The advancement of modern communication， radar， and electronic warfare systems imposes stringent requirements on microwave signal sources， including exceptional spectral purity， low phase noise， broad frequency tunability， and operation at high-frequency bands. Conventional electronic oscillators， such as quartz crystal oscillators， typically require multiple frequency-multiplication stages to generate high-frequency signals. This process inherently degrades phase noise by 20log N （where N is the multiplication factor）， thereby limiting their applicability in high-frequency systems. In contrast， the optoelectronic oscillator employs an optoelectronic feedback loop to generate microwave signals， offering the distinctive advantage of low phase noise that is independent of oscillation frequency. This makes the optoelectronic oscillator a pivotal solution for high-frequency， high-stability microwave generation. Since its inception by YAO X S in 1996， research on high-frequency optoelectronic oscillators has advanced considerably. The K-band （18~27 GHz）， with its broad available bandwidth， compact antenna size， and promising applications in satellite communications， high-resolution radar， and future fifth-generation and sixth-generation mobile systems， is regarded as an ideal frequency range for such investigations.

However， conventional optoelectronic oscillators operating at high frequencies are susceptible to multi-mode oscillation and frequency hopping due to the limited quality factor of available radio frequency filters， resulting in degraded side-mode suppression ratio and frequency instability. Injection locking is a well-established technique to suppress side modes and stabilize the output. Nevertheless， it requires an injection signal with a frequency close to the free-running oscillation frequency of the optoelectronic oscillator. At high frequencies， this typically depends on expensive and complex high-frequency signal sources， which hinders the adoption of injection locking in high-frequency optoelectronic oscillators.

This paper proposes and experimentally demonstrates a novel scheme for a fifth-order subharmonic injection-locked optoelectronic oscillator in the K-band， utilizing a dual-polarization Mach-Zehnder modulator. The system exploits the polarization independence of the two optical paths within the dual-polarization Mach-Zehnder modulator. An external， relatively low-frequency radio frequency signal is injected into the modulator that drives the X-polarization state， generating high-order optical sidebands. Following photodetection， the electrical spectrum contains harmonics of the injected signal. A subsequent bandpass filter then selects the fifth harmonic component. This filtered high-frequency signal， precisely at the target K-band frequency （five times the injection frequency）， is injected into a conventional optoelectronic oscillator loop constructed using the Y-polarization state of the same dual-polarization Mach-Zehnder modulator. This architecture effectively integrates harmonic frequency multiplication with injection locking within a single， compact photonic configuration. Crucially， it eliminates the need for a dedicated high-frequency signal source for injection， as the high-frequency locking signal is internally generated from a low-frequency input.

An experimental system was implemented to validate the proposed concept. A 1 550 nm laser diode served as the optical source. The dual-polarization Mach-Zehnder modulator provided independent modulation paths for the X-and Y-polarization states. A low-frequency radio frequency signal from a signal generator was injected into the X-polarization modulator. A photodetector converted the modulated optical signal into an electrical signal. A broadband bandpass filter （24~26 GHz） selected the fifth harmonic， which was then amplified and fed into the optoelectronic oscillator loop formed by the Y-polarization path； this loop included an additional modulator bias point， a fiber delay line， an amplifier， and a filter. When an injection signal with a power of 17.5 dBm and a tunable frequency range of 4.8~5.2 GHz was applied， the system successfully achieved fifth-order subharmonic injection locking， producing stable single-mode oscillation outputs at 24.0 GHz， 24.5 GHz， 25.0 GHz， 25.5 GHz， and 26.0 GHz， respectively.

The performance of the injection-locked optoelectronic oscillator was thoroughly characterized. Output spectra at all five frequencies exhibited excellent spectral purity， with side-mode suppression ratio values consistently exceeding 70 dB—a significant improvement over free-running optoelectronic oscillators， which are prone to multi-mode oscillation. The output power variation across the 24-26 GHz tuning range was less than 1 dB， indicating good gain flatness. Phase noise measurements revealed outstanding performance： below -70 dBc/Hz at 10 Hz offset and below -129 dBc/Hz at 10 kHz offset for all output frequencies. The near-in phase noise is primarily determined by the quality of the low-frequency injection source， whereas the far-out phase noise retains the inherently low noise floor of the optoelectronic oscillator's long delay line， thereby effectively circumventing the 20log N degradation associated with pure electronic frequency multiplication. Frequency stability， assessed via Allan deviation measurements over averaging times （τ） from 1 μs to 10 s， demonstrated consistent behavior across the five output frequencies. For short averaging times （τ<1 s）， the stability followed that of the injection source due to the locking effect. For longer τ， stability was influenced by environmental perturbations on the fiber delay.

In conclusion， this work successfully demonstrates a tunable， high-performance K-band optoelectronic oscillator based on a dual-polarization Mach-Zehnder modulator-enabled subharmonic injection-locking scheme. The system efficiently generates high-frequency （24~26 GHz）， high-spectral-purity microwave signals using only a low-frequency radio frequency source， thereby overcoming key limitations of traditional approaches. The demonstrated performance in terms of side-mode suppression ratio （>70 dB） and phase noise （<-70 dBc/Hz at 10 Hz offset， <-129 dBc/Hz at 10 kHz offset） meets the requirements for advanced microwave systems. Although the current tuning range is constrained by the components employed （filter bandwidth， modulator response）， the underlying principle is not inherently frequency limited. Utilizing devices with higher bandwidths or adopting cascaded modulation structures could potentially extend operation to even higher frequencies， including millimeter-wave and terahertz bands. This approach offers a promising and practical photonic pathway toward realizing compact， low-noise， and tunable high-frequency oscillators

Ionic liquids， as a new type of molten salts with high thermal stability， low vapor pressure， and strong designability， have important application value in cutting-edge fields such as electrochemistry， catalytic synthesis， and biomedicine. However， the accuracy and efficiency of ionic liquid type identification still need to be continuously explored and optimized. Traditional characterization methods， such as infrared spectroscopy and nuclear magnetic resonance， usually rely on large precision instruments， which have limitations such as complex operating procedures， high equipment costs， and long analysis cycles. At the same time， the inherent strong hygroscopicity of ionic liquids makes the control of sample purity more stringent， and existing moisture detection methods find it difficult to achieve rapid and precise measurement. Against this background， metasurfaces， as two-dimensional artificial materials that can flexibly control the amplitude， phase， and polarization of electromagnetic waves， provide a new technical path for the development of high-performance sensing technologies. This type of structure has both high sensitivity and non-contact detection advantages， and has shown significant potential in dielectric property analysis and substance identification. However， existing metasurface sensors still have certain limitations in practical applications， such as being easily affected by external electromagnetic interference or requiring direct contact with samples. These issues not only reduce measurement accuracy but may also cause sensor contamination， thereby limiting their widespread application in practical scenarios.

Aiming at the technical bottlenecks of ionic liquid type identification and moisture content detection mentioned above， this paper proposes a metasurface microwave sensor based on a dielectric substrate integrated with a double-layer metal resonant structure. The sensor converts the dielectric properties of ionic liquids into significant changes in resonant frequency shift and resonance linearity through its unique electromagnetic field localization and enhancement mechanism， providing a new way to achieve rapid and precise sensing analysis. To deeply study the working mechanism of the sensor， this study adopted a multi-level research method： from the physical mechanism level， the formation and energy distribution of electromagnetic resonance were intuitively presented through surface current distribution analysis； from the model construction level， the physical structure was transformed into circuit parameters through equivalent circuit analysis， and the regulation law of resonant frequency was quantitatively revealed； from the performance prediction level， the electromagnetic response characteristics of the sensor were accurately obtained through full-wave numerical simulation， and the structure was optimized； from the final verification level， experimental tests confirmed that the sensor can not only accurately distinguish six different types of ionic liquids but also achieve high-precision detection of trace moisture content.

Before conducting experimental characterization， this study first compared and analyzed the reflection characteristic changes of the sensor before and after loading ionic liquids in the 7~10 GHz frequency band based on electromagnetic simulation software. The simulation results show that the introduction of ionic liquids not only changed the original resonant mode of the sensor but also induced a stronger electromagnetic response through the dielectric regulation mechanism， thereby verifying that the metasurface sensor has excellent dielectric sensitivity and electromagnetic regulation capabilities. Subsequently， six representative ionic liquids were selected as the measured samples for actual measurement analysis. The experimental measurement results show that when the sample to be tested in the sample holder is changed from ［EMIm］［BF₄］ to ［OMIm］［BF₄］， the resonant peak position of the reflection spectrum shifts from 8.37 GHz to 8.86 GHz， resulting in a significant frequency shift of 490 MHz. Calculations show that the sensor's average sensitivity to dielectric constant changes can reach 185.42 MHz/ε′. In addition， this study systematically evaluated the sensor's ability to detect trace moisture content. Experimental data show that when the water content increases from 0% to 10%， the resonant peak of the reflection spectrum shows a significant frequency shift of 180 MHz （8.22 GHz→8.40 GHz）， proving that the sensor can effectively detect moisture changes in ionic liquids at the ppm level.

In summary， this paper successfully designed and verified a metasurface microwave sensor based on a double-layer metal resonant unit. By using a three-layer structure constructed with an FR4 epoxy resin substrate， combined with an open sample holder and a fully copper-plated bottom plate design， the sensor exhibits excellent detection performance in the 7~10 GHz working frequency band， achieving non-contact and high-precision detection of ionic liquid types and their moisture content. Simulation and experimentalresults show that the sensor has different characteristic frequency responses for six typical ionic liquids （including ［EMIm］［BF₄］， ［BMIm］［SCN］， ［BMIm］［OTf］， ［BMIm］［BF₄］， ［HMIm］［NTf₂］， and ［OMIm］［BF₄］）， with a maximum frequency shift of 490 MHz and a detection sensitivity of 185.42 MHz/ε′. In terms of moisture detection， the sensor shows a good resonant response to 0~10% moisture content changes in ［EMIm］［BF₄］ solutions， with a resonant frequency shift of 180 MHz. The metasurface sensor designed in this study has high sensitivity and good measurement repeatability， providing an effective technical means for ionic liquid purity detection and deterioration monitoring， and has important engineering application prospects in fields such as chemical process control and real-time monitoring in hazardous environments.

Frequency-Modulated Continuous-Wave （FMCW） radar is widely used in military， autonomous driving， and other fields for its high resolution， low power consumption， and strong anti-interference. However， traditional microwave electronic radars fail to meet broadband signal generation/processing needs， leading to the development of microwave photonic radar. By combining photonics and electronics， it overcomes the “electronic bottleneck，” with optical frequency multiplication and dechirping reception architectures gaining attention for large bandwidth and simple structure. Nevertheless， in this architecture， frequency multiplication degrades phase noise （by 20 log₁₀（n） dB for multiplication factor n）， while electro-optic/optoelectronic conversion worsens it. Phase noise impairs radar accuracy， resolution， and anti-interference， limiting broadband advantages. Existing suppression technologies for microwave photonic radar often suffer from complexity， high cost， or new noise introduction， demanding more effective compensation.

This paper proposes a phase noise compensation scheme for microwave photonic FMCW radar using deskew filtering. The system adopts an optical quadrupling structure （boosting distance resolution） plus reference delay and mixing branches. The baseband linear frequency-modulated （LFM） signal splits into two paths： one drives the microwave photonic quadrupling module to generate a transmitted signal （4× baseband frequency/bandwidth， 4× phase noise）， whose echo is processed via a microwave photonic mixer to get an echo dechirped signal with phase jitter； the other undergoes reference delay/mixing to produce a reference dechirped signal. Deskew filtering compensates the echo dechirped signal as follows： apply Hilbert transforms to both signals for complex signals， estimate phase noise via the reference， remove phase noise's delay dependence in the echo using the deskew filter， and eliminate phase noise to mitigate radar performance impacts.

An experimental setup was built to verify the feasibility of the proposed scheme. The initial frequency of the baseband linear frequency-modulated signal was 5 GHz， with a bandwidth of 100 MHz. After passing through the microwave photonic quadrupling module， a quadrupled frequency signal in the range of 20~20.4 GHz was generated， effectively expanding the bandwidth. The reference and echo dechirped signals were collected and processed using the deskew filtering algorithm. To evaluate the effectiveness of phase noise compensation in the dechirped echo signal， we analyze two key aspects： first， comparing the stability of the half-period of the dechirped echo signal before and after compensation， and second， examining its phase noise characteristics. A reference group processed using the equal phase interval sampling method was introduced for comparative analysis. The results show that before compensation， the standard deviation of the half-period was 0.54 ns. After compensation with the equal phase interval sampling method， this value decreased to approximately 0.24 ns. Further compensation using the deskew filtering method reduced the standard deviation to 0.15 ns， representing a 3.6 times improvement in stability compared to the pre-compensation state. This indicates that the phase noise compensation achieved through the deskew filtering method significantly enhances the stability of the half-period of the dechirped echo signal. Regarding phase noise characteristics， the experimental results demonstrate that within the frequency offset range of less than 10 kHz， the deskew filtering method outperforms the equal phase interval sampling method in suppressing phase noise， resulting in a lower phase noise level in the processed signal. Additionally， a time-frequency analysis was conducted on the signals before and after compensation to compare the range profiles. The results reveal that the target energy in the compensated range profile becomes more concentrated， and the deviation range of the distance measurement results is effectively suppressed. Specifically， the distance corresponding to 10 dB bandwidth decreased from 49.57 m （pre-compensation） to 41.28 m （post-compensation）， while the standard deviation of distance measurement results reduced from 0.97 m （pre-compensation） to 0.78 m （post-compensation）. Collectively， these findings demonstrate that the deskew filtering method effectively improves the range resolution and distance measurement stability of the radar system.

This work aims to design， fabricate， and characterize a low-power， reconfigurable 16×16 thermo-optic switch array on a polymer-based photonic platform， addressing the critical challenges of high consumption and thermal crosstalk associated with scaling large-scale photonic integrated circuits. The primary goal is to develop a reliable hardware platform that demonstrates the feasibility of utilizing the unique material properties of polymers， specifically a high thermo-optic coefficient and low thermal conductivity for efficient and dense on-chip dynamic optical path control. The overarching purpose is to provide a foundational device solution to enable future low-power， flexible， and intelligent photonic systems for applications such as data center optical interconnects， photonic neural networks， and secure optical communications. The central research questions involve validating the performance metrics of a scalable polymer waveguide switch architecture and establishing its advantages over traditional inorganic platforms.

The study employed a comprehensive methodology integrating theoretical design， numerical simulation， process fabrication， and systematic experimental characterization. The core architectural innovation was the design of a cascadable unit cell termed the Directional Coupler-Honeycomb （DC-HC） structure， which combines a DC for power switching and a honeycomb HC interferometer for phase modulation. Multi-segment S-bend waveguides interconnect these units to achieve the required 127 μm port pitch for fiber array compatibility. A low-loss waveguide structure was meticulously designed and simulated. The core layer utilized a fluorinated photosensitive polymer， FSU-8， chosen for its low optical absorption at the 1 550 nm communication wavelength. The cladding material was an Organic-Inorganic Grafting Polymethyl Methacrylate （OIG-PMMA）， selected for its enhanced thermal stability， self-planarization capability， and precise refractive index tunability. The optimized cross-section featured a 3 μm × 3 μm core， a 2 μm coupling gap between adjacent DC waveguides， and a 3 μm separation between the aluminum thin-film heater and the waveguide core. Beam Propagation Method （BPM） simulations using R-soft software were extensively conducted to optimize the waveguide geometry， including the DC coupling length， bending losses， and fiber-to-chip coupling loss. Finite Element Method （FEM） thermal simulations in COMSOL Multiphysics were performed to analyze heat distribution and cross-talk， confirming effective thermal confinement within individual switch units. Fabrication leveraged standard， cost-effective， and Complementary Metal-Oxide-Semiconductor （CMOS）-backend-compatible processes. The waveguide layers were defined through spin-coating， Ultraviolet （UV） lithography， and etching. Aluminum electrodes with a serpentine geometry were patterned via wet etching and precisely aligned atop the modulation arm of each DC unit. The fabricated devices were characterized using optical microscopy and SEM to verify dimensional accuracy and morphology. A dual-system testing approach was implemented for performance evaluation. A static switching performance test system was constructed using a 1 550 nm continuous-wave laser source， a polarization controller， single-mode fibers for edge coupling， and an optical power meter. This system measured key static parameters： insertion loss and the required switching power consumption by applying a controlled DC voltage to the heaters. A separate dynamic pulse response system was built， incorporating an Arbitrary Waveform Generator （AWG）， a Photodetector （PD）， and an oscilloscope. This system measured the temporal response， specifically the rise and fall times， of the switches under square-wave modulation at frequencies of 500 Hz and 1 kHz.

The fabricated 16×16 polymer thermo-optic switch array exhibited compact dimensions of approximately 7.0 cm in length and 0.2 cm in width. Comprehensive testing at the 1 550 nm operational wavelength yielded a comprehensive set of performance data. The device achieved a minimum insertion loss of 11.4 dB. A detailed loss budget analysis attributed this to constituent factors： waveguide propagation loss， structural loss from cascaded bends， fiber-to-chip coupling loss， and additional scattering losses arising from fabrication imperfections such as sidewall roughness and imperfect cleavage planes. A core achievement was the demonstration of low-power operation. The minimum power required to toggle a single channel between its cross and bar states was measured to be 33.38 mW. This corresponds to applying a temperature change of approximately 21 K to the modulation arm， as predicted by thermal-optical simulations. The maximum extinction ratio achieved was 12.12 dB. While this value shows room for improvement compared to some inorganic platforms， it is attributed in part to a slight broadening of the fabricated waveguide width， which can support higher-order modes and introduce phase errors， as confirmed by supplementary simulations. Dynamic performance tests confirmed operation in the sub-millisecond regime. Under 500 Hz square-wave modulation， the measured rise time was 226.7 μs， and the fall time was 294.0 μs. When driven at a higher frequency of 1 kHz， the response times were 222.2 μs （rise） and 255.9 μs （fall）， establishing this as the practical operational limit for the current device design. Simulation results for the full array predicted an average optical transmission of 71.87% and an adjacent channel crosstalk better than -31.94 dB for a signal routed from a single input to any output， indicating good routing fidelity. Crucially， thermal simulation results validated a key material advantage： the temperature field from an active heater decayed to ambient levels within 20~30 μm from its center. Given that adjacent switch electrodes are spaced approximately 172 μm apart， this confirms effective suppression of thermal crosstalk， a major bottleneck in densely packed inorganic switch arrays. A comparative analysis with state-of-the-art switches on platforms like silicon-on-insulator （SOI）， Silica， and lithium niobate on insulator （LNOI） contextualizes the results. The polymer-based array demonstrates a compelling trade-off： its switching power is significantly lower than that of typical SOI or silica-based units， its unit-length propagation loss is advantageous， and its response speed is competitive with other polymer and hybrid systems. Most notably， it delivers this performance at a substantially larger port count， highlighting the scalability benefits of the polymer platform for large-scale photonic networks.

This research successfully validates the polymer material platform as a highly viable and competitive candidate for implementing scalable， low-power reconfigurable photonic integrated circuits. The developed DC-HC architecture and the associated fabrication methodology provide a concrete pathway toward constructing large-scale optical switching networks. The work conclusively demonstrates that the inherent material properties of polymers， specifically the high thermo-optic coefficient and low thermal conductivity， can be effectively harnessed to overcome key limitations of traditional platforms， namely high consumption and thermal crosstalk in dense arrays. The fabricated device， with its integrated combination of low switching energy， acceptable optical performance， microsecond-scale reconfigurability， and inherent programmability， establishes a significant hardware prototype. It serves as a critical enabling component for next-generation systems requiring dynamic optical path management. The findings are offering a practical device solution and a clear material and structural strategy for future work aimed at achieving even larger scale， lower loss， and higher-speed intelligent photonic processing systems.

Non-polarizing beam splitter is an optical component widely used for beam splitting. It is primarily designed to divide incident light into two beams with specified reflection and transmission ratios while maintaining the original polarization state of the input light. Thanks to its low polarization discrimination， minimal stress birefringence， and strong polarization-maintaining capability， non-polarizing beam splitters are extensively employed in optical systems such as space remote sensing， projectors， and Michelson interferometers. Although an ideal non-polarizing beam splitter is designed to preserve the polarization state of the incident light， practical non-polarizing beam splitters exhibit certain non-ideal polarization characteristics due to inherent limitations in materials and coating designs. Moreover， these polarization properties are highly sensitive to both the angle and direction of the incident light. In some complex optical systems， a non-polarizing beam splitter may need to simultaneously process light incident from both forward and reverse directions， inevitably operating under reverse incidence. Therefore， a systematic study of the polarization properties of the non-polarizing beam splitter under reverse incidence is of great significance for high-precision optical measurement and polarization-sensitive systems. Currently， most research focuses on the influence of factors such as temperature and angular deviation on the polarization performance of the non-polarizing beam splitter， while studies on polarization characteristics under reverse incidence remain limited. This paper addresses scenarios in complex optical systems where the non-polarizing beam splitter must be used in reverse. We systematically analyze the polarization properties of the non-polarizing beam splitter under different incident directions from three perspectives： fundamental principles， simulation analysis， and experimental validation. The variations in polarization characteristics of both reflected and transmitted channels with respect to incident wavelength are analyzed and compared， and the mechanism underlying the influence of incident direction on the polarization properties of the non-polarizing beam splitter is revealed.

To achieve this objective， a combined theoretical， numerical， and experimental approach was adopted. Numerical simulations were performed using Essential Macleod thin-film design software to construct a realistic model of a non-polarizing beam splