MethodsFirst, a complete system architecture comprising three principal subsystems, i.e., beat signal acquisition, locking logic execution, and result recording/analysis, was established. A parametric model for the loop filter was subsequently developed based on the error signal characteristics. The initial frequency locking of the slave laser to the iodine-stabilized reference laser enabled the acquisition of beat frequency data. Second, a systematic investigation of the degradation mechanisms underlying its long-term stability was performed. This step included rigorous documentation of the correlation between the laser tube temperature and PID parameters during the locking procedures. To validate these findings, the reference source was substituted with an ECDL, and relocation experiments were conducted. The resultant beat frequencies exhibited enhanced stability metrics, with no observable deterioration in long-term stability performance. Because the reference laser exhibited non-negligible frequency fluctuations, the measured beat frequency stability inherently represented only the relative stability between the slave and reference lasers. Consequently, a comprehensive characterization of the slave laser’s optical frequency stability must account for the residual fluctuations in the reference source. The direct determination of the intrinsic frequency stability of a slave laser theoretically requires beat frequency analysis against a secondary reference laser with superior stability; however, such metrological-grade references are often unavailable in practical scenarios. Although the root-sum-square combination of the individual laser stabilities provides a nominal estimate, this approach introduces systematic uncertainties. Therefore, a precise evaluation of the absolute frequency stability of the slave laser necessitates computational reconstruction of its real-time frequency fluctuations using advanced signal decomposition techniques rather than relying solely on relative beat frequency measurements.Results and DiscussionsThe experimental results demonstrate that the frequency stability achieved by the proposed method, while delivering an output power of 1 mW, is superior to that of power-balanced thermal frequency-stabilized lasers. When employing an iodine-stabilized laser as the reference, the slave laser attains short-term optical frequency stability comparable to that of the reference source, reaching 2.6×10-11 at τ=1 s. To improve long-term stability, the fully intracavity, thermally stabilized He-Ne laser is frequency-locked to an ECDL, achieving optical frequency stability of 3.8×10-12 at τ=1 s (Fig. 7), with a relative standard measurement uncertainty of 4.0×10-12 (Table 1). Extended integration time testing reveals further stability enhancement (1.9×10-13 achieved at τ=1000 s; Fig. 8). These metrics confirm the efficacy of the ECDL-based locking scheme in suppressing long-term drift while maintaining metrological-grade precision. Statistical results from multiple experimental trials confirm that when implementing frequency-offset locking with high-stability references, computational correction for reference laser fluctuations becomes less critical. Conversely, applying the method for calculating the synthesized frequency stability is essential when employing lower-stability references such as iodine-stabilized lasers, as evidenced by the observed diverging stability metrics in such configurations.ConclusionsThis paper presents a method and experimental implementation for enhancing laser frequency stability through OPLL-based frequency-offset locking of a fully intracavity, thermally stabilized He-Ne laser to reference sources. The method simultaneously, systematically accounts for the influence of reference laser frequency fluctuations on the actual optical frequency stability of the slave laser via synthetic computation. Experimental and computational results demonstrate that when locked to an ECDL, the composite Allan deviation curve indicates that the performance of the laser system improves by nearly an order of magnitude compared to that of conventional iodine-stabilized laser systems. In addition, its output power surpasses that of iodine-stabilized systems by more than four-fold. Nevertheless, the long-term stability achieved by locking iodine-stabilized lasers remains suboptimal. To address this limitation, future studies will be focused on replacing thermal actuation with a piezoelectric transducer(PZT)-based cavity length control mechanism. This modification is anticipated to eliminate the thermal hysteresis and equilibrium instability inherent in thermal regulation, thereby further improving the frequency stability of fully intracavity He-Ne lasers in frequency-offset locking configurations with iodine-stabilized references.

ObjectiveFiber lasers are known for their high conversion efficiency, compact structure, lightweight design, and excellent beam quality. Owing to rapid progress in fiber and fiber device manufacturing technologies as well as pump source technologies, ytterbium-doped fiber lasers are finding widespread use in advanced industrial processing, national defense, military applications, and aerospace. Currently, the focus of fiber laser development is shifting from merely increasing power output to expanding applications in specialized fields and improving environmental adaptability. However, in extreme conditions such as freezing cold, intense heat, or environments with large temperature fluctuations, the output performance of fiber lasers can vary significantly and thereby lead to unstable operations or even potential damage. Research on the temperature characteristics of fiber lasers is crucial for broadening their application range and enhancing operational stability.MethodsIn this study, two fiber laser oscillators were constructed using semiconductor lasers (LD) with central wavelengths of 976 and 940 nm as the pumping sources, respectively. Based on a temperature control platform, the temperature characteristics of the two LD were first tested over an ultra-wide temperature range of -40 to 55 ℃. Subsequently, the LDs were connected to their respective lasers. Comparative experiments were conducted on two fiber laser oscillators with different pumping wavelengths under four conditions: individual temperature control of the LD, individual temperature control of the ytterbium-doped fiber (YDF), individual temperature control of the fiber Bragg grating (FBG), and simultaneous temperature control of all temperature-sensitive components inside the laser. The variation laws of the output characteristics of the two lasers under these four conditions were obtained. The formation reasons of these laws and their impacts on the wide temperature range operational stability of the fiber laser oscillators were analyzed from the perspective of the temperature characteristics of the components.Results and DiscussionsWithin the temperature range of -40 to 55 ℃, the performance variations of the 940 and 976 nm LDs exhibit similar trends (Figure 2). As the temperature increases, the output power of the LD continuously decreases, and the central wavelength of the output spectrum gradually shifts toward longer wavelengths. When the LD, YDF, and FBG in the laser system are individually temperature-controlled, the impact of the temperature characteristics of a single component on the laser system can be investigated (Figure 6). The results show that applying temperature changes solely to the YDF or FBG has a minimal impact on the laser system, which is far less than the impact observed when temperature changes are applied to the LD. When temperature changes are applied simultaneously to the LD, YDF, and FBG, the output characteristics of the laser system in the wide-temperature range can be examined (Figure 7). In the low-temperature range of -40 to 20 ℃, the oscillator pumped by the 940 nm LD exhibits an output power fluctuation of only 8% and an optical-to-optical efficiency fluctuation of only 0.89%, whereas the oscillator pumped by the 976 nm LD shows an output power fluctuation of 22.51% and an optical-to-optical efficiency fluctuation of 29.03%. In the high-temperature range of 30 to 55 ℃, the oscillator pumped by the 940 nm LD has an output power fluctuation of 13.4% and an optical-to-optical efficiency fluctuation of 6.40%, whereas the oscillator pumped by the 976 nm LD has an output power fluctuation of 28.58% and an optical-to-optical efficiency fluctuation of 21.39%. Over the entire experimental temperature range of -40 to 55 ℃, the oscillator pumped by the 940 nm LD shows an output power fluctuation of 25.67% and an optical-to-optical efficiency fluctuation of 11.26%, whereas the oscillator pumped by the 976 nm LD exhibits an output power fluctuation of 29.77% and an optical-to-optical efficiency fluctuation of 31.20%. The fiber laser oscillator pumped by the 940 nm LD has higher output stability and better low-temperature performance.ConclusionsThis study investigates the temperature characteristics of 940 and 976 nm LDs, as well as the fiber lasers pumped by them, over an ultra-wide temperature range of -40 to 55 ℃. The results indicate that the temperature characteristics of the ytterbium-doped fiber laser oscillator system are primarily influenced by the temperature characteristics of the LDs. The temperature characteristics of FBG and YDF have a significantly smaller impact on the laser system compared with the LDs. Additionally, the laser pumped by the 940 nm LD exhibits higher wide-temperature operation stability and better low-temperature performance than the laser pumped by the 976 nm LD. Without active thermal management, the optical-to-optical efficiency fluctuation of the laser pumped by the 976 nm LD reaches 31.20% over the temperature range of -40 to 55 ℃, whereas that of the laser pumped by the 940 nm LD is only 11.26% and drops to 0.89% in the low-temperature range of -40 to 20 ℃. These findings are highly beneficial for the research of wide-temperature-range fiber lasers. Moreover, the wide-temperature operation stability of fiber lasers can be further enhanced by introducing appropriate thermal management structures.

ObjectiveTerahertz waves exhibit the unique characteristics of both microwave and optical radiation, enabling their widespread application in spectroscopic analysis, biomedical diagnostics, metrology, imaging, optical communications, and related fields. Nonlinear difference-frequency generation is a widely used technique for generating terahertz waves. Dual-wavelength semiconductor lasers are extensively employed in terahertz wave generation systems owing to their compact size and high stability. Distributed feedback (DFB) and distributed Bragg reflector (DBR) semiconductor lasers are suitable for achieving dual-wavelength emission. In DFB semiconductor lasers, dual-wavelength emission can be realized by fabricating gratings with different periods on the surface of the ridge waveguide or by embedding buried gratings within the epitaxial structure. However, these methods typically require narrow-ridge waveguides or a two-step epitaxial growth process, which complicate the lithographic alignment of the electrode window and increase fabrication complexity. In DBR semiconductor lasers, a set of DBR gratings is placed at one end of the resonant cavity to align the reflection spectrum of the DBR gratings with the longitudinal modes, thereby enabling dual-wavelength selection. However, this selection process is highly sensitive to the precision of grating fabrication. Alternatively, dual-wavelength emission can be achieved by placing two DBR gratings longitudinally at one end of the cavity; however, this approach typically requires low-order gratings, resulting in higher costs. We proposed a dual-wavelength semiconductor laser incorporating a laterally varied-order DBR grating. By employing a 20 μm wide ridge waveguide structure, the laser supports both the fundamental and first-order lateral modes. Based on the spatial distribution characteristics of the lateral modes, DBR gratings with different widths were integrated at the rear end of the ridge waveguide to serve as cavity end reflectors. These gratings effectively provide feedback for each lateral mode, enabling dual-wavelength emission with comparable intensities. Notably, this design eliminates the necessity for narrow-ridge waveguides and low-order grating structures, thereby reducing fabrication complexity and cost.MethodsThe device was analyzed in terms of two aspects: the design of the ridge waveguides and DBR gratings. By optimizing the width of the ridge waveguide, the laser was designed to support only the fundamental and first-order lateral modes within the dual-wavelength operation range. The gratings were designed by adjusting the widths of the Core-DBR and Lateral-DBR based on the optical field distribution characteristics of the fundamental and first-order lateral modes. This approach effectively modulates the reflection intensities of the Core- and Lateral-DBRs. Therefore, the device can achieve dual-wavelength emissions with comparable intensities.Results and DiscussionsThe device achieves dual-wavelength emission with a wavelength spacing of about 0.9 nm and comparable intensity. Within the current range of 170?210 mA, the laser operates under relatively low injection conditions and the fundamental mode predominates. Under these conditions, a single emission peak λcore at 1064 nm diffracted by the Core-DBR was observed. At an injection current of 210 mA, the first-order lateral mode reaches its threshold gain, activating a second emission peak λlat at 1065 nm diffracted by the Lateral-DBR [Fig. 7(a)]. As the current exceeds 210 mA, the intensity of λlat gradually increases owing to enhanced gain in the first-order lateral mode, resulting in both wavelengths exhibiting similar intensities [Fig. 7(b)]. When the injection current increases from 210 mA to 330 mA, junction temperature rise induces a redshift in both wavelengths: λcore shifts from 1064.39 nm to 1064.56 nm and λlat shifts from 1065.31 nm to 1065.49 nm. The dual-wavelength spacing remains approximately constant at 0.9 nm (Fig. 8). At an injection current of 330 mA, the maximum dual-wavelength output power reaches 88.26 mW (Fig. 10), with both wavelengths exhibiting comparable intensities.ConclusionsBy integrating Core-DBR and Lateral-DBR with different grating orders and periods, the device achieves dual-wavelength emission. A 20 μm wide ridge waveguide is employed to support only the fundamental and first-order lateral modes within the dual-wavelength operation range. Additionally, the widths of the Core-DBR and Lateral-DBR are adjusted based on the optical field distributions of the respective modes. This enables precise modulation of the reflection intensities from the Core-DBR and Lateral-DBR, resulting in dual-wavelength emissions with comparable intensities. Within the injection current range of 210?330 mA, the dual-wavelength spacing remains stable at about 0.9 nm. At an injection current of 330 mA, the device emits two distinct wavelengths—1064.56 nm and 1065.49 nm—with comparable intensities, achieving a maximum dual-wavelength output power of 88.26 mW.

ObjectiveIn recent years, chiral metamaterials composed of subwavelength-scale nanostructures with symmetry-breaking characteristics have attracted significant attention from researchers owing to their great potential for enhancing circular dichroism (CD) effects. The structural parameters and unit arrangements of most conventional chiral metamaterials (CMTMs) are fixed, leading to a critical limitation in which their modal resonance responses lack dynamic tunability. These materials typically generate CD signals with fixed intensities and polarities within specific wavelength bands, which restricts their application in multifunctional optical devices. The introduction of dynamic modulation capabilities to achieve the real-time control of CD signals in chiral metamaterials has substantial scientific and practical significance. This advancement could lead to new application prospects in fields such as adaptive optics, tunable sensors, dynamic imaging, and information encryption. Although there have been numerous studies on tunable chiral optical responses based on VO2 phase-change materials, current designs of tunable chiral metasurface devices predominantly adopt a hybrid configuration that combines phase-change materials with metallic structures. The inherent Ohmic losses in metals result in broad linewidths of circular dichroism (CD) responses, with quality factors mostly confined to the range of 10?20. Furthermore, most tunable chiral metasurface devices operate predominantly in the terahertz band, whereas relatively few devices function effectively in the near-infrared wavelength range.MethodsIn this work, we designed a chiral metamaterial structure with zigzag-shaped VO2 as resonant units and discussed its optical absorption properties and circular dichroism (CD) in the near-infrared band in detail. To study the optical chiral response of the tunable chiral metasurface, we conducted simulations using the finite-element software COMSOL Multiphysics. In the calculations, the refractive index of the PMMA background material was set to 1.47. The dielectric constant of the phase-change material VO2 was described using the Drude model. Periodic boundary conditions were applied in the x- and y-directions of the Z-shaped VO2 resonant unit structure to simulate the metasurface structure of an infinite array. Periodic port boundary conditions and a perfect matched layer (PML) were used in the positive and negative directions of the z-axis to prevent the reflected waves from interfering with the simulation results. A plane wave with left- or right-handed circular polarization state was vertically incident on a chiral metasurface along the z-direction, and its absorption rate can be obtained by A=1-T-R, where T and R are the transmittance and reflectance, respectively. The CD signal of a chiral metasurface was defined as the difference in absorption between right- and left-handed circular polarization incident on the metasurface; that is, ξCD=ARCP-ALCP.Results and discussions Numerical simulations reveal significant differences in the absorption spectra of the chiral metasurface under LCP and RCP incidence in the near-infrared range of 900?1200 nm. When the incident light is LCP, the chiral metasurface exhibits almost no absorption at other wavelengths, except for a strong peak with an absorption rate of approximately 0.5, at a wavelength of 967 nm, and a weak absorption peak at 1011 nm (peak of approximately 0.026). For RCP incidence, the chiral metasurface only exhibits an absorption peak of approximately 0.48 at a wavelength of 1011 nm, while there is almost no absorption in other wavelength ranges. When VO2 is in a metallic state, the designed Z-shaped VO2 chiral metasurface exhibits selective absorption properties for left- and right-handed circular polarization, owing to symmetry breaking. By using the formula for calculating circular dichroism, it can be concluded that the CD signal at a wavelength of 967 nm has a negative maximum value of approximately -0.48, while at a wavelength of 1011 nm, the CD signal has a positive maximum value of approximately +0.45. Furthermore, it is found that the designed metasurface has very narrow linewidths for the absorption peaks of LCP at a wavelength of 967 nm and RCP at a wavelength of 1011 nm, with full width at half maximum (FWHM) of 7.3 and 12.2 nm, respectively. The corresponding quality factors are Q≈132 and Q≈83, respectively. In order to more clearly demonstrate the trend of the CD signal of the metasurface with the variation of VO2 conductivity, we researched the CD spectrum of the metasurface when the VO2 conductivity increased from σ=200 to 2000 S/m. It can be seen that each CD spectrum has two opposite polarity characteristic peaks, which are determined by the fact that the metasurface absorbs LCP more than RCP at the short wave characteristic peak and LCP less than RCP at the long wave characteristic peak. By utilizing the change in conductivity during the VO2 phase transition process, the peak values of the two CD characteristic peaks on the chiral metasurface can be dynamically controlled within the ranges of [-0.02, -0.48] and [+0.02, +0.45], respectively. On this basis, we introduced another set of Z-shaped VO2 resonant units with the same geometric parameters and opposite chiral characteristics to those of the original chiral structure. When the conductivities of the left- and right-handed chiral VO2 bands are the same, the unit structure exhibits mirror symmetry with respect to the xz plane. Therefore, the CD values generated by the left- and right-handed chiral structures are always different, resulting in no chiral response on the metasurface, that is, a state of closed chirality. When the Z-shaped VO2 bands of left- and right-handed chirality are in different states, that is, when their conductivities are different, the mirror symmetry of the unit structure is broken, and the metasurface produces a CD response corresponding to the chiral open state. By switching the states of the left- and right-handed chiral VO2 bands, a dynamic polarity reversal function of the CD signals with the same intensity can be achieved.ConclusionsDynamic control of CD in chiral metamaterials has broad application prospects in fields such as tunable sensors, dynamic imaging, and information encryption. A chiral metamaterial with Z-shaped vanadium dioxide as the resonant unit was designed to obtain a CD response with high quality factor (Q>100) in the near-infrared band. By utilizing the tunability of the conductivity of phase change material VO2 during the phase transition process, dynamic control of the CD response signal intensity from -0.5 to +0.5 has been achieved. In addition, we designed a structure comprising Z-shaped VO2 resonant units with identical geometric parameters and opposite chiral characteristics, and controlled the phase transition states of the VO2 resonant units in both the chiral structures, thereby achieving CD response signal switching and an equal-intensity polarity reversal function.

ObjectiveThe Risley prism system (RIPS) changes the propagation direction of a beam via the coaxial independent rotation of a pair of wedge prisms. Increasing the prism apex angle expands its imaging field-of-view but deteriorates its pointing performance; the larger the prism apex angle, the larger the deviation between the theoretical and actual beam pointing for the same assembly error. Therefore, for prism systems with large apex angles, much attention is paid to pointing correction methods aimed at improving pointing performance. To address the problem of pointing errors in large apex angle RIPS, we proposed a rat swarm optimizer (RSO)-based pointing error correction method and constructed an RIPS prototype to improve the pointing accuracy of RIPS and correct its pointing performance. Our methodology and findings provide useful insights for the design of a time-varying optical target pointing and tracking control system based on the RIPS.MethodsFirst, an assembly error model of the prototype was established according to the deviation mechanism between theoretical and experimental prototype beam pointing, based on the beam pointing principle of the RIPS. Second, the RSO algorithm was employed to identify the error parameters of the assembly error model of the prototype system. Subsequently, a data-driven error parameter correction study was conducted for the inverse solution of the actual prism apex angle setting and refractive index setting of the RIPS. Finally, experiments were conducted.Results and DiscussionsThe RSO-based correction method for the pointing error of the RIPS demonstrates its superior performance in a number of simulations and experiments. (1) Compared with the PSO-based method, the RSO-based error identification method exhibits a much faster convergence speed and higher convergence accuracy (Fig. 9, Table 1). The RSO-based RIPS correction method has a smaller pointing error than the PSO-based method (Fig. 15). (2) The proposed RSO-based RIPS shows better performance in terms of the mean error, standard deviation, mean pointing deviation, and standard deviations of the pointing deviations (Table 2). (3) A comparison between the results before and after correction via the RSO-based method shows that the mean pointing error is reduced by 48.21% and that the root mean square error decreases by 44.34%. (4) The centroid of the fitted circle changes from (9.24 pixel, -4.79 pixel) to (4.78 pixel, -1.78 pixel), and the radius of the fitted circle achieves a reduction of 30.9% (Figs. 15 and 16).ConclusionsTo enhance the pointing accuracy of the RIPS, this study proposed a pointing error correction method based on the RSO algorithm. The assembly error model of the prototype is established based on the beam pointing principle of the RIPS. Then, by introducing the RSO, the error parameters of the assembly error model of the prototype RIPS are identified in a data-driven manner. A data-driven error parameter correction study is conducted on the inverse solution of the actual prism apex angle setting value and RIPS refractive index setting value. In summary, the pointing error of the RIPS corrected by the RSO algorithm is significantly lower than that of the RIPS corrected by the PSO algorithm.

ObjectivePrecise surface metrology is fundamental for quality control in manufacturing, particularly in fields such as space optics, ultrahigh-intensity ultrashort laser devices, free-electron lasers, and extreme ultraviolet (EUV) lithography. Achieving subnanometer accuracy in surface measurements is essential for manufacturing multifunctional, high-precision, and low-defect optical components. However, conventional interferometry, which relies on relative measurements, is limited by the quality of the reference flat, thus potentially reducing precision. Absolute measurement techniques have emerged as an effective solution for isolating and mitigating wavefront errors in both test and reference flats. This study proposes an advanced absolute-flatness measurement technique that combines the shift-rotation method with a second-order partial derivative algorithm. This approach is designed to enhance stability, reduce environmental error sensitivity, and simplify the experimental process while maintaining high accuracy. By expanding wavefront error analysis to second-order derivatives in polar coordinates, this technique offers improved robustness and applicability of large-aperture optical devices.MethodsThe proposed method integrates the shift-rotation technique with a second-order derivative analysis to achieve absolute-flatness measurements. In the shift-rotation method, lateral and rotational shears are applied to a test flat while the reference flat is maintained stationary, thereby enabling the elimination of reference-related errors through integration. To address noise and mechanical error issues in gradient calculations, this study incorporates additional rotational and translational steps. The test flat is subjected to two rotations and two translations, thus generating second-order derivatives of the surface errors along the radial and azimuthal directions. Numerical calculations of the derivatives and Zernike polynomial expansions are employed to characterize and reconstruct the surface profile. Second-order derivatives are computed using finite-difference approximations, and a matrix-based least-square approach is applied to solve for the Zernike coefficients. These coefficients describe the absolute surface shapes. The robustness of the method is enhanced by incorporating defocus and tilt error corrections into the matrix formulation. Furthermore, the translation and rotation intervals are optimized to minimize errors associated with the pixel size and mechanical deviations.Results and DiscussionsThe effectiveness of the proposed method is validated through simulations and experiments. MATLAB simulations demonstrate the accuracy and reliability of the proposed method under ideal conditions. The surface profiles are constructed using 231 Zernike polynomials, with added defocus and mid-frequency errors. Comparisons between the original and calculated surface shapes show excellent agreement, with residual root mean square (RMS) errors below 2.7×10-14 nm (Fig. 2). Optimization of the rotation and translation intervals reveals that a rotation angle of 45° and a translation interval equivalent to one pixel (0.098 mm) yield the lowest residual RMS errors (Fig. 4). Simulations assessing the effect of rotational and translational deviations indicate that the residual RMS errors increase with the deviations. To maintain the precision at λ/1000 (λ=632.8 nm), rotational and translational errors are constrained to within 0.1° and 0.07 mm, respectively (Fig. 5). The algorithm robustness to random noise is evaluated by introducing a noise RMS of 0.5 nm into the simulated measurements. The method successfully reconstructs the surface profiles with residual RMS errors of 0.156 nm, thus demonstrating high resistance to environmental disturbances (Fig. 6). Experiments are conducted using a Zygo MST interferometer operating at λ=632.8 nm. The test and reference flats indicate peak-to-valley (PV) value of λ/20. The experimental setup includes a five-dimensional holder for the test flat, which provides high-precision rotation and translation. The results obtained using the proposed method are compared with those obtained using the conventional three-flat method. Surface profiles derived from both methods show high consistency, with PV and RMS differences of 7.29 nm and 1.66 nm, respectively (Fig. 13 and Table 1). Notably, the proposed method captures mid-frequency information more effectively, although further optimization is required to address higher-order errors.ConclusionsThis study presents an innovative absolute-flatness measurement technique that combines the shift-rotation method with second-order partial derivatives. This method simplifies the experimental procedures by reducing the number of required measurements while enhancing robustness against environmental and mechanical errors. Validation through simulations and experiments confirms the accuracy and consistency of the proposed method compared with conventional techniques. The proposed approach is particularly suitable for large-aperture optics, where robustness and precision are critical. Future studies shall focus on optimizing the method for capturing high-frequency surface errors using additional Zernike terms or stitching techniques. In general, the shift-rotation second-order derivative method represents a significant advancement in optical metrology and offers a robust, accurate, and practical solution for absolute-flatness measurements in advanced optical manufacturing.

ObjectiveIn the process of detecting gravitational waves in space, external environmental vibrations can cause the incident laser in the resonant cavity of the gravitational wave interferometer arm to deviate from the cavity axis, resulting in a decrease in detection sensitivity. The purpose of this study is to improve the laser directional stability in the horizontal direction, reduce the optical losses, and enhance the coupling efficiency between laser and cavity by using a resonant cavity alignment error signal enhancement scheme based on high-order Hermitian Gaussian optical fields, thereby improving the detection accuracy of space gravitational waves.MethodsThe experimental setup is shown in Fig. 1. First, the classical processing is performed: injecting an n-order mode optical field, generating two modulation sidebands through an EOM electro-optic modulator, and using two electric mirror frames with high reflectivity (one of which excites the error signal by tilting) to retain the high-order modes of n+1 and n-1 orders. Second, the modulated optical field is incident into the resonator, where it is resonantly enhanced before being reflected out by the input mirror. It is ultimately detected by a dual-quadrant photodetector (to simplify the study, this paper only focuses on the deflection pointing of the laser in the horizontal direction). After demodulation, the pointing alignment error signal is obtained through a low-pass filter. Third, the relationship between error signal and laser deflection angle in the horizontal deflection direction is studied through classical methods. Further, the scheme is quantized and the signal-to-noise ratio of the error signal is made equal to 1. Finally, the influence of the mode order of the high-order mode light field and the incident light power on the minimum deflection angle of the laser in the horizontal deflection direction is investigated.Results and DiscussionsIn the process of detecting gravitational waves in space, external environmental vibrations can cause the incident laser in the resonant cavity of the gravitational wave interferometer arm to deviate from the cavity axis, resulting in a decrease in detection sensitivity. This article proposes a scheme for enhancing laser alignment error signals by injecting high-order mode optical fields into an optical resonant cavity to address the issue of laser pointing stability in interferometric measurements. This scheme is used to improve the stability of laser pointing alignment and reduce laser pointing deviation caused by external environmental vibrations. The process of extracting the error signal is first subjected to classical processing to obtain the error signal diagram generated by different laser deflection angles as shown in Fig. 2. From this figure, the larger the deflection angle of the laser in the horizontal direction, the larger the alignment error signal obtained, and the higher the mode order, the more sensitive the error signal. The process of extracting the error signal is further quantized to obtain a three-dimensional graph of the minimum tilt angle as a function of mode order and incident light power, as shown in Fig. 3. From this figure, increasing the orders of high-order Hermitian Gaussian modes or the incident light power can reduce the deflection angle of the laser relative to the cavity axis. The smaller the minimum deflection angle, the greater the anti-interference ability of the system. This is of great significance for reducing error accumulation, improving system robustness, maintaining high stability and accuracy of laser systems, and improving response speed.ConclusionsThe laser directional stability is crucial for improving the detection accuracy of gravitational waves. By using classic methods such as precise optical alignment, advanced anti-vibration technology, and automated control systems, the laser directional stability can be effectively improved, ensuring clear and accurate interference signals. However, it is still limited by the classical physical limits, making it difficult to achieve extremely high accuracy. The laser alignment error signal enhancement scheme proposed in this article can further achieve higher laser pointing stability and meets high-precision detection requirements. By using two different methods, classical and quantum, the results show that when the laser deviates horizontally due to external environmental vibrations, the larger the deflection angle, the greater the alignment error signal, and the higher the mode order, the more sensitive the error signal. Increasing the mode order of the high-order mode light field or increasing the incident light power reduces the minimum deflection angle of the laser in the horizontal direction. This not only helps to improve the laser directional stability and reduce noise interference, but also enhances the coupling efficiency between the laser and the resonant cavity, thereby improving the sensitivity of the detector to space gravitational wave detection. The theoretical method proposed in this article is also applicable to the situation where the laser tilts in the longitudinal direction as well as to the situation where the laser tilts simultaneously in the horizontal direction and in the longitudinal direction. If studying the situation in two directions, a four-quadrant detector can be used in experiments to detect and extract error signals. At the same time, existing research has shown that introducing high-order mode light fields in gravitational wave detection research can also reduce the influence of thermal noise. Using high-order modes for gravitational wave detection is a win-win solution. In addition, using the proposed scheme in this article, one can obtain a new method to improve the accuracy of yaw angle measurement.