ObjectiveTo further decrease lithographic resolution, specific illumination modes are required for different mask patterns. The freeform pupil-shaping module is a standard component of lithography illumination systems at the 28 nm node and below. To ensure stable and uniform energy distribution at the optical pupil, a homogenization unit is used before the freeform pupil-shaping module. The current mainstream solution involves using a microlens array (MLA) for homogenization. The MLA divides the incident beam into a multitude of sub-beams, which are superimposed on the back focal plane of the condenser to obtain a homogeneous illumination field. Although a low-spatial-coherence excimer laser is used in lithography, it still produces interference patterns in the back focal plane of the condenser, significantly impacting pupil performance. In this paper, we propose a decoherence method based on the deformation design of MLAs that improves the uniformity without introducing additional elements.MethodsIn this paper, we propose a new design method for decoherent MLAs. First, considering the partial coherence of a laser, transmission of partially coherent light in the homogenization unit is modeled using mutual intensity theory. Based on the mutual intensity distribution in the back focal plane of the condenser, it can be concluded that the intensity distribution of the light field is modulated by the coherence length and related to the aperture function P(?,η). Changing this function not only affects the initial phase φ(m,n) of each sub-beam but also changes the frequency of sinc function. As a consequence, φ(m,n) affects the interference results and sinc function affects the amplitude modulation. Based on the aforementioned model, an optimized design of the mean value of the pitch size of the MLA was carried out. To increase the phase difference between the microlenses within the coherence length, degrees of freedom for pitch variation and border line tilting were introduced based on the optimized design described above.Results and DiscussionsFirst, the mean value of the pitch size of the MLA was optimized. The design results (Figs. 5 and 6) show that when the microlens pitch size is 0.5 mm, non-uniformity is at a minimum of 43.87% and energy utilization is 85.39%. While this optimization solution satisfies the energy utilization requirement of the freeform pupil-shaping module, it is not able to achieve a non-uniformity less than 40%. Introducing a small random pitch variable in the pitch size of the microlens, the design results (Figs. 8 and 9) show that non-uniformity is minimum at 41.53% and energy utilization is 84.16% at the amplitude of the pitch variation of 0.05 mm, which also satisfies the requirement for energy utilization. However, non-uniformity does not fulfill the aforementioned requirement yet. Making the microlens at the cylindrical border line in the xy plane introduces a tilt factor k, which is a random small quantity. The design results (Figs. 11 and 12) show that when the amplitude of the tilt factor is 5 μm, non-uniformity is at a minimum of 38.67%, and energy utilization is 82.74%, thereby fulfilling specifications. Combining the optimization solutions of pitch size variation and border line tilting, non-uniformity of 36.51% (Fig. 14) and energy utilization of 83.90% are achieved when the amplitude of the pitch variation is 0.03 mm and that of the tilting factor is 4 μm. This co-optimization approach results in a more significant reduction in non-uniformity, along with improved energy utilization.ConclusionsIn present paper, we propose a decoherence method based on the deformation design of MLA to improve homogeneity without introducing additional elements. First, the mean value of the pitch size of the MLA was optimally designed. Subsequently, degrees of freedom for pitch variation and border line tilting were introduced. The simulation results show that with the optimal combination of suitable pitch variation and border line tilting, non-uniformity and energy utilization reach 36.51% and 83.90%, respectively, which satisfy the requirements for the use of a freeform pupil-shaping module.

ObjectiveHigh-power fiber lasers and their sub-beam combining technology are effective for achieving high-brightness and high-power laser outputs. With the continuous improvement of output laser power and energy concentration in the research and development of high-power laser system engineering, multiple sub-beam lasers are required to operate simultaneously for system testing. The output sub-beam laser exhibits high power density, a small divergence angle, and strong destructiveness. To prevent damage to the test environment and ensure personnel safety, a laser absorption device is necessary to effectively absorb and control multi-channel high-power-density laser energy. This ensures a high-efficiency, pollution-free, and safe testing process. When a multi-channel high-power-density laser is incident on the absorber, light-field coupling can cause excessive local temperature rise inside the absorber, leading to laser melting, structural deformation, and debris attachment. These issues pollute the optical environment and damage both the absorber and the laser output end. Additionally, excessive reinjection of laser return power into the laser causes the laser to burn out. To address the effective control requirements of multi-channel high-energy lasers in high-power laser system development, a laser absorption device is designed for the test system, and its thermo-optical characteristics are analyzed through simulations and experimental studies.MethodsA novel three-channel high-power-density laser beam absorption device is designed. Unlike single-aperture absorption devices, multi-beam lasers exhibit a small divergence angle, a small spot size, high power density, and independent distribution. A discrete light-cone arrangement is employed for single-channel reflection beam expansion and multiple coupling absorption. Combined with an inner surface absorption coating and a surrounding extinction microstructure, the multi-aperture structure can independently absorb sub-beam laser energy simultaneously. Additionally, the fully sealed design of the absorption cavity allows for internal gas replacement through charging and exhaust mechanisms, ensuring the cleanliness and purity of the internal medium atmosphere while maintaining the safety of the light output. Based on beam tracing analysis, combined with the parameters of the beam-expanding cone, the absorber substrate material, the coating absorption coefficient, and the surface microstructure, the light field distribution on the internal absorption surface after coupling and superposition of the three-beam laser fields is simulated. The distribution pattern of the peak intensity and position of the internal light field, as well as the influence of the cone-tip fillet on internal light field distribution, is analyzed. The temperature rise in various regions inside and outside the absorber is quantitatively calculated using laser irradiation at 10.4 kW for 135 s. A three-beam high-power light output test is conducted to verify absorption temperature rise, anti-damage performance, and return power.Results and DiscussionsThe new laser absorber is studied using simulation analysis and experimental testing. The simulation results show that the sub-beam laser power is 3.5 kW, and the three-beams emit light simultaneously at a total power of 10.5 kW. After passing through the expanding light cone, the optical power density on each absorption surface inside the absorber is effectively attenuated. Following beam coupling, the light field is superimposed onto the absorption area. The absorbed power in the light cone area is 5418.2 W, while the sidewall absorbs 3495 W (Fig. 4). The fiber end cap installation surface absorbs 5.05 W, and the optical aperture of the fiber end cap absorbs 0.06 W (Fig. 7). The radius of the cone tip significantly influences the laser power distribution on the bottom and side surfaces but has little effect on the return power (Fig. 8). At an ambient temperature of 20 ℃, when the three-beam laser operates at 10.4 W@135 s, the highest internal temperature of 131.667 ℃ is observed near the light cone (Fig. 5). The highest external temperature of 74.4 ℃ is recorded outside the heat insulation board in the top absorption area (Fig. 6). A high-power light output test is conducted. For a single laser output of 3.5 kW@135 s, the maximum temperature rise at the end cap is 5 ℃, and the maximum temperature rise at the front end is 15.8 ℃ (Fig. 12). When the three-beam laser operates at 10.4 W@135 s, the maximum external surface temperature of the absorber reaches 79.1 ℃, with a temperature rise of 59.1 ℃, occurring on the sidewall of the absorber ring. The highest temperature location relatively aligns with the simulation results (Fig. 13). The detected return light power is 130 mW, and the return light throughout the entire system remains within the safety threshold (Fig. 11).ConclusionsTo address the challenges of multi-beam output lasers with small beam diameters, high power densities, and small divergence angles, a new three-channel high-power-density laser absorption device is designed. The device incorporates optical cone beam expansion, cavity multiple coupling absorption, and stray light suppression. Using the beam-tracing method, simulations and experimental studies are conducted to analyze the laser field distribution inside the absorber, the influence of return power, the effect of cone tip radius, and the temperature rise distribution during the light output process. The temperature distribution of the absorber aligns with the simulation results. The full-link laser return power remains below the safety threshold, and the absorption temperature rise, anti-damage capability, and laser return power suppression effects are successfully verified. This research provides valuable insights for the efficient absorption of multi-channel high-power-density lasers, the design of measurement devices, and the studies on internal anti-damage mechanisms and return-light suppression. The findings can be extended to the development of similar applications in high-power laser systems.

ObjectiveIn recent years, space laser communication technology has developed rapidly, distinguishing itself from traditional microwave communication by its compact size, lightweight design, low power consumption, high transmission rates, and superior resistance to interference. These advantages have made it a prominent area of research in the field of international space communication. Given the vast distances involved in satellite-to-satellite communication, maintaining a high-quality laser beam wavefront is crucial, which in turn places high demands on the optical system. Currently, wavefront error is the primary metric used to evaluate the design, manufacture, and alignment of the optical systems used in space laser communication terminals, without specifically considering individual aberrations. However, many scholars in the academic community have observed that different aberrations affect space laser communication in distinct ways. This study focuses on the impact of aberrations on laser communication, establishing a transmission model for space laser communication based on the far-field distribution of the complex amplitude of the optical wave. The study analyzes the effects of the cross-coupling of various aberrations on the received intensity and centroid shift, and proposes an optimal aberration tolerance allocation method for different wavefront errors. This research provides valuable insights for the development and optimization of optical systems with the goal of ensuring high-stability signal transmission in space laser communication.MethodsThis study utilized Zernike polynomials to model wavefront errors and performed optical field transmission simulations. First, a comprehensive optical field propagation model was developed, which covered the path from the transmitter to the focal plane of the receiver. An analysis demonstrated that aberrations at the transmitter could affect the centroid intensity at the focal plane of the receiver. Next, the interactions between aberrations were examined, identifying coupled aberrations among tilt, coma, defocus, and spherical aberration. Subsequently, based on the relationship between the Zernike polynomials and wavefront errors, coefficients were computed for individual aberrations under various root mean square (RMS) wavefront errors. Finally, the impact on the capture deviation and centroid intensity in the laser communication system was assessed using the derived coefficient allocation relationships, leading to the determination of optimal aberration allocation ratios for each component of the system.Results and DiscussionsSimulation analyses are conducted on the different terminals of the laser communication system. For the receiver terminal, considering the presence of cross-coupling aberrations, the impact of the aberration tolerance allocation on the received centroid intensity and capture deviation is studied. The presence of a spherical aberration and defocus at the receiver end is found to increase the received centroid intensity, with the optimal allocation ratio being 0.67 (Fig.10). It is observed that when the receiver end exhibits a combination of tilt and coma, the aberration distribution will have a compensatory effect on the capture deviation only when the total wavefront error exceeds a certain threshold (Fig. 6). For the transmission from the transmitter to the focal plane of the receiver, aberrations at the transmitter are found to have almost no impact on the received centroid shift but do affect the received focal plane intensity. Therefore, when the transmitter contains interacting aberrations, such as tilt and coma, and defocus and spherical aberration, tolerance allocation of these aberration combinations can effectively improve the capture centroid intensity (Fig.8), with fixed ratios of 0.82 and 0.43, respectively. Additionally, a universal validation of the results shows that the tolerance allocation method exhibits high stability (Figs. 7, 9, and 11).ConclusionsThis paper proposes a novel and effective tolerance allocation method for aberrations based on laser communication optical field transmission and aberration theory, which can significantly enhance the overall optical performance of laser communication systems. The impact of aberration tolerance allocation on laser communication performance includes its effects on the received centroid intensity and centroid position shift. Regarding centroid intensity, both the transmitter and receiver terminals exhibit negligible cross-coupling effects from aberrations when the wavefront error is small. However, when the wavefront error becomes large, certain specific combinations of aberrations can effectively improve the centroid intensity, even achieving a better overall performance compared to that with a smaller wavefront error. As for centroid position shift, because of the long-distance transmission, the wavefront error at the transmitter has no significant impact, and only the wavefront error at the receiver affects the performance. Similarly, when the wavefront error is large, specific combinations of aberrations can effectively mitigate the centroid shift phenomenon, leading to better alignment. The above conclusions can provide valuable guidance for the efficient development of optical systems for space laser communication to achieve superior communication performance at minimal cost, or offer detailed technical references for the active compensation of wavefront distortions, enhancing system stability and reliability.

ObjectiveDistributed fiber-optic sensing technology is crucial for monitoring various key parameters such as strain, temperature fluctuations, and vibrations. Among these technologies, Brillouin optical time-domain reflectometry (BOTDR) systems have gained prominence in fields like civil engineering, transportation, electric power, and oil and gas pipelines because of their distinct advantages. These advantages include the use of single-ended fiber-optic cables, ease of deployment, operational efficiency, and real-time continuous measurements, making them highly suitable for long-term monitoring in diverse environments. However, in practical applications, BOTDR systems often encounter various noise sources, including environmental and operational interference, which can severely compromise the accuracy of the demodulated Brillouin frequency shift (BFS) measurements. Because the system relies on detecting and demodulating weak, spontaneous Brillouin-scattering signals propagating along the sensing fiber, it is inherently susceptible to background noise interference. Therefore, effective noise mitigation and signal-to-noise ratio (SNR) enhancement are essential for improving BOTDR system performance and reliability in practical applications.MethodsWe propose a denoising algorithm that inverse free sparse Bayesian learning (IFSBL) with K-singular value decomposition (KSVD) (IFSBL-KSVD). The proposed algorithm effectively combines the adaptive sparse representation capabilities of IFSBL with the efficient iterative optimization and reconstruction advantages of KSVD. First, the IFSBL utilizes a Bayesian framework to adaptively select sparse components from the spectral-demodulated signals in a BOTDR system. This approach enables the algorithm to effectively retain the primary signal features associated with the BFS while simultaneously suppressing background noise, thereby accurately isolating the BFS signals from noise interference. Subsequently, KSVD optimizes the dictionary atoms through iterative updates based on the sparse representation provided by IFSBL. This iterative process enhances the dictionary’s ability to accurately capture and represent the characteristic signal frequencies, thus enhancing the overall noise suppression effect. By leveraging the dictionary-updating mechanism inherent in sparse coding, the IFSBL-KSVD algorithm achieves high noise-suppression capabilities while maintaining high efficiency and accuracy in BFS extraction from the BOTDR system. Thus, the proposed algorithm significantly enhances the signal quality and accuracy of frequency shift extraction, leading to better overall performance in real-world applications.Results and DiscussionsTemperature detection experiments are conducted using engineering-grade temperature-sensing fiber-optic cables, and the experimental data are analyzed and processed using the proposed algorithm. The results show that the IFSBL-KSVD algorithm significantly reduces random noise in the three-dimensional Brillouin gain spectrum (BGS) and its top view, improving data smoothness and making heating segments more distinguishable (Fig. 5). After applying the proposed algorithm, the fluctuations in individual BGS curves are notably suppressed, and their smoothness is greatly enhanced. After noise reduction, the central frequency of the BGS curve is determined more accurately, thereby aiding in the precise quantification of frequency shift variations by the BOTDR system (Fig. 6). The proposed algorithm achieves substantial noise reduction, with the SNR improving to 38.46 dB, which is 6.90 dB and 4.21 dB higher than the SNR of the original data and the data provided by the discrete cosine transform (DCT) algorithm, respectively. In the non-temperature-variable region, the fluctuation range decreases to 1.35 MHz, while that in the temperature-variable region decreases to 0.88 MHz; these reductions correspond to an improvement in temperature measurement accuracy to ±0.83 ℃ and ±0.40 ℃, respectively, with an additional runtime increase of only 26.38 s (Fig. 7). By adjusting the pulse width (50‒100 ns), the proposed algorithm enhances the SNR by 6.32 dB‒6.90 dB (Fig. 8). Furthermore, the algorithm effectively reduces the BFS standard deviation in the temperature-variable region to below 2 MHz across all pulse widths. This improvement in SNR and measurement accuracy is achieved without compromising the spatial resolution, highlighting the algorithm’s robustness and flexibility (Table 1).ConclusionsAn innovative denoising algorithm based on IFSBL and dictionary learning (i.e., KSVD) is proposed to improve the detection performance of BOTDR systems in engineering applications. The proposed algorithm exploits the adaptive sparse representation capability of IFSBL and the efficient iterative optimization feature of KSVD in dictionary learning, thereby enabling effective noise reduction for BOTDR spectral signals. Experimental results from temperature change detection using engineering-grade temperature-sensing fiber-optic cables demonstrate that the proposed algorithm significantly improves the SNR and increases the BFS detection accuracy of the BOTDR system by 2.16 MHz. Despite its improved performance, the proposed algorithm requires only an additional runtime of 26.38 s, demonstrating its high computational efficiency. These findings confirm that the proposed algorithm excels in both noise reduction and computational efficiency, significantly enhancing the overall performance of low-cost BOTDR systems. The algorithm’s high efficiency and robustness strongly support the widespread adoption of BODTR technology in complex and challenging engineering environments.

ObjectiveIn recent years, space laser communication has gradually replaced traditional microwave communication as a key research field in various countries owing to its high-speed transmission rate, excellent anti-interference and anti-interception abilities, and good confidentiality. Quadrature phase shift keying (QPSK) is widely used in space laser communication systems owing to its high spectrum utilization and strong anti-interference ability. Owing to the long-distance transmission of high-speed QPSK optical signals through the space channel, the signal power is severely attenuated, and the signal is therefore amplified at the transmitting node with high power to overcome the loss of long-distance transmission in space. However, the high-power QPSK signals show significant phase degradation under the influence of the fibre optic nonlinear effect inside the transmitting node. To relay the degraded QPSK high-speed optical signals under the premise of meeting the current application requirements, a dual-pumped nonsimplex phase-sensitive amplifier based on a microcavity optical frequency comb is proposed to relay QPSK high-speed optical signals.MethodsA coupled-wave model of signal optical and pump optical phase locking was established (Fig. 2). A numerical analysis was conducted based on this model. Based on the numerical analysis, a QPSK all-optical regeneration and multicast experimental system for a dual-pump non-simplex phase-sensitive amplifier with a microcavity optical frequency comb was designed (Fig. 5). First, a 10 Gbit/s QPSK all-optical regeneration and multicast simulation system was constructed using the VPI simulation platform to carry out a simulation analysis of the experimental system. Then, experimental verification was carried out based on the simulation analysis (Fig. 9), and conclusions were drawn.Results and DiscussionsThe results of the numerical analysis (Fig. 4) show that the pump optical power Pm affects the phase sensitivity fluctuation that and the input relative phase φr affects the phase compression effect. By controlling these parameters, the phase noise can be compressed to improve the quality of the signal. Moreover, the results of the VPI simulation analysis show that the three signals have the best integrated performance when the input relative phase is 20° and the pump optical power is 24 dBm [Fig. 7(a) and Fig. 7 (b)]. The phase-sensitive gain fluctuation is approximately 6.1 dB [Fig. 7(c)]. The final results show that the optical signal-to-noise ratio (OSNR) values of the three signals improve by 1.5 dB, 2.1 dB, and 0.6 dB, respectively, compared with the degraded signals when the BER is 10-3 and the overall performance of the three signals is optimal Fig. 8(e). Additionally, experimental verification based on simulation is carried out. First, the phase-sensitive amplification characteristics are verified by changing the relative phase by changing the pump optical phase. The results show that the signal optical power fluctuates periodically with the change of the relative phase [Fig. 11(a)] and that the phase-sensitive gain fluctuates by approximately 7.5 dB [Fig. 11(b)]. The experimental system is optimized by adjusting the phase of the pump optical within a certain range, and the three signals have the best overall performance when the phase of the pump optical is 90°, with the signal optical and one of the multicast optical signals improving by three orders of magnitude in terms of bit error rate, compared with the phase-deteriorated optical signals. The other multicast optical signal improves by one order of magnitude. When the bit error rate is 10-3, compared with the phase-degraded optical signal, the receiving sensitivities of the all-optically regenerated optical signal and the two-way multicast optical signal are improved by 1.1 dB, 1.8 dB and 0.4 dB, respectively. Hence, the simulation analysis and experimental verification show that the all-optical regeneration and multicasting scheme designed in this study simultaneously achieves the phase regeneration of QPSK optical signals and wavelength multicasting. Moreover, the performance achieved by the three optical signals is better than that of the original degraded signal.ConclusionsIn this study, a dual-pump nonsimplex phase-sensitive amplifier based on a microcavity optical frequency comb is proposed to relay degraded high-speed QPSK. A coupled wave model of the optical signal and pump optical phase locking is constructed. First, a numerical analysis is carried out, and the results show that the effect of phase regeneration can be optimized by controlling the pump optical power, relative phase, and other parameters. The QPSK all-optical regeneration and multicast experimental system are designed based on these results to regenerate the degraded QPSK high-speed optical signals all-optically and generate two multicast optical signals. The simulation analysis and experimental verification show that the proposed scheme achieves phase compression for phase-degraded signals, improves the signal performance, and simultaneously copies two optical signals containing the same modulation information for multicast output. This scheme significantly improves the quality of transmitted signals and provides an innovative solution for the multiplexing of signals in space networks, thereby providing strong support for the enhancement of the reliability and scalability of future space laser communication networks.

ObjectiveFiber optic interferometric sensors (FOIS) are characterized by numerous advantages, including high sensitivity, large dynamic range, compact size, lightweight construction, and immunity to electromagnetic interference. However, in practical applications, the continuously fluctuating external environment can significantly disrupt the FOIS array, particularly affecting the optical transmission path. This disruption introduces additional noise, which negatively impacts detection capabilities. The phase generated carrier (PGC) algorithm exhibits superior suppression of common mode noise generated by optical paths, owing to its compatibility with nearly-balanced interferometers, thereby surpassing conventional heterodyne techniques. Furthermore, it utilizes a singular optical pulse for both transmission and reception, which provides advantages over the 3×3 method in terms of time-division multiplexing and the reduction of required hardware channels. Nonetheless, the PGC algorithm must accurately calculate the phase delay and modulation depth of the received interference signal to mitigate nonlinear errors in the demodulation results. This calculation process is intricate and time-consuming, particularly in large-scale array scenarios. To address this challenge while maintaining the advantages of PGC in optical configurations and overcoming the complexities associated with parameter calculations, this paper proposes an improved demodulation technique for FOIS.MethodsThe methodology utilizes a periodic linear frequency-modulated (LFM) continuous wave to drive a singular acousto-optic modulator (AOM). This configuration produces a frequency-modulated optical pulse that experiences self-mixing interference within a nearly-balanced Michelson interferometer. Consequently, this procedure results in the generation of a difference carrier component, facilitating the heterodyne demodulation of the signal, designated as AOM-LFM heterodyne (ALH). The ALH is fully compatible with the conventional PGC algorithm in terms of optical configuration. It also supports the transmission and reception of individual optical pulse, demonstrates robustness against environmental disturbances, and achieves a time slot utilization rate approaching 100%. Furthermore, the ALH demonstrates reliability without necessitating calculations for carrier phase delay and modulation depth, significantly reducing the computational demands. To address the discrepancy in diffraction efficiency of the AOM resulting from different frequencies, an amplitude pre-distortion (APD) compensation module is incorporated. Additionally, to address the carrier frequency deviation arising from differences in the optical path difference (OPD) of the FOIS, the implementation of orthogonal signal normalization (OSN) is recommended. This paper provides a detailed discussion on the simulation of algorithmic principles, the amplitude pre-distortion of frequency modulation drive signals, the normalization of orthogonal signals, and the analysis of empirical experimental data.Results and DiscussionsThe paper systematically adjusts the phase values and observes the corresponding changes in total harmonic distortion (THD) and signal-to-noise and distortion (SINAD) in the demodulation results. The research findings indicate that as the phase delay varies from 0° to 360°, the actual variations of THD and SINAD are approximately ±3.5 dB, without significant fluctuations observed. This suggests that the ALH algorithm, similar to traditional dual-frequency heterodyne algorithms, demonstrates insensitivity to changes in the initial phase.Subsequent to the employ of the APD module, the inconsistency in amplitude among the time-division pulse lights within the array is significantly reduced. The introduced OSN module proficiently tackles the issue of orthogonal signal distortion caused by variations in optical path difference, thereby alleviating the nonlinearity present in the demodulation outcomes. The experimental results demonstrate that at a frequency of 1 kHz, the demodulation noise can be minimized to -108 dB/Hz, while the maximum dynamic range reaches 24.4 dB. Furthermore, during an uninterrupted operational period of 8 h, the amplitude variation of the array demodulation results remains below 0.4 dB, with no spurious line spectrum detected within the specified frequency band. All performance metrics satisfy the criteria for practical applications.ConclusionsThe ALH algorithm directly drives the AOM using a periodic linear frequency-modulated sine pulse signal, achieving dual modulation of both the frequency and pulse of the input light. The generated interrogation optical pulse enters the nearly balanced interferometric sensor element, where it experiences self-mixing interference, and produces a difference frequency carrier term, thereby enabling low-frequency heterodyne demodulation of external signals. The ALH scheme effectively retains the high duty cycle and robust anti-interference capabilities of the nearly balanced interference optical path, while simplifying the engineering implementation of the algorithm software. Additionally, it offers the advantage of flexible configuration for both the modulation period and the difference frequency carrier frequency, allowing it to better accommodate sensing arrays with varying application requirements. Furthermore, unlike traditional phase modulators, which necessitate high polarization maintenance and vibration resistance in the optical path, AOM devices do not require polarization-maintaining inputs. This characteristic significantly mitigates the integration challenges associated with multi-wavelength laser sources. Simultaneously, the high stability of AOM devices ensures that the entire demodulation results are devoid of spurious line spectra, while maintaining consistent demodulation amplitude and SINAD across array elements.

SignificanceAs an important electro-optical modulation technique, the optical single sideband (OSSB) modulation technique has been widely used in the fields of laser communication, LIDAR, quantum optics, and quantum sensing owing to its advantages of easy electro-optical detection, low signal noise, and high spectral efficiency. For example, in optical communication, the OSSB modulation technique not only overcomes the power-fading problem caused by the mutual interference of phases of two sidebands in optical double sideband (ODSB) modulation but also improves the system receiving sensitivity and antidispersion ability, thus providing effective technical support for broadband communication. For cold atomic interferometry, OSSB modulation technology eliminates the adverse effects of redundant sidebands introduced by phase modulation, thus resulting in low phase noise and pure spectral Raman light. It is conducive to more accurate control of the atomic phase, reduces the effect on the accuracy of cold atomic interference, and improves the contrast of interference stripes. Consequently, the accuracy of cold atom interferometry has been significantly improved. OSSB modulation technology has been realized through various schemes, including optical filtering, phase-shift interference, and other methods. However, this technology has not been summarized systematically; therefore, its theory, progress, and application must be reviewed.ProgressThe optical-filtering method achieves OSSB modulation by filtering out the sideband of the ODSB signal. This method primarily utilizes fiber Bragg gratings (FBGs) and micro-ring resonators (MRRs) for optical-frequency screening to generate OSSB signals. Both techniques suppress specific sidebands through precise spectral selection to obtain the desired single-sideband signal. The fiber gratings typically used in optical filtering are uniform fiber Bragg gratings (UFBGs), phase-shift fiber gratings (PS FBGs), and Fabry?Perot fiber gratings (F-P FBGs). The refractive-index change amplitude and change period of the UFBG fiber core remain constant, and the bandwidth of the reflection spectrum is between 0.1 nm and 0.2 nm. Both PS FBGs and F-P FBGs are fabricated based on UFBGs. Extremely narrow filtering is achieved by introducing a phase-shift point or Fabry?Perot interferometer. The filtering bandwidths of the PS FBG and F-P FBG can reach less than 1 pm, which are three orders of magnitude higher than that of the UFBG, thus resulting in better filtering performance. The small footprint of the MRR allows it to be easily integrated into a single chip or photonic integrated circuits, thus enabling highly integrated optical systems. Additionally, the filtering characteristics of the MRR can be adjusted by fine-tuning the size of the ring or the environmental conditions, which provides a certain degree of flexibility. However, when the input power is extremely high, the MRR may exhibit nonlinear effects, such as four-wave mixing, which deteriorates its filtering performance. Moreover, the filtering bandwidth of the MRR is limited by its quality factor, which renders it difficult to achieve a wider bandwidth. Both the FBG and the MRR are sensitive to the ambient-temperature change, which results in transmission spectral drifts and affects the modulation. Thus, temperature control is required to stabilize the filtering characteristics. This paper summarizes the research status of OSSB modulation techniques based on the optical-filtering method (Table 1).The phase-shift interferometry method allows different beams to coincide and interfere in space by setting the driving conditions of the electro-optic modulator [dual-drive Mach-Zehnder modulator (DDMZM) or in-phase and quadrature (IQ) modulator] and precisely controlling the phases of different branched light waves; subsequently, the OSSB signal is generated by precisely controlling the phase difference. The DDMZM-based OSSB modulation can operate in a wide operating bandwidth for applications in different frequency ranges, thus allowing a large modulation depth to be realized. The DDMZM offers high filtering flexibility. However, it is easily affected by the external environment, thus resulting in subpar filtering stability. Therefore, the modulator filtering performance must be stabilized via temperature control; however, this increases the system complexity. Moreover, the OCSR of the OSSB signal generated by this method depends only on the modulation index, which renders further performance optimization challenging. The IQ modulator-based OSSB modulation technique allows the OCSR to be tuned within a wide range by controlling the bias voltage and the power of the radio frequency drive signal. However, the IQ modulator has a complex structure and requires multiple drive circuits. Moreover, its optical transmission loss can exceed 20 dB. Meanwhile, the electro-optic modulator is easily affected by the external environment, thus causing the optimal operating point to drift; however, this can be overcome via automatic bias control. We summarize the main technical indicators of the OSSB modulation technique based on phase-shift interferometry in Table 2.In addition to the methods above, OSSB modulation can be realized using Serrrodyne modulation, Sagnac interferometry, stimulated Brillouin scattering, and electro-absorptive modulation methods, which have been demonstrated experimentally.Conclusions and ProspectsThis paper reviews the research progress of OSSB modulation techniques. We first introduced the OSSB signal characteristics and modulation methods; subsequently, we described the principles and research progress of each modulation method. By systematically reviewing the related literature, we focused on analyzing and comparing the principles of the optical-filtering and phase-shift interferometry methods as well as their main technical indicators. Combined with other OSSB modulation methods, we elaborated the current status of their applications as well as their development trends and technical bottlenecks. Additionally, we highlighted the key development direction of on-chip integrated OSSB modulators. Owing to the rapid development of thin-film lithium niobate platforms, the prospect of fabricating large-bandwidth high-performance electro-optical modulators based on thin-film lithium niobate materials is promising.

ObjectiveThe demand for high capacity and large instantaneous bandwidth has driven radio frequency (RF) systems to operate at higher frequencies and in a greater number of bands, thereby placing more stringent requirements on microwave frequency conversion technology. However, the traditional electronic frequency conversion methods cannot meet the current demand due to its limited frequency and bandwidth, poor tunability, complex system, and susceptibility to electromagnetic interference, making it difficult to realize high-precision frequency conversion with ultra-broadband and large spans. Microwave photonic technology, which effectively utilizes the advantages of broadband, high-speed, low power consumption, and resistance to electromagnetic interference in the optical domain, can successfully address the challenges inherent in traditional electronic solutions. However, this technology exhibits certain deficiencies in precision tuning, while traditional electronic methods achieve high precision at the expense of being unable to realize ultra-broadband and large-span frequency conversion. The scheme proposed in this study aims to realize the high-precision frequency conversion of broadband microwave signals over a large span with a small volume and simple structure, breaking through the “electronic bottleneck” and solving electromagnetic interference and other problems in the traditional scheme.MethodsIn this study, a parallel multichannel joint optimization scheme with photonic-electronic collaboration is proposed. This approach maximizes the inherent advantages of the optical domain, such as broad bandwidth, extensive dynamic range, and resistance to electromagnetic interference, as well as the precise and flexible characteristics of the electronic domain, thereby achieving a large-span, high-precision frequency conversion of broadband signals. The system is mainly composed of three parts: 1) optical frequency comb generation, 2) channelization filtering and channel selection, and 3) frequency shifting and signal loading. First, two Mach?Zehnder modulators (MZMs) were utilized to generate optical frequency combs (OFCs) with free spectral ranges (FSRs) of 25 and 30 GHz, respectively, which served as local oscillators (LOs) for frequency conversion. Subsequently, channelization filtering and channel selection were performed using a 1×13 demultiplexer and 13×1 high-speed optical switch to manage the switching of the frequency channels and thereby obtain the signal carrier and LO. Finally, dual parallel MZMs (DP-MZMs) were employed to modulate the signal onto the carrier and control the frequency shift of the local oscillator. The modulation format was carrier-suppressed single-sideband modulation. Frequency conversion was then realized using a photodetector (PD) after the signal and LO were combined. Through theoretical analysis and simulation experiments, we verified that the proposed scheme is capable of large-span high-precision broadband frequency conversion.Results and DiscussionsTo verify the feasibility of the proposed scheme, we established an experimental simulation platform for the frequency conversion system (Figs. 1 and 3), with detailed parameter settings listed in Table 1. First, we analyzed the frequency conversion range. By setting input signal frequencies to 3 GHz and 5 GHz, the simulation results (Fig. 6) demonstrated converted signals spanning 8 to 68 GHz and 10 to 70 GHz, both with 5 GHz intervals. The carrier-to-noise ratios (CNRs) of the two signals exceeded 50.6 dB and 49.7 dB, respectively, while power fluctuations were 2.14 dB and 2.00 dB. Next, we tested 512 MSym/s QPSK input signals at 3 GHz and 5 GHz. As shown in Fig. 6, the system output exhibited signal-to-noise ratios (SNRs) exceeding 31.2 dB and 30.6 dB, respectively, with power fluctuations of 3.19 dB and 4.59 dB. To further evaluate signal quality across modulation formats, input signals were configured as follows: 5 GHz 512 MSym/s QPSK, 300 MSym/s 8PSK, and 200 MSym/s 16QAM. After conversion to 70 GHz, the error vector magnitudes (EVMs) for these formats (Fig. 7) were 6.97%, 7.51%, and 9.62%, respectively, all meeting communication quality standards. Finally, we assessed precise frequency shifting capability using a 5 GHz 512 MSym/s QPSK signal with frequency shifts ranging from 100 MHz to 500 MHz. The results (Fig. 8) showed slight signal quality degradation post-shift. These findings confirm that the proposed scheme achieves large-span, high-precision frequency conversion while maintaining signal integrity.ConclusionsTo address the limitations of traditional electronic frequency conversion technologies, including restricted frequency bandwidth, large size, high energy consumption, poor tunability, and susceptibility to electromagnetic interference, this study proposed a photonic-electronic collaborative multichannel parallel microwave photonic frequency conversion scheme. This scheme enables the large-span, high-precision frequency conversion of broadband signals while ensuring conversion quality.The feasibility of the proposed scheme was first demonstrated through a theoretical derivation, followed by a simulation validation of the functionality of the system. The frequency conversion of broadband signals was then verified under a conversion range of 10 to 70 GHz, covering the C, Ku, and K bands up to the EHF band. The quality of the frequency-converted signals at different rates and modulation formats was then analyzed, confirming that the converted signals meet communication quality standards. Finally, the frequency-shifting performance was validated, enabling the precise tuning of the converted signals while maintaining signal quality. The system also allows for flexible frequency selection strategies tailored to various scenarios. This endows the system with significant adaptability and potential applications in future fields such as wireless communications, radar systems, phased array antennas, and electronic warfare.

ObjectiveWith the rapid development of internet businesses and information technology, optical fiber communication has become one of the cornerstones of our rapidly developing information society. With the rise of broadband services, such as augmented reality, 5G wireless networks, and cloud computing, global data traffic is growing exponentially. However, the capacity of standard single-mode fibers is gradually approaching the Shannon limit. Multiplexing techniques, including polarization division, wavelength division multiplexing (WDM) and mode division multiplexing (MDM), are often employed to improve the capacity and transmission rate of communication systems, with extensive studies conducted on MDM technologies. The multimode switch makes MDM more flexible, which is of great importance. However, most multimode switches are mode sensitive and cannot regulate the fundamental and higher-order modes simultaneously. This paper presents a mode-insensitive thermo-optic switch based on silicon waveguides, realizing mode insensitivity by optimizing the multimode interference coupler and phase shifter, whereby the first three transverse electric (TE) modes are simultaneously regulated through the thermo-optic effect. In addition, the influence of air trenches on power consumption is discussed.MethodsThe design of the proposed mode-insensitive thermo-optic switch uses a silicon-on-insulator (SOI) chip with an optical waveguide thickness of 220 nm. The heating resistance is generated by titanium nitride (TiN). First, we simulated the relationship between different modes and waveguide widths to determine the waveguide width that can transmit the first three TE modes. The Mach-Zehnder interference (MZI) structure, composed of multimode interference couplers and insensitive phase shifters, realizes the switching of optical paths. The parameters of the multimode interference coupler (the input position of the waveguide, maximum width and length of the gradient coupler, and length of the multimode waveguide) were optimized to achieve the 3 dB splitting ratio of TE0, TE1, and TE2 modes. Subsequently, the relationship between the thermal optical coefficients of the different modes and waveguide width was simulated to determine a suitable width, to ensure that the phase change of each mode is the same at the same temperature. The waveguide temperature was varied by applying different heating powers to the heating resistor, to achieve light modulation. Finally, the influence of adding air trenches on power consumption is discussed, which has reference significance for the optimization of optical switches.Results and DiscussionsIn calculating the effective refractive indices of three modes at different widths, the TE2 mode was observed to transmit at a width of 1.2 μm, and the waveguide width was determined to be 1.45 μm. The optimized multimode interference coupler achieved a 1∶1 splitting ratio for the TE0, TE1, and TE2 modes (Fig. 2). Simulation results show that as the waveguide width increases, the thermo-optic coefficients of the first three TE modes become increasingly closer, and the difference at 4 μm is already less than 2%. Therefore, the width of the phase shifter was determined to be 4 μm [Fig. 3(c)]. Simulations of the optical switch indicated that the TE0 mode has a loss of less than 0.45 dB within the C-band, demonstrating good wavelength independence. The losses for the TE1 and TE2 modes were less than 1 dB in the range of 1550?1560 nm, with both achieving the minimum transmission loss at 1555 nm [Fig. 4(a)]. Without increasing the air trench thickness, switching of the optical signal output paths for the three modes was achieved at 22 mW [Figs. 4(b) and 4(c)]. By etching an air trench, power consumption was reduced. As the depth and width of the air trench increased, power consumption decreased to 9 mW. The extinction ratios of the three modes were greater than 20 dB (Fig. 7).ConclusionsIn this paper, a 2×2 mode optical switch based on silicon is proposed. The switch was cascaded by a mode-insensitive multimode interference coupler, a mode-insensitive phase shifter, and an S-bend waveguide. The modulation of the input optical signals of the TE0, TE1, and TE2 modes was realized at the same heating power. The effects of adding an air trench on the power consumption of the optical switch and transmission of optical signals were discussed. The results indicate that the power consumption of the optical switch was significantly reduced after adding the air trench. The extinction ratio of the three modes at 1550 nm was not less than 29 dB, and the extinction ratio of the TE0 mode in the C-band was more than 30 dB; the extinction ratio of the TE1 and TE2 modes in the C-band was more than 20 dB. The above results can provide a reference for the design of Mach?Zehnder interferometer-multimode interferometer thermo-optic switches based on SOI.

ObjectiveHigh-power ultrafast solid-state lasers play an important role in various industrial and scientific applications, including high-precision micromachining, high-resolution microscopic imaging, and medical diagnosis. However, the thermal effects in solid-state media become a limiting factor at high pumping powers, restricting the scalability of the output power in the ultrafast pulse regime. In high-power ultrafast lasers, a gain-medium geometry with high aspect ratio is critical for efficient heat dissipation. Common solid-state laser geometries, such as fibers and thin disks (TDs), are widely used for the generation and amplification of ultrafast laser pulses. Although fiber lasers offer advantages, high nonlinear effects remain a significant challenge in achieving high peak power. In contrast, TD, with favorable characteristics, is the medium of choice for directly generating high-power ultrafast femtosecond laser pulses. TD has a disk-shaped gain medium, typically with a thickness of 100?300 μm, and a much larger diameter of up to several mm. The back side of the disk is thermally coupled to a water-cooled heat sink, effectively mitigating the thermal lensing effects. The TD-geometry facilitates the direct generation of ultrafast laser pulses in mode-locked oscillators because of its good thermal management combined with small optical nonlinearities and has successfully generated femtosecond pulses using Kerr lens mode-locking (KLM) and a semiconductor saturable absorber mirror (SESAM). Although SESAM-based oscillators are not limited by average power scaling, achieving shorter pulses beyond the bandwidth limit remains challenging because of intrinsic SESAM characteristics. In contrast, the TD concept, integrated with a mode-locked (ML) regime, is the method of choice for generating pulses beyond the gain bandwidth limit, owing to its large modulation depth and ultrafast relaxation time. Thus, the study of KLM thin-disk laser (TDL) is of significant importance for generating high-power ultrafast pulses. However, because of the technical constraints related to thin-disk laser heads, most disk heads used for TDLs are sourced from the German companies Trumpf and D&G GmbH, with few reports on KLM TDLs based on domestic disk heads. The potential of domestic disk heads in high-average-power ultrafast oscillators in the femtosecond regime is yet to be fully developed and applied.MethodsIn this study, we investigated a KLM TD oscillator using a homemade thin-disk laser head that used doped Yb∶YAG crystal as the gain medium with a thickness of 150 μm and a diameter of 8.8 mm. The back end of the crystal was coated with highly reflective (HR) films at 1030 nm and 969 nm (reflectivity R>99.9%), and the front end was coated with anti-reflection (AR) films (R<0.1%). The Yb∶YAG disk head employed a 969 nm zero-phonon-line (ZPL) pumping source and a 48-pass pumping system to achieve high absorption of the pump laser (absorptivity of >95%). The crystal pump diameter was 2.3 mm. For the Kerr mode-locked-operation oscillator, a simple Z-shaped folded cavity was adopted, and the TD was placed between the HR end-mirror and output coupler (OC). For a high gain per pass, the laser beam was reflected twice through the TD using a pair of 45° mirrors, enabling an 8-pass configuration in one round trip. The mode diameters of the thin disk for the two reflections were 2 mm and 1.65 mm. To compensate for the high gain, the transmittance of the output coupling mirror was set to 15%. The total length of the cavity was about 4.8 m, and the repetition rate was 31.35 MHz. Considering the small thickness of TD and large mode size, a separate Kerr medium (KM) of 2 mm thick CaF2 plate was placed at the Brewster angle at the focal point of concave mirrors CM1 and CM2. The radius of curvature of both curved mirrors was 500 mm. A Kerr medium with a lower nonlinear refractive index and higher band gap is beneficial for obtaining high peak-power pulses and preserving the single-pulsed regime. Along with a hard aperture of 3.8 mm near the OC, anomalous group delay dispersion was introduced through highly reflective mirrors HD1 and HD2, with a total negative dispersion of -24000 fs2 per round trip.Results and DiscussionsTo start off KLM, a strong sensitivity to the resonator mode was obtained by operating the laser at the edges of the stability zones. This corresponds to an increase in the separation between the curved mirrors. At this stage, mode-locked operation was initiated by perturbing the end mirror. A stable mode-locked operation with an output power of 50.4 W at 206 W pumping was realized using 15% OC. In the laboratory environment, we recorded the pulse train using an oscilloscope, and no Q-switched mode locking was observed. The output spectrum width at full width half maximum (FWHM) was 3.01 nm, and the pulse duration was 392 fs. This corresponds to a time-bandwidth product of 0.333, which is slightly larger than the theoretical value of 0.315. The signal-to-noise ratio (SNR) of the 31.35 MHz fundamental signal in the radio frequency (RF) spectrum was 67 dB. The laser beam quality factors were measured to be Mx2=1.05 and My2=1.1, which are close to the diffraction limit. The mode-locked operation remained stable for over 30 min, with an average root mean square (RMS) power fluctuation of 1.07%.ConclusionsIn this study, a femtosecond thin-disk oscillator was demonstrated with high average power and short pulse duration using the Kerr lens mode-locking technique based on our custom-designed thin-disk head. The laser beam underwent multiple direct passes (8-passes) through the thin disk to enhance optical-to-optical conversion efficiency. The TD-KLM oscillator generated 392 fs pulses with an average power of 50.4 W at a repetition rate of 31.35 MHz, using a 969 nm ZPL pumping source with a power of 206 W. The corresponding pulse energy was 1.6 μJ. Future improvements in average power, pulse energy, and optical efficiency are anticipated by increasing the mode size of both the Kerr medium and thin disk, using larger radius of curvature (ROC) focusing mirrors, thereby increasing the transmittance of the output coupler and the number of passes through the TD per round trip. Additionally, the oscillator can be placed inside a water-cooled housing in clean, dust-free environment to decrease the influence of air and temperature fluctuations.

ObjectiveA high-power polarization-maintaining fiber laser with a linewidth in the 10 GHz range holds significant potential in beam combining applications such as coherent and spectral beam combining because of its ability to reduce the precision required for optical path control while maintaining high beam quality after spectral combination. However, the low threshold of stimulated Brillouin scattering (SBS) in fibers has become a key limiting factor in further increasing the output power of narrow-linewidth lasers. Recent advancements in phase-modulation techniques for laser linewidth broadening have demonstrated the capability of extending the linewidth of single-frequency lasers to the tens of GHz range, thereby effectively reducing the peak power associated with the SBS effect and substantially increasing the SBS threshold. In this paper, we present a high-power narrow-linewidth fiber laser system that employs pseudo-random binary sequence (PRBS) phase modulation. This method is expected to facilitate power scaling of narrow-linewidth fiber lasers within the 10 GHz linewidth range.MethodsIn this study, we carefully selected the pseudo-random binary sequence phase modulation parameters and cutoff frequency of the low-pass filter to achieve optimal suppression of stimulated Brillouin scattering for a given spectral linewidth. Spectral pre-shaping of the modulated signal was achieved through precise control of the modulation depth of the filtered PRBS signal, as well as fine-tuning of the baud rate and code pattern. This process effectively mitigates the degradation in spectral flatness caused by power fluctuations at the top of the modulated spectrum, which arise from the nonlinear response of the radio frequency (RF) amplifier and phase modulator at high frequencies. The discrete flat-top spectrum generated using this method uniformly distributes the backscattered Stokes signal among multiple sidebands, preventing any single mode from prematurely reaching the SBS threshold. Following the PRBS phase modulation, the spectrum exhibited a discrete flat-top profile, providing robust suppression of the SBS in high-power fiber lasers with linewidths below 10 GHz.Results and DiscussionsThe modulated spectrum was characterized by a steep roll-off at the out-of-band edges, with the spectral peak transitioning smoothly from sharp to full. The full width at half maximum (FWHM) of the discrete frequency comb spectrum was 8.97 GHz, and the flat-top section comprised five frequency lines with an in-band flatness of less than 1 dB. The frequency spacing between the newly generated spectral lines was consistent at 66 MHz, which is larger than the Brillouin gain bandwidth (30 MHz) of the main amplifier gain fiber. This effectively prevents overlap and crosstalk between the Brillouin gain regions caused by the longitudinal mode frequencies. The reduced coherent interaction between the optical signal and backward-propagating Stokes wave during the phonon lifetime significantly enhanced the SBS threshold. Additionally, the modulated spectrum was injected into a Yb-doped, double-clad, polarization-maintaining fiber with a core-to-cladding diameter ratio of 20/400 μm. This configuration yielded a maximum output power of 2041 W, polarization extinction ratio of 96.15%, beam quality factor of less than 1.3, and optical-to-optical conversion efficiency of 87.2%. During the power scaling process, no stimulated Brillouin scattering or mode instability was observed, and the linewidth remained stable without broadening.ConclusionsThis paper introduces a novel method for generating a discrete flat-top-modulated spectrum to broaden the linewidth of fiber lasers. By precisely controlling the modulation depth and optimizing multiple parameters to precompensate for the modulated signal, the method effectively minimizes the power fluctuations between the high- and low-frequency components of the spectrum. The discrete flat-top spectrum generated by filtered PRBS signals not only maintains the advantages of SBS suppression observed in previously reported discrete flat-top spectra but also enhances the SBS threshold by reducing phonon accumulation time through rapid π-phase transitions of the modulated signal. Furthermore, by optimizing the modal control of the gain fiber in the main amplifier and employing a counter-pumping scheme to suppress transverse mode instability (TMI), a narrow-linewidth laser output of 2041 W was achieved.

ObjectiveSeed lasers have the advantages of narrow linewidths, low noise, high-frequency stability, and tuning capabilities. They are widely used in optical frequency standards, gravitational wave detection, light-controlled phased-array radars, quantum optics, and space-coherent communication. Most recent studies, in addition to remaining in the desktop stage, have primarily focused on reducing the structure of the split crystal, increasing the output power of the seed laser, and reducing the relative intensity noise. The adaptability and long life of seed lasers in space environments have not been verified, thus limiting their application. Due to the complexity of space environments, extreme temperature changes are accompanied by vibrations and shocks. In orbit, seed lasers must maintain low-noise and stable-frequency operations, and their lifetime characteristics are crucial. Therefore, developing an integrated, low-noise, high-frequency, tunable, and high-reliability laser is necessary to satisfy the normal operational requirements of lasers in extreme space environments.MethodsA compact solid-state laser with a structure size of 62 mm×42 mm×16 mm was designed by integrating a pump source and a nonplanar ring oscillator (NPRO) crystal. Optical components such as pump chips, crystals, lenses, thermoelectric cooler (TEC), hot-face resistors, and covers were welded and encapsulated using metal welding, laser welding, and hermetic packaging technologies. The pump source adopted a main and backup dual-chip structure, and the output power of a single chip was approximately 1 W. When the main and backup chips were tasked with working independently, the output light was pumped into the crystal after focusing, which coincided with the intrinsic laser mode, and the light from the crystal was focused onto the polarization-maintaining fiber. The coupling-fiber assembly was fixed to the housing output by laser welding, and permanent magnets were glued onto the cover. Metal welding technology, laser welding technology, and hermetic packaging technology were used to weld and package the pump chips, crystals, lenses, TEC, hot-surface resistors and other optical components, as well as the cover plates.Results and DiscussionsThe performance of the compact double-chip sealed seed laser was analyzed and the results are presented as follows. When the chip is pumped at 576 mW, the output power of the seed laser and conversion efficiency reach 133.7 mW and 37.2%, respectively [Fig. 3(a)]. The linewidth frequency noise and relative intensity noise (RIN) of the seed laser were next analyzed. Results show that the seed laser linewidth is 201 Hz, the frequency noise is 5.2 Hz/Hz @10 kHz (Fig. 4), and the RIN is -170 dBc/Hz @100 MHz (Fig. 5). A narrow linewidth and low noise indicate that the seed laser has good frequency jitter and power stability. The tuning characteristics of the seed laser were next tested. Results show that the temperature tuning coefficient is -2.99 GHz/℃, and the continuous tuning range is 44.97 GHz (Fig. 6). The piezoelectric transducer (PZT) tuning coefficient is 3.34 MHz/V, and the continuous tuning range is 315 MHz (Fig. 7). The corresponding tuning method can be selected based on the specific requirements of the laser. The seed laser was then subjected to temperature, mechanical (random, sinusoidal, and shock), irradiation, and thermal vacuum tests in the space environment. Results reveal that the power change is 0.16%, and the wavelength change is 1.7 pm (Fig. 8). Following an accelerated-life test of 2400 h, the power of the laser decreases by 4.5% (Fig. 10), and the laser can be expected to work in orbit for 8 a. The linewidth, frequency noise, and RIN of the NPRO laser change only minimally and still meet the requirements for laser use (Fig. 11). Finally, the primary backup can be switched to further improve the reliability of the seed laser.ConclusionsA primary/backup compact seed laser with an output power of 260 mW, linewidth of less than 201 Hz, and RIN of -170 dBc/Hz @100 MHz was developed. The temperature tuning coefficient of the laser is -2.99 GHz/°C, and the PZT tuning coefficient is 3.34 MHz/V, which can achieve continuous tuning of 315 MHz. After completing temperature, mechanics, irradiation, and thermal vacuum tests in the space environment, the laser has a power change of 0.16% and a wavelength change of 1.7 pm. Accelerated lifetime tests were simultaneously conducted on the seed lasers to verify their performance. In addition to traditional power, a lifetime characterization method for the linewidth and noise was established. Within the acceleration lifetime of 2400 h, the laser power, linewidth, and noise changes are minimal, meeting the requirements for narrow linewidth and low-noise laser use. The expected orbital lifetime is greater than 8 a. In addition, the main/backup pump can be switched without affecting the overall seed laser performance, further improving the reliability of the laser. The results reveal that the problems of large mechanical size, large linewidth, high noise, insufficient life test data, and unclear risk of on-orbit operation of seed lasers are effectively solved, providing a test basis for the application of these lasers in gravitational wave detection, laser communication, and lidar.

ObjectiveMonolithic nonplanar ring oscillators (NPROs) are widely used in high-precision laser interferometry owing to their compact structure, low susceptibility to external perturbations, and flexible frequency-tuning capabilities. Such optical resonators are typically fabricated from single crystals. To ensure the lasing performance while maintaining a cost-effective production, the geometric tolerance of the resonator must be determined prior to its optical processing. Central to this task is identifying a self-producing eigen-optical path inside the resonator based on predefined positions and orientations of the multiple reflection planes forming the resonator.MethodsTo analyze the effects of the geometric variations of a monolithic NPRO on the intracavity eigen-optical path, we developed a technique to solve the eigen-optical-path problem. Beginning from the basic law of light reflection by flat mirrors, we showed the conditions that must be satisfied such that the path traversed by an optical beam reflecting from multiple planes is closed and self-reproducing. These conditions allow the construction of a set of matrix equations with which each reflection point on the optical path is located, thus yielding an eigen-optical path for a specific resonator geometry. Subsequently, the general procedure for analyzing the geometric tolerances of a resonator was summarized by converting the various limiting factors into constraints on the resonator geometry. These factors include but are not limited to the intracavity optical path, diffraction loss, and coupling with external optics. Following this procedure, two NPROs with different geometries (Fig. 6 and Table 1) were analyzed via numerical simulations to obtain the tolerances (Fig. 8) of the four reflecting surfaces of each resonant in terms of a set of predetermined constraints (Table 2). To demonstrate the feasibility of the proposed method, we conducted a case study in which a large translational deviation of one surface of an NPRO (Fig. 10) was observed after an initial round of optical processing, which complicated the coupling of the output laser to the external optics. The deviations and possible corrections were analyzed using the proposed method, and the effectiveness of the correction was examined.Results and DiscussionsChanges in the location of the on-plane laser spot, round-trip diffraction loss, and output-axis offset with translations of the four NPRO surfaces (h0?h3) along their normal directions were first calculated (Fig. 7) in the numerical simulation. This information, along with the corresponding constraints (Table 2), provides itemized tolerances for the four surfaces of the NPRO. Figure 8 shows a comparison of the tolerances required for two NPROs with the same geometric configuration but different sizes. For the larger resonators, the assembly restrictions impose stricter tolerances on the deviations of all optical surfaces, thus indicating that fabrication errors have a high probability of inducing alignment issues in the assembly stage. However, for the small resonators, the diffraction loss can potentially increase, which may impose a stricter tolerance. The constraints originating from the optical path and the diffraction loss result in an almost identical tolerance. This similarity is primarily because the beam spot size is smaller than the dimensions of the reflecting surface, as well as because the beam can be approximated as a geometric ray. However, in extreme cases where the dimensions of the optical surface are comparable to or smaller than the beam spot size, the diffraction loss becomes pronounced and hence must be included in the analysis of geometric tolerance. For an NPRO with a fabrication error, as shown in Fig. 10, the resultant intracavity eigen-optical path was analyzed. This analysis shows that a viable solution is to translate both the h1 and h3 surfaces inward along their normal directions by 0.23 mm, thereby restoring the original intracavity optical path and the positions of the pump and output laser beams. After the correction is implemented, the pump and output beams are within the adjustment constraints when the laser is assembled, whereas the lasing of the NPRO is unaffected.ConclusionsGeometric tolerances of monolithic NPROs were analyzed by solving the eigen-optical-path problem in systems with multiple reflecting planes. By analyzing the effect of changes in the resonator geometry on the eigen-optical path, combined with constraints on the intracavity optical path, the diffraction loss, optical alignment, and geometric tolerance of a monolithic NPRO can be analyzed and discussed. If a large geometrical deviation occurs during optical fabrication, then its effect on the optical properties of the resonator can be evaluated based on changes in the eigen-optical path, thereby providing guidance for implementing a cost-effective correction. The method introduced herein is applicable to the design and optical fabrication of laser gyroscopes and optical resonators with complex geometries.

ObjectiveDistributed feedback (DFB) lasers incorporating narrow-ridge waveguides and grating structures can effectively achieve fundamental-mode laser emission, which have broad applications in fields such as optical communication and laser ranging. Conventional DFB semiconductor lasers use buried gratings, which increase the complexity and cost of device fabrication. Researchers have employed surface gratings, such as the laterally coupled DFB (LC-DFB) laser, and enhanced laser performance by improving the grating structures and utilizing novel dielectric materials. Although a narrow-ridge waveguide can effectively confine the lateral modes of the laser and facilitate fundamental-mode operation, it results in a relatively small mode area, leading to lower output power. Therefore, narrow-ridge waveguides are often integrated with optical amplifiers to enhance the output power. However, optically integrated lasers involve complex fabrication processes and incur higher costs. Fabricating a broad-ridge waveguide is a simple and effective method for enhancing output power. However, owing to its weaker lateral mode confinement, mode competition between the fundamental and higher-order modes can reduce the output power. The lateral diffusion of carriers provides a higher gain for higher-order modes, increasing the number of lateral modes and reducing the injection efficiency, which is one of the key factors contributing to mode degradation and output power reduction. This paper proposes an LC-DFB semiconductor laser with a surface slit structure (SS-LC-DFB). Introducing the surface slit structure mitigates the accumulation of carriers in the lateral grating regions and enhances the ability of the ridge waveguide to confine higher-order lateral modes. The SS-LC-DFB laser exhibits higher output power than the LC-DFB laser and effectively suppresses the lateral modes.MethodsThe optical field distributions of both devices were simulated using the Lumerical MODE solver. With an LC-DFB laser, the fundamental mode typically concentrates its energy at the center of the waveguide, whereas higher-order modes gradually shift away from the waveguide center and extend towards the grating region as the mode order increases [Fig. 2(b)]. After introducing the slit structure [Figs. 2(c) and (d)], the energy distribution of the optical field moves further away from the center of the waveguide. As the slit widthincreases, the optical field intensity near the sides of the grating decreases, and the coupling feedback becomes insufficient, hindering higher-order modes in reaching lasing conditions. This indicates that the introduction of the slit structure improves the lateral mode discrimination of the laser. The carrier distributions and concentrations in both the LC-DFB and SS-LC-DFB lasers were simulated using the Pics3D simulation software. With the LC-DFB laser, after the current injection, significant carrier diffusion occurs in the lateral grating region [Fig. 3(a)]. In this area, the intensity of higher-order modes is relatively strong, and their coupling with carriers can lead to the lasing of higher-order modes. In contrast, with the SS-LC-DFB laser, the carrier diffusion is suppressed by the slit structure, resulting in the reduction of carriers flowing towards the side of the grating and flowing downwards. Consequently, more carriers are concentrated beneath the ridge waveguide [Fig. 3(b)]. From the perspective of the carrier concentration distribution in the active region, the carrier concentration in the ridge waveguide region of the SS-LC-DFB laser is higher than that of the LC-DFB laser [Fig. 3(c)]. This demonstrates improved carrier injection efficiency and enhanced output power of the device.Results and DiscussionsThe fabricated SS-LC-DFB laser improves the lateral mode characteristics and enhances the output power. As the injection current increases from 0.16 A to 0.8 A, the far-field optical spot profile of the SS-LC-DFB laser maintains a well-defined near-single-lobe shape (Fig. 7). By contrast, as the current increases, the mode confinement capability of the LC-DFB laser weakens, resulting in the appearance of multiple modes, indicating that the slit structure effectively suppresses the lateral modes. Figure 6 shows that the SS-LC-DFB laser exhibits superior performance over the LC-DFB laser in terms of lasing spectral mode characteristics. Figure 5 shows the continuous wave power-current-voltage (P-I-V) characteristics of the SS-LC-DFB laser at 25 ℃. At an injection current of 0.8 A, the output power of the SS-LC-DFB laser reaches 335.27 mW, which represents an increase of approximately 18.3% compared to that of the LC-DFB laser (283.01 mW). This improvement is attributed to the introduction of the slit structure, which reduces lateral carrier leakage and provides sufficient gain for the laser.ConclusionsAn LC-DFB semiconductor laser featuring a surface slit structure is fabricated. The experimental results demonstrate that the slit structure effectively confines higher-order lateral modes, improves the modal characteristics of the device, and reduces the multilobe phenomenon in the far-field optical spot while simultaneously increasing the output power. As the injection current increases, the far-field optical spot distribution of the LC-DFB laser exhibits multiple side lobes, indicating an inability to suppress higher-order lateral modes. In contrast, the far-field optical spot distribution of the SS-LC-DFB laser remains close to a single-lobe output. At 0.8 A, the output power of the SS-LC-DFB laser reaches 335.27 mW, representing an approximate 18.3% improvement compared to that of the LC-DFB laser.

ObjectiveSubnanosecond pulsed lasers with pulse durations ranging from 100 ps to 1 ns have the advantages of both high peak power and high energy, which play an important role in laser processing, laser ignition, photoacoustic imaging, nonlinear optical frequency conversion, and laser-induced breakdown spectroscopy (LIBS). Improving the output power while maintaining good beam quality has always been the focus of research on high-performance lasers, especially for high-repetition-rate lasers that encounter severe thermal effects. Passively Q-switched microchip lasers are commonly used to generate sub-nanosecond laser pulses due to their compact structure, robustness, high beam quality, good spectral purity, and low cost. However, their power scaling is strictly limited by the bonded crystal structure with double-end coatings as the cavity, as thermal management and cavity design are impracticable. Fortunately, the master oscillator power amplifier (MOPA) is an ideal alternative. In this paper, a high-beam-quality subnanosecond MOPA laser system operating at a 1-kHz repetition rate with a peak power of approximately 20 MW based on spherical aberration self-compensation is reported.MethodsThe pump absorption in the gain medium of the end-pumped amplification stage leads to a significant thermal lens effect with substantial optical aberrations, making it difficult to achieve high beam quality during high-power operation. As a guide for the experiment, the temperature distributions inside the gain media of the two-stage amplifiers are simulated, and the thermal focal lengths f1and f2 are calculated using Seidel aberration theory based on the optical path difference (OPD) caused by thermally-induced refractive index changes. A passively Q-switched Nd∶YAG/Cr∶YAG microchip laser with a cavity length of 6 mm is used as the master oscillator to generate a sub-nanosecond seed pulse. The output power of the microchip laser is 180 mW at 1 kHz, corresponding to the single-pulse energy of 180 μJ. Then, the seed pulse is sent to the amplifier stages through a collimating lens and isolator. Both amplifiers use an identical bonded YAG/Nd∶YAG/YAG crystal as the gain medium and a similar end-pumped dual-pass structure, enabled by a polarizing beam splitter (PBS), quarter-wave plate (QWP), and reflecting mirror. The linearly polarized input and output lasers are orthogonal, while the laser inside the gain medium is circularly polarized to alleviate the impact of thermally-induced birefringence. To avoid laser-induced damage, the pump spot sizes are 0.9 mm and 1.2 mm, corresponding to pump peak powers of 170 W and 200 W, respectively. The reflecting mirrors are set at distances of f1and f2 from the gain media, where the sign of the spherical aberration after single-pass amplification is reversed. In this way, the spherical aberration becomes self-compensated after dual-pass amplification. In addition, the thermal lens and reflecting mirror form a 2f imaging system exactly to guarantee good mode matching. This scheme can also be applied to multi-stage amplification systems to further improve output power while maintaining good beam quality.Results and DiscussionsSimulation results show that the temperature distributions of two end-pumped bonded crystals in the amplifier are axisymmetric along the center of the crystal, where the high-temperature region is concentrated at the front end of Nd∶YAG owing to strong absorption, resulting in a gradient distribution of the refractive index inside the crystals, and additional OPD is introduced to the incident seed pulse. The values of OPD along the radial direction caused by thermal-induced refractive index change are presented (Fig. 2). Using the Seidel aberration theory, the thermal focal lengths f1=136 mm and f2=220 mmof the two amplifier stages are calculated based on OPD within the laser beam cross-section, which are consistent with the measured values. The two-stage amplifiers adopt a similar end-pumped dual-pass structure but with orthogonal output polarization to maintain the entire system within a tabletop size of 30 cm×70 cm (Fig. 3). The measured seed pulse possesses an average power of 180 mW, pulse width of 517 ps, and beam quality factor of M2=1.53, whereas unstable high-order modes symmetrically surrounding the fundamental mode are observed due to a relatively large pump waist (Fig. 4). The detrimental higher-order modes are effectively suppressed after amplification by optimizing the filling factor. In addition, benefiting from the self-compensation of spherical aberration and good mode matching, a high-beam-quality sub-nanosecond MOPA laser with an average power of 9.7 W and beam quality factor of M2=1.71 is obtained (Fig. 6). The total magnification reaches 54 times. The pulse width is 500 ps, corresponding to a peak power near 20 MW and coefficient of variation (CV) of power of 1.6% (Fig. 7).ConclusionsA high-beam-quality sub-nanosecond 1064-nm MOPA pulse laser with a pulse width of 500 ps, repetition rate of 1 kHz, average power of 9.7 W, and peak power of approximately 20 MW is reported. Benefiting from self-compensated spherical aberration and good mode matching, two end-pumped dual-pass power amplifier stages based on bonded YAG/Nd∶YAG/YAG crystals boost the power of the seed laser by 54 times, with a beam quality factor of M2=1.71. Owing to its simple structure, good stability, high average power, and peak power, such a MOPA system is believed to have great potential in LIBS, laser machining, and pumping nonlinear optical frequency converters.

ObjectiveChemical lasers, as a significant class of high-energy lasers, have long relied on numerical analysis for optimal design. However, the underlying processes in chemical lasers are complex and involve chemical reactions, supersonic flows, and resonant laser amplification within a cavity. Owing to their inherent complexity and strong nonlinearity, traditional numerical methods often incur high computational costs and face challenges in achieving convergence. This study focuses on the interaction between laser gain and intracavity laser fields. The forward problem involves predicting the complex laser field distribution from a given gain profile, while the inverse problem involves reconstructing the gain profile from the complex laser field distribution. Our objective is to employ deep learning techniques to address both the forward and inverse problems.MethodsThis paper proposes a substantial numerical methodology by introducing physics-informed neural networks (PINNs) to address both the forward and inverse problems in chemical lasers. The performance of the PINNs is evaluated using a paraxial wave equation, which is derived from the Helmholtz equation under the paraxial approximation and homogeneous medium assumption. Because traditional neural network optimizers cannot directly compute the gradients of complex variables, we decompose the complex-valued laser and corresponding complex-valued partial differential equations into their real and imaginary components. The network architecture consists of a 12-layer neural network, including 1 input layer, 1 output layer, and 10 hidden layers, each with 100 neurons. The Swish activation function is used in the hidden layers, and the output layer has no activation function. The Adam optimizer is employed to achieve convergence. The database contains approximately 4×105 data points for each spatial coordinate and variable. During training, the mini-batch size is set to 1×104, with a total of 105 iterations. A dynamic learning rate is adopted during training. The optimizer iteratively adjusts the network parameters and minimizes the total loss function towards the target value.Results and DiscussionsThe dataset contains 7 planes perpendicular to the laser propagation direction (z-axis). Each plane includes 241×241 uniformly distributed sampling points, which constituted a dataset of 406567 sampling points. These data are obtained through numerical calculations in MATLAB, where the fast Fourier transform algorithm is used to simulate laser propagation within the resonant cavity. However, residuals exist between the numerically computed data and governing equation, with an average residual of 13.71% for the real part and 14.32% for the imaginary part. In the forward problem, the intracavity gain distribution and initial laser distribution (the first plane along the laser propagation direction) are known, and the laser field distribution on subsequent planes is predicted using PINNs. The PINN-based approach achieves relative errors of 2.82% and 6.76% for the real and imaginary components of the complex laser field, respectively. Moreover, PINNs significantly outperform traditional numerical methods in terms of computational efficiency, reducing the inference time from 17.6 s to 0.43 s. In the inverse problem, a complex laser field distribution across the 7 planes is given, and PINNs are used to reconstruct the intracavity gain distribution. The average relative error between the PINN-predicted and numerically-obtained gain distributions is 17.98%. By incorporating the boundary gain as a label, the relative error of the predicted gain decreases to 6.78%. Additionally, if the homogeneous medium assumption is applied to the active resonant cavity model, it is essential that the data be sampled from the equiphase surface to obtain accurate results when using the PINNs to solve both the forward and inverse problems. This reflects an inherent property of PINNs: the governing equations in the loss function must accurately represent the physical laws governing the system without the inclusion of empirical terms or approximations. However, in engineering practice, it is often challenging to obtain complete control equations and precise coefficients, which limits the broader applicability of PINNs in real-world engineering. Therefore, future research should focus on developing new methods for the numerical simulation of chemical lasers that integrate both physical laws and data-driven approaches, particularly in cases where some detailed physics is unavailable.ConclusionsThis paper presents a numerical study of chemical lasers using PINNs. Focusing on the active paraxial wave equation, the forward and inverse problems of intracavity complex-valued laser fields are addressed using PINNs. Although this study specifically targets chemical lasers, the methodology is generalizable to calculating the gain distribution and complex laser fields in any laser cavity. During the training of neural networks, optimizers cannot differentiate between complex numbers. Therefore, the complex laser field and associated partial differential equations are decomposed into their real and imaginary components. The results demonstrate that, in the forward problem, the PINNs accurately predict the laser field distribution and significantly enhance the computational efficiency. In the inverse problem, PINNs successfully reconstruct the intracavity gain distribution, a task that traditional numerical methods cannot achieve, and further improve the accuracy by incorporating known boundary conditions. The accurate and efficient solutions provided by PINNs for both the forward and inverse problems offer new approaches for the design and optimization of lasers.

ObjectiveLasers are widely used in traditional interferometry due to their high coherence. However, good coherence leads to multi-surface crosstalk, and optical components such as parallel plates, prisms and thin films cannot be directly measured. Using short-coherence lasers as light sources can isolate non-measurement surfaces and realize direct measurement of such special optical components. Compared with the wavelength stability of 0.0001 nm of He-Ne lasers, the stability of short-coherence semiconductor laser is still not good enough, limiting its application in high-precision interferometry scenarios. The temperature of short coherence semiconductor laser directly affects its wavelength, spectral width, and power, influencing the accuracy of the measurement system. At the same time, the slow response speed and poor resistance to environmental disturbances also make the use of short coherence semiconductor lasers poor. The performance can be improved by proportional-integral-derivative (PID) algorithm, but the parameter adjustment process takes a lot of time, and the temperature control accuracy is difficult to reach below 0.01 ℃. The temperature-current dual closed-loop control can achieve a temperature control accuracy of 0.002 ℃, but the structure is complex and difficult to implement. Here we use fuzzy sliding mode control to improve the temperature control performance and enhance the stability and response speed of short coherence semiconductor lasers.MethodsAiming at the stability of temperature control, the principles of semiconductor coolers and thermistors are studied, and the physical model of the temperature control system is established. Sliding mode control is used to improve the control effect and robustness of the temperature control system, and fuzzy control is combined to change the approach rate to speed up the response speed. Two semiconductor coolers are used to independently control the upper and lower surface temperatures of the semiconductor laser diode to further speed up the response speed and enhance the robustness. The simulation results show that compared with sliding mode control and PID control, fuzzy sliding mode control has fast response speed, small overshoot, and high stability. A verification experiment is built to collect temperature information through a negative temperature coefficient thermistor, and the control voltage is outputted after running the fuzzy sliding mode control algorithm on the microcontroller control unit. After the control voltage passes through the 20 bit digital-to-analog converter, the analog signal is transmitted to the semiconductor cooler driver, so that it drives the semiconductor cooler to control the laser temperature. There is a monitoring thermistor in the laser, and the temperature information is collected and recorded as the temperature measurement result through a digital multimeter and a computer. The laser is connected to the power meter and spectrometer to measure its power, central wavelength, and spectral width stabilities.Results and Discussions The laser was tested using three algorithmsfuzzy sliding mode control, sliding mode control, and PID control. The temperature measurement results are shown in Fig. 9. The experiment shows that the rise time of fuzzy sliding mode control is 6.1 s, the steady-state time is 3.3 s, and the overshoot is 0.04%. Fuzzy sliding mode control algorithm has the characteristics of fast response speed and small overshoot. In contrast, the steady-state time and rise time of sliding mode control are longer, and the response speed is slow. PID control has more serious oscillations at the beginning, and its overshoot is larger. The comprehensive performance of fuzzy sliding mode control is the best. After the laser using fuzzy sliding mode control enters the steady-state temperature range, the temperature is continuously monitored for 6 h. The temperature control accuracy is measured to be ±0.003 ℃, and the temperature fluctuation range is 0.004 ℃, indicating the fuzzy sliding mode control algorithm has good temperature stability. Spectrum and power measurements are performed on the short coherence semiconductor laser using fuzzy sliding mode control. The central wavelength stability of the short coherent semiconductor laser is better than 0.00032%, the spectral width stability is better than 0.31%, and the power stability is 0.18%, indicating it has good performance stability.ConclusionsBased on the principles of semiconductor refrigerators and thermistors, this study establishes a physical model of the temperature control system. Fuzzy sliding mode control is used to improve the stability and response speed of the temperature control system, and an experiment is built based on the single-chip microcomputer control unit. The experiment verifies that fuzzy sliding mode control has good temperature control response speed and stability, and the short coherent semiconductor laser using fuzzy sliding mode control has good spectral and power stabilities. The fuzzy sliding mode control algorithm proposed in this study provides a reference for the design and optimization of semiconductor laser temperature control algorithms.

ObjectiveAs one of the most representative families of structured light, high-order Hermite?Gaussian (HG) mode lasers have garnered increasing interest because of their importance in cutting-edge applications, including laser communication, gravity wave detection, and quantum optics. The most commonly used technique for generating HG-mode lasers is off-axis pumping, which is based on different sizes (intensity distributions) of different orders of HG modes. Because the HG beams have their maximum intensities at the outermost peaks with the pump beam deviating from the axis of the laser cavity, the high-order modes with maxima close to the pump spot have higher overlap with the pump beam than the other modes, thereby dominating the lasing. Using this simple and efficient approach, researchers have demonstrated certain very high-order HG modes with at least one mode index of greater than 100. However, generating two-dimensional (2D) HG-mode beams with two non-zero mode indices remains challenging. When the pump beam deviates from the cavity axis in two orthogonal directions, the lasers operate in a tilted one-dimensional (1D) mode rather than in two 2D modes. Therefore, the generation of 2D HG mode to date has usually relied on complex precision pump shaping, with the HG25,27 based on a modulated pump beam demonstrating the highest order with an optical efficiency of only 0.2%. In this study, we propose a simple method to generate well-controllable very-high-order 2D HG modes via an off-axis pump by confining the eigenmodes of the cavity employing astigmatism.MethodsAs mentioned above, 2D pump displacement does not excite the 2D HG modes but tilts the 1D modes. This is because of the cylindrical symmetry of the laser cavity. A cylindrically symmetric cavity can support both 2D and tilted 1D modes. In other words, the 2D pump displacement in a cylindrically symmetric system is equivalent to the 1D pump displacement after coordinate transformation, as shown in Fig.1. Therefore, generating 2D HG modes via 2D off-axis pumping requires breaking the symmetry by employing astigmatism. The laser cavity is depicted in Fig. 2. The cavity of 1064 nm Nd∶YVO4 laser is a folded cavity consisting of a flat total reflector M1, a concave folding mirror M2 with a 200 mm radius of curvature, and a flat output coupler with a transmittance of T=3% at a laser wavelength of 1064 nm. The full fold angle was 2θ=20°. The pump beam delivered from a fiber-coupled diode laser at 878.6 nm was focused onto a 0.5% (atomic fraction) doped, 5 mm×5 mm×8 mm Nd∶YVO4 crystal with a spot radius of 100 μm. Because concave folding mirror M2 has different effective focal powers in the tangential and sagittal planes, that is, astigmatism, the cylindrical symmetry is broken. In this system, the eigensolution of the Helmholtz equation is confined to the HG modes along the directions of the two astigmatic symmetric axes. The tilted 1D HG modes are no longer the eigenmodes of the cavity, in that, they do not self-reproduce after a round trip in the cavity and experience losses. In this case, a simple 2D pump displacement excites the 2D HG modes.Results and DiscussionsWhen the position of the pump spot deviates from the cavity axis, the oscillating mode of the laser changes from the fundamental mode to higher order HG modes, and the 2D HG modes are obtained by displacing the pump in both x and y directions, as expected. The relationship between the mode order and pump position aligns well with the theoretical calculations based on the overlap integral. The highest order HG214,216 is obtained with the pump spot displaced from the cavity axis by 1.9 mm in both x and y directions, as shown in Fig. 3, which is an order of magnitude higher than the previously demonstrated 2D HG modes. The laser threshold is 36 mW for the fundamental mode and gradually increases with the mode order as determined by the pump displacement. The threshold and slope efficiency of the HG214,216 mode laser are 1.74 W and 13.4%, respectively.ConclusionsIn this study, an ultra-high-order 2D HG-mode laser output is realized for the first time. By introducing astigmatism to confine the eigenmodes of the laser cavity, 2D HG modes are obtained by simple off-axis pumping, and the HG214,216 achieves its highest-order mode with a watt-level pump power. The well-controllable HG-mode laser also provides a basis for generating Laguerre?Gaussian (LGp,l) mode vortices with controllable angular and radial indices through astigmatic mode conversion, significantly expanding the degrees of freedom in structured light field manipulation.

ObjectiveThe small geometric size and complex spatial distribution of gas film holes in the hot-end components of aircraft engines make it essential to use digital image correlation (DIC) methods to investigate deformation localization and its effects on mechanical behavior. This process requires the preparation of uniformly fine speckle patterns at the micrometer level to enhance spatial resolution and strain measurement accuracy. Among the available techniques, the spraying method has become a preferred approach for speckle preparation due to its cost-effectiveness and adaptability. However, optimizing spray parameters to achieve small, uniformly distributed speckles is often hindered by limitations related to experimental conditions and atomization devices. The aerodynamic atomization characteristics of fluids reveal that droplet size depends on atomization parameters (e.g., air-liquid flow ratio, air pressure) and liquid properties (e.g., viscosity, surface tension).To address the challenges of refining and homogenizing speckle size using the spraying method, this study modifies the viscosity and surface tension of the premixed solution. These adjustments improve the speckle size and enhance its distribution uniformity, ensuring sufficient resolution and precision for characterizing deformation around the holes.MethodsTo address the challenges of refining speckle size and achieving uniformity in speckle preparation via the spraying method, this study prepared smaller and more uniformly distributed speckles by modulating the liquid properties—specifically viscosity and surface tension—of the premixed solution based on optimized spray process parameters. The viscosity and surface tension of acrylic paint-water solutions at various ratios were measured using a viscometer and a plate tensiometer, respectively. Pneumatic atomization tests were subsequently conducted using a twin-fluid air-assisted airbrush under different spray parameters, with droplet size distribution analyzed using a laser diffraction analyzer. A correlation model was developed to link droplet characteristic diameters (Dv0.5 and Dv0.9) with parameters such as the air-liquid flow ratio (ALR), Reynolds number, and Weber number. The model demonstrated the influence of liquid properties, including the viscosity and surface tension of the premixed solution, and spray process parameters, such as the air-liquid flow ratio, on speckle size. This provided a framework for optimizing speckle size for improved uniformity.Results and DiscussionsUnder specific air-liquid flow ratios (ALR values of 0.5, 0.7, and 1.0), an increase in air flow rate enhances the aerodynamic forces that facilitate droplet breakup, resulting in a notable decrease in Dv0.5 and Dv0.9, as shown in Figs. 4(a) and 4(b). When the air flow rate (AFR) increases to a critical value (3.0 L/min), the refinement effect on droplet size diminishes, causing Dv0.5 and Dv0.9 to approach an asymptote. Reducing liquid viscosity (η) contributes to a decrease in the viscous forces that maintain droplet cohesion. As illustrated in Figs. 4(c) and 4(d), under higher viscosity conditions, reducing liquid viscosity gradually decreases Dv0.5 and Dv0.9. For lower viscosity conditions, the influence of viscosity on droplet size becomes more pronounced, leading to a significant reduction in Dv0.5 and Dv0.9 with decreasing liquid viscosity. The influence of liquid properties and spray parameters on droplet size can be predicted by constructing functional relationships using dimensionless numbers. The ALR reflects spray parameter influence, with higher ALR values reducing droplet size. The Reynolds number (Re) and Weber number (We) reflect the effects of liquid viscosity and surface tension, respectively. For high-viscosity liquids, such as glycerol-water mixtures (η=80 mPa·s), the exponent of Re is considerably smaller than that of We, indicating that surface tension exerts a greater influence on droplet size. In contrast, for low-viscosity liquids (η≈10 mPa·s), such as the acrylic paint-water mixture used in this study, liquid viscosity plays a more significant role in determining droplet size.ConclusionsThis study achieved refinement and homogenization of speckle size by regulating the viscosity and surface tension of the premixed solution and optimizing spray parameters. Increasing the air flow rate and reducing the liquid flow rate to enhance the air-liquid flow ratio resulted in a decrease in the average droplet size. However, the refinement effect on droplet size was also influenced by the Reynolds number and Weber number of the fluid. For speckle solutions with a viscosity of approximately 10 mPa·s and a surface tension of around 30 mN/m, the average droplet size exhibited a linear relationship with the 0.386th power of the surface tension coefficient, as influenced by the fluid Weber number. Similarly, due to the Reynolds number, the average droplet size displayed a linear relationship with the 0.699th power of the liquid viscosity, demonstrating that reducing liquid viscosity significantly decreases droplet size. Additionally, droplet size in pneumatic atomization was found to be closely correlated with speckle size, where smaller droplet sizes yielded smaller speckles. The statistical mean and variance of speckle sizes were directly proportional to the droplet characteristic sizes Dv0.5 and Dv0.9-Dv0.5, respectively, underscoring the critical role of droplet size in speckle refinement.

ObjectiveBecause of its advantages of non-contact, flexibility, and high measurement accuracy, phase-shift profilometry is widely used to obtain three-dimensional shape information, which is particularly valuable in the fields of industrial inspection, precision manufacturing, and medical imaging. However, traditional phase-shift fringe calibration methods involve cumbersome steps, high error sensitivity, and high time consumption. To solve these problems, a polynomial calibration model is introduced to improve calibration accuracy. Theoretically, the higher the order of the calibration model, the higher the 3D reconstruction accuracy. However, as the order of the calibration model increases, the number of parameters grows rapidly. For example, the third-order polynomial calibration model needs to fit 60 parameters, which not only increases the computational complexity but also leads to computational instability, which in turn affects the calibration accuracy and computational efficiency. Therefore, there is an urgent need for an algorithm that can quickly solve the high-order polynomial calibration model to improve the accuracy and efficiency of 3D reconstruction methods based on polynomial calibration models. In this paper, we propose a fast calibration method for fringe projection based on high-order polynomial models, which has both the efficient iterative property of the stochastic sparse Kaczmarz algorithm and the selective strategy of the greedy algorithm, realizing fast fitting of high-order polynomial calibration models and thus improving the computational efficiency and accuracy of 3D reconstruction.MethodsIn this paper, a fast calibration method for high-order polynomial calibration models is proposed with the aim of addressing the cumbersome steps, time-consuming computation, and low accuracy in the calibration of traditional phase-shift profilometry (PSP) systems. First, based on the construction of a high-order polynomial calibration model, the sparse greedy random Kaczmarz algorithm (SGRK) is used to fit the model parameters and obtain the coefficient matrix of the calibration model. This algorithm combines the efficient iterative properties of the stochastic sparse Kaczmarz algorithm with the selective strategy of the greedy algorithm, which significantly improves the speed of model fitting while ensuring computational accuracy and stability. Specifically, the method establishes the relationship among object 3D coordinates, pixel coordinates, and their phases through polynomial fitting, thus realizing fast optimization of high-order polynomial models. The application of the algorithm not only accelerates the calibration process but also effectively reduces the computational complexity and avoids the computational instability and efficiency bottlenecks that may occur in traditional methods. Ultimately, by substituting the pixel coordinates of the object fringe image with the corresponding absolute phase into the polynomial model, a high-precision 3D reconstruction of the object is accomplished. The proposed method provides a more efficient and accurate calibration solution for PSP systems, which has important theoretical significance and a wide range of practical applications, particularly in the fields of industrial inspection and precision manufacturing.Results and DiscussionsTraditional polynomial-fitting methods often face problems such as computational speed degradation and unstable computational results, which limit their wide application in complex applications. Therefore, this paper proposes a high-order polynomial calibration method that incorporates the SGRK algorithm. Compared with the traditional least squares fitting method (LSM), the SGRK algorithm significantly improves the computational efficiency and stability through its efficient iterative property and greedy strategy and successfully overcomes the problems of slow computation speed and poor instability that exist in the traditional method. With this method, the fitting of high-order polynomial models can be completed in a shorter time, which significantly improves the speed (Tables 1 and 2) and accuracy (Figs. 6 and 7) of 3D reconstruction. The experimental results verify that the proposed method can effectively reduce the calibration time and significantly improve the reconstruction accuracy while ensuring the calibration accuracy (Table 3). In different scenarios, the proposed method shows obvious advantages compared with the traditional calibration method (Table 3 and Fig. 8), particularly when dealing with complex geometries, and the calibration error and reconstruction accuracy are significantly improved (Fig. 9). By optimizing the iterative process of the algorithm, the proposed method not only improves the overall computational efficiency but also effectively copes with the demand for high-precision and high-efficiency 3D reconstruction.ConclusionsIn conclusion, this paper proposes a fast calibration method based on the SGRK algorithm, which effectively solves a series of problems in traditional phase-shift profilometry calibration. By introducing the SGRK algorithm, the fitting efficiency and accuracy of the high-order polynomial calibration model are significantly improved, providing new ideas and methods for the development of 3D reconstruction technology. The experimental results verify the advantages of the proposed method in terms of calibration speed and 3D reconstruction accuracy, indicating that the method has important application value, especially in fields requiring efficient and accurate 3D reconstruction, such as cultural relic protection and biomedicine.

ObjectiveAberrations in optical systems are key factors that influence image quality and optical performance. With the advancement of optical technology, precision optical systems are increasingly being used in various fields, such as remote sensing imaging, medical imaging, and machine vision, where controlling aberrations is particularly essential. In optical systems with reflective devices, such as large astronomical telescopes, the aperture is often designed to be large to achieve enhanced resolution, with the primary mirror typically made up of multiple segmented submirrors. Manufacturing and alignment errors can influence the co-phasing of these submirrors, making reflective system’s aberration measurement and correction crucial in optical engineering. Although aberrations are inherent to optical systems, deviations introduced during the manufacturing and alignment of optical components can also contribute to additional aberrations. Therefore, accurately measuring and analyzing the inherent and additional aberrations of the reflective system can improve the manufacturing process of optical components, optimize system alignment, and enhance the optical system performance. The aberration measurement and analysis process is vital for ensuring high-precision, high-resolution imaging. Traditional measurement methods, such as Foucault knife-edge testing, Ronchi testing, star testing, interferometry, and Shack?Hartmann testing, are used for aberration analysis. Among these, Foucault, Ronchi, and star testing are primarily used for qualitative analysis. Interferometry, a commonly used high-precision measurement method, calculates aberrations in the system from observations of changes in the shape and number of interference fringes. However, interferometric testing has a limited dynamic range, is sensitive to environmental influences, and is expensive, making it impractical for large mirror alignments. Shack?Hartmann testing samples the wavefront using an array of lenses to obtain wavefront slope information. The wavefront can be reconstructed from the integration of slopes, thereby achieving aberration measurements. Although simple and highly precise, Shack?Hartmann testing is limited by the manufacturing precision of the lens array and is a cost-intensive method. Phase measuring deflectometry (PMD), a noncontact and noninterferometric measurement method, has gained popularity for high-precision measurements in various optical systems because of its high accuracy, ease of implementation, and low cost. However, for use in wavefront aberration measurements, PMD requires knowledge of the structural parameters of the optical system to perform ray tracing, which introduces pose errors or errors in complex structures. Therefore, a general method for measuring and aligning wavefront aberrations in optical systems is still lacking.MethodsFor efficient wavefront aberration measurement without knowledge of the structural parameters of an optical imaging system, a method based on vision ray calibration deflectometry is proposed in this study. The proposed method captures multiple sets of phase-shifted fringe images from a display at different postures to directly calibrate the directions of the exiting rays from the tested optical system. The wavefront aberrations are then calculated using a wavefront aberration formula, enabling in-situ alignment based on the aberration results. The feasibility of the proposed method was verified through a numerical simulation of an Ritchey?Chrétien (RC) system with a primary mirror aperture (diameter: 150 mm), a radius of curvature of -742.857 mm, and a conic constant of -1.046. The secondary mirror has a radius of curvature of -290.233 mm and a conic constant of -2.915. The wavefront aberration distribution and values obtained from the simulation closely match the theoretical calculations. The experimental results further validate the effectiveness of the proposed method for aberration measurement and alignment in a real RC system and a planoconvex lens. A comparison with interferometry results demonstrate good consistency, confirming the proposed method’s validity.Results and DiscussionsThis study presents a method for in-situ wavefront aberration measurement and alignment of optical systems that does not require system parameters. The proposed method is based on a vision ray calibration model. The method’s effectiveness of the method is validated through numerical simulations and experiments. In the numerical simulation, additional surface features were introduced into the system (Fig. 4), and the results (Fig. 5) demonstrate that the wavefront aberrations obtained using this method are consistent with those derived from theoretical calculations, with nearly identical Zernike coefficients. In the experiment, the method was applied to align and measure an RC system with a primary mirror aperture of 150 mm. The experimental results (Fig. 9) demonstrate that after alignments, the low-order off-axis aberrations are significantly reduced, indicating that the primary and secondary mirrors are nearly coaxial. Additionally, an in-situ measurement and alignment were performed on a planoconvex lens with an effective aperture of approximately 60 mm. The experimental results (Figs. 12 and 13) show that the Zernike coefficients of terms Z5?Z8 are almost zero. After alignments, the wavefront aberration measurement, with the first 10 Zernike terms removed, yields an root mean square (RMS) of 111 nm, which is consistent with the interferometry results. These findings validate the effectiveness of the vision ray calibration?based deflectometry method for wavefront aberration measurement and alignment.ConclusionsThis study proposes a method for in-situ alignment and wavefront aberration measurement for optical imaging systems that does not require structural parameters. The proposed method is based on a vision ray calibration model. The proposed method can be applied for the in-situ measurement and alignment of an RC system, as well as a planoconvex lens. This study first outlines the basic principles of wavefront aberration measurement and the application of vision ray calibration in the measurement process. A numerical simulation of the wavefront aberration measurement optical path of an RC system is presented to analyze the changes in low-order off-axis aberrations due to secondary mirror misalignment. The experimental results of in-situ wavefront aberration measurements and alignments of the RC system and planoconvex lens are presented. The results are consistent with interferometry measurements, thus validating the effectiveness of the proposed method and offering a feasible solution for multimirror system alignment.

ObjectiveThe objective of this study is to investigate the propagation dynamics of finite-energy Airy beam (FEAB) at the interface between a linear dielectric and a nonlinear medium in the fractional Schr?dinger equation (FSE). This research aims to explore the influence of system parameters, such as the Lévy index, nonlinear diffusion coefficient, guiding parameter, incident angle, and initial beam amplitude, on the propagation characteristics of FEAB. The aim is to enhance the current understanding of light-matter interactions in composite media and provide guidance for optical device design.MethodsA split-step Fourier method is employed to numerically solve the nonlinear fractional Schr?dinger equation (NLFSE) for FEAB propagating at the interface between linear and nonlinear media. The model incorporates the fractional diffraction effect by varying the Lévy index (1≤α≤2) and considers key parameters, including the nonlinear diffusion coefficient μ, guiding parameter p, incidence angle v, and initial beam amplitude A. The Airy beam is launched from the nonlinear medium (x<0) with a specific transverse position relative to the interface. The beam evolution is explored systematically with parameter variations under both standard (α=2) and fractional diffraction regimes.Results and DiscussionsThe results reveal that the transverse oscillation of FEAB at the interface strongly depends on the initial incident position and Lévy index. For example, when the incident position d increases from negative to positive, the oscillation period first decreases and then increases (Fig. 2), showing a nonlinear dependence on d. Under fractional diffraction conditions, a critical Lévy index is observed at α=1.4?1.5. Below this threshold, the beam forms a linear propagating breathing soliton, while above this threshold, transverse oscillation of localized waves is maintained. The nonlinear diffusion coefficient μ significantly affects FEAB propagation in the standard diffraction regime (α=2). Increasing μ enhances transverse oscillation and reduces the oscillation period (Fig. 4). The waveguide parameter p induces transverse oscillation and slightly shortens the oscillation period. The incidence angle v controls oscillation amplitude and period, where larger absolute values of v lead to higher oscillation amplitudes and longer periods. Lastly, the initial beam amplitude A directly influences the beam’s focusing effect, increasing localized beam intensity, reducing beam width, and shortening the transverse oscillation period.ConclusionsThis study provides a comprehensive analysis of the propagation dynamics of FEAB at the interface between linear and nonlinear media under both standard and fractional diffraction regimes. The results demonstrate the critical role of the Lévy index in determining the beam evolution mode: below a threshold value (α=1.4?1.5), the beam forms a linear propagating breathing soliton, while above the threshold, transverse oscillation is maintained. System parameters such as the nonlinear diffusion coefficient, guiding parameter, incident angle, and initial beam amplitude provide effective means to control the transverse dynamics of FEAB. These findings offer valuable theoretical insights into the active control of beam propagation at complex interfaces and hold potential applications in optical device design and optical switching.

ObjectiveAccurately identifying the vertical structure of aerosols is essential for a comprehensive understanding of atmospheric processes and climate change. Conventional aerosol-identification methods primarily include the empirical threshold method and the selective iterative boundary location (SIBYL) method, although both have certain limitations. Therefore, this paper presents an automatic aerosol-classification algorithm based on the Attention-Unet. This method is suitable for lidar-based atmospheric observations and enables the automatic identification of aerosols.MethodsTo address the existing issues, this paper proposes an improved method for cloud-aerosol identification. First, the proposed method directly uses raw lidar data as input to train an intelligent cloud-aerosol identification model, thus avoiding the information loss that occurs during the conversion of raw data into images. Second, to achieve more accurate identification results, the U-Net model architecture was enhanced via the introduction of attention mechanisms and a pyramid pooling module. The pyramid pooling module integrates multiscale feature information, thereby improving the model robustness. Meanwhile, the attention mechanism assigns different weights to features, thus enhancing the model ability to recognize details such as edges.Results and DiscussionsThis study compared the performances of four models—the FCN, SegNet, U-Net, and Attention-Unet—on the same dataset, with the results shown in Table 4. The Attention-Unet model performs exceptionally well across all evaluation metrics, achieving an overall accuracy of 96.5%, an average precision of 91.5%, and an average recall of 89.9%. By contrast, the performances of the FCN, SegNet, and U-Net are slightly inferior, thus indicating that the Attention-Unet model is more adept at managing complex information. Figure 4 presents the confusion matrix for the cloud-aerosol classification model based on the Attention-Unet. The figure shows that the classification accuracy for all categories exceeds 84%, thus indicating favorable overall classification performance.ConclusionsUsing lidar and millimeter-wave cloud radar observation data obtained from the southern suburb station of Beijing between October 2022 and May 2023, this study proposes an aerosol-cloud identification algorithm based on the Attention-Unet. The proposed algorithm was tested against the FCN, SegNet, and U-Net models on the same dataset. The results show that the proposed method achieves excellent performance in terms of both quantitative metrics and visual evaluation, thus demonstrating its high application value in aerosol research and atmospheric operational observations. Although the Attention-Unet model offers outstanding performance in the current tests, the radar parameters used in this study are limited, and factors such as humidity were not considered. Therefore, the dataset requires further optimization.

ObjectiveThe atmospheric boundary layer is a major site for human activities, necessitating the establishment of a micrometeorological support system centered on safety and efficiency, particularly regarding the impact of microscale variations in wind speed on flight safety. Coherent Doppler wind LiDAR has the advantages of high accuracy and high temporal and spatial resolution. Computational fluid dynamics (CFD) can simulate the wind field in a refined manner, particularly in the case of complex terrain or building obstructions. In the absence of field observational data, CFD can be used as a complementary method to estimate wind fields. In this paper, a CFD-based multi-source heterogeneous sensing fusion wind field construction method is proposed, which uses wind-speed data obtained from direct observations by multiple wind LiDAR devices and combines data assimilation with a CFD model to realize the real-time construction of a low-altitude three-dimensional wind field in a complex environment. This method provides refined meteorological information for developing low-altitude economies.MethodsFirst, based on the terrain, vegetation, and building information of the target area, a CFD model was constructed to obtain the flow field data of multiple sectors. After quality control of the LiDAR data, the coordinates were calculated according to the range gate, elevation angle, and azimuth angle of the LiDAR measurement points and then matched with the corresponding grid as the perception input. To ensure the effective transfer of the measured wind speed in the model while retaining an accurate description of the local wind speed and direction by CFD, different fusion strategies were adopted for the wind speed and direction of the nonperception grids. For wind speed, the weight relationship between the LiDAR observation data and CFD was used to transfer the data to non-perception grids. Specifically, the K-Nearest Neighbors (KNN) algorithm was first used to find the k closest perception grids and calculate the deduced wind-speed values of these grids. Then, the inverse distance weighted interpolation method was used to obtain the final wind-speed value. For the wind direction, the KNN algorithm was also used, and the final wind direction was obtained by performing the vector inverse distance weighted interpolation on the k wind directions. Owing to the vector characteristic of wind direction, vector weighting must be used in the calculation. Finally, the accuracy of the fusion model was verified using wind-speed sensors installed on the wind tower.Results and DiscussionsIn the ten-minute wind-speed comparison between the fusion grid and individual sensors (Fig. 7 and Table 3), the wind speed exhibits an increase and subsequent decrease before and after the passage of the typhoon “Babinca”. The sensors are located within a wind-speed range of approximately 2?18 m/s, which clearly reflects the drastic change in wind speed during the passage of the typhoon. Sensor 1 has a significantly higher mean error (ME) than the other sensors owing to the large difference in height from the matching grid. The ME of the other sensors is within 1 m/s of the absolute value, and the mean absolute error (MAE) is approximately 1 m/s. In the ten-minute wind direction comparison with a single sensor (Fig. 8 and Table 4), the wind direction gradually decreases from 360° to 100°, and the rate of change first increases and then decreases with the movement of the typhoon, clearly portraying the trend of wind direction change when the typhoon passes by. Except for sensor 1, which has a large wind direction deviation, the fitting results of the other sensors are excellent, with a coefficient of determination (R2) above 0.9697. The overall evaluation results (Fig. 9 and Table 5) reveal that the ten-minute fit has a higher R2 and lower MAE. This is due to the fact that the ten-minute intervals provide more stable time-series data, which helps the model capture trends in wind speed and direction. In addition, the wind LiDAR deployed closer to the wind tower (Fig. 11 and Table 6) is analyzed, and the results indicate that the wind-speed accuracy of the fused grid is improved. The findings reveal that the fusion results depend not only on the neighboring sensing devices but also on the variation of the local wind field to a certain extent.ConclusionsIn complex environments, the traditional meteorological observation means struggle to meet the demand for microscale and high real-time wind field information. To address this challenge, this study adopts high-precision wind measurement equipment, such as wind LiDAR, and combines it with CFD modeling. Through the fusion of high-precision wind measurement data and CFD, the low-altitude 3D wind field is reconstructed. The reliability of our proposed wind field construction method is verified by empirical analysis of wind field data during the impact of typhoon “Bebinca”. This method is capable of generating microscale, high-precision, and real-time wind field information with real-time updates, which is of substantial practical significance for enhancing urban meteorological services and ensuring the safety of low-altitude flights.

ObjectiveExhaust emissions from motor vehicles have a significant impact on air quality and human health. Among them, nitrogen oxides, the main pollutants in motor vehicles, are particularly critical and highly sensitive to concentration detection. Commonly used NO detection techniques include chemiluminescence (CL),Fourier transform infrared spectroscopy (FTIR), and differential optical absorption spectroscopy (DOAS). However, none of these can easily fulfil the requirements of miniaturization, portability, high sensitivity, and high selectivity of NO detection systems. Faraday rotation spectroscopy (FRS) detects the concentration of molecules by measuring the changes in the rotational signal, whereby the concentration of the paramagnetic absorbing molecules is obtained from the demodulated spin signals. This paper describes the design of a magnetic rotation absorption cell applied to a motor vehicle exhaust NO detection system based on Faraday rotation spectroscopy, and the performance was examined in terms of the characteristics of the magnetic field it can generate. Simulation experiments were conducted to explore the use of this absorption cell in a motor vehicle exhaust NO detection system.MethodsA magnetic rotation absorption cell model was constructed based on finite element (FEM) simulations and analysis. The magnetic field characteristics generated by the coil were simulated and analyzed, to fabricate the magnetic rotation absorption cell based on the FEM analysis results and parameters of the coil wire: the diameter and number of turns. The development of the magnetic rotation absorption cell was divided into three steps: cavity design, coil design, and window sheet selection. Repeated experiments and step-by-step approximation methods were used to determine whether the three parts of the absorption cell reached the optimal state, as determined by the quality of the collected spectral lines. A Tesla meter was used to check the magnetic field characteristics generated by the absorption cell coil. The consistency between the performances of the designed and simulated absorption cell was analyzed by relative error, and long-term measurements were conducted to check the stability of the magnetic field generated by the absorption cell. The simulation experimental setup of the NO detection system for motor vehicle exhaust gas was built using this absorption cell. The mathematical model of the peak-to-peak value of the rotating signal and NO volume fraction was established by spectral signal calibration, and the minimum detection limit of the system was evaluated by Allan variance for different magnetic induction strengths.Results and DiscussionsThe standard deviations and relative errors of the measured magnetic induction strength indicate that the magnetic field performance of the designed absorption cell is consistent with that of the simulated absorption cell. Measurement results for the magnetic field stability showed that the average value of the generated magnetic induction strength was 25.6 mT; the polar deviation was 65 μT; and the generated magnetic field was very stable. A simulation of the motor vehicle exhaust NO detection system showed that the peak value of the optical rotation signal displayed an excellent linear relationship with NO volume fraction C, with a correlation coefficient of 99.5%, which indicates that the motor vehicle exhaust NO detection system constructed with this absorption cell can detect changes in NO volume fraction. The continuous measurement results and Allan variance calculations of a fixed NO volume fraction with different magnetic induction strengths indicated that the minimum detection limit of the system can be increased by 20% when the magnetic induction strength is increased from 0 to 36.4 mT.ConclusionsIn this study, a model of a magnetic rotation absorption cell was constructed for a motor vehicle exhaust NO detection system, and a single-optical-range magnetic rotation absorption cell with an optical range of 250 mm was designed based on a simulation analysis of the principle. The effective optical range in the magnetic field was 180 mm, and the size was ?60 mm×250 mm. Performance of the cell was examined based on the magnetic induction strength and motor vehicle exhaust NO detection system simulation test results revealing that: 1) The magnetic field performance of the designed absorption cell is consistent with that of the simulated absorption cell, with a relative error of less than 2%. 2) The system built using this absorption cell can accurately detect NO volume fraction changes for magnetic induction strengths of 0?36.4 mT, and the minimum detection limit is increased by 20%. This lays the foundation for the design of a high sensitivity/high selectivity motor vehicle exhaust NO detection system, which can be extended to other paramagnetic molecular detection systems or application scenarios.

ObjectiveAs a cutting-edge spectral technology with characteristics including high resolution, broadband spectral range and fast measurement, dual comb spectroscopy has shown great potential in many applications in modern optical research. The premise of high resolution spectral measurement with dual comb spectroscopy is that the dual-comb system has a high degree of mutual coherence. Therefore, how to improve the mutual coherence of the dual-comb system has been a key challenge restricting its performance improvement and wide applications. At present, the traditional methods such as active coherent control have problems of high complexity and high cost, the passive coherent control method has problems of limited measurement bandwidth and poor tunability, and the self-reference error correction method involves complex algorithms and models. Focusing on this problem, this paper takes the radio-frequency-locked dual-comb system as the research platform and proposes a self-reference correction algorithm for dual comb spectroscopy based on an innovation-based adaptive extended Kalman filter, which corrects the distortion of the interference signal in the time domain and recovers the mutual coherence.MethodsIn order to solve the problem of frequency drift caused by noise interference in dual-comb system with low mutual coherence, the spectral self-reference error correction algorithm of the dual-comb system based on an innovation-based adaptive extended Kalman filter is used to extract and compensate the noise information accurately, and gradually restore the mutual coherence of the dual-comb system. Because of the nonlinearity of the dual-comb system, the extended Kalman filter is chosen as the research algorithm, and the noise matrix is calculated by the innovation-based adaptive method to reduce the dependence on the prior knowledge of the noise matrix. First, the continuous dual-comb interference signal sequence is segmented in time domain according to the repetition period to separate the interference signal frame by frame. In the process of correction, one frame is taken as the reference frame, and the time jitter, center frequency jitter and carrier envelope phase jitter of other frames relative to the reference frame are calculated. Then, Hilbert transform is used to extract the envelope of the time domain interference signal, and the time jitter is calculated by the distance between the envelope peaks, so as to reflect the jitter of the relative repetition frequency of the dual-comb system. Subsequently, the carrier frequency and carrier envelope phase of the interference signal are selected as the state variables, and the state space model of the interference signal is established. Based on the innovation-based adaptive extended Kalman filter, the carrier frequency and carrier envelope phase of each frame are optimally estimated, and the frequency and phase jitter values are calculated. Finally, according to the extracted jitter information, the numerical operations such as translation and phase rotation of the interference signal are carried out to realize the correction of dual comb spectroscopy and restore its mutual coherence.Results and DiscussionsTo fully verify the effect of the self-reference correction algorithm based on the innovation-based adaptive extended Kalman filter for the dual-comb system with low mutual coherence, the research work is carried out from two perspectives of simulation and experiment, and the effectiveness of the algorithm is verified from the aspects of extracted jitter error, spectral resolution and mutual coherence. Simulation and experimental results show that this method can first accurately extract and compensate the jitter signal of the dual-comb system, and then realize the error correction of the signal. The experimental results show that before correction, due to the existence of various noises, the mutual coherence of the dual-comb system is seriously affected. This results in the distortion of the interference signal, and significant broadening of the longitudinal modes in the radio frequency domain, with the linewidth of the longitudinal mode being far greater than the 1 kHz repetition frequency difference. After correction, within 1 s acquisition time, the longitudinal mode linewidth in the radio frequency domain is reduced from far more than 1 kHz to 1 Hz, and the spectral resolution is significantly improved. The signal-to-noise ratio after the interference signal coherence average is increased from 382 to 16446, which is about 40 times higher. These results prove that the method can effectively improve the spectral quality and restore the mutual coherence of the dual-comb system.ConclusionsIn this paper, a self-reference correction algorithm for dual comb spectroscopy based on an innovation-based adaptive extended Kalman filter is proposed by using the radio-frequency-locked dual-comb system and the simulation model of dual-comb system. This method can effectively restore the coherence in the dual-comb sources, reduce the longitudinal mode linewidth in the radio frequency domain from the original greater than 1 kHz to 1 Hz within 1 s acquisition time, significantly improve the spectral resolution, and at the same time, the signal-to-noise ratio after the interference signal coherence average is increased by about 40 times. Compared with those of the traditional extended Kalman filter algorithm, the model complexity is reduced, and the calculation process does not require the number of combs, which can solve the problem that the traditional method has difficulty in calculating for large mode-locked lasers.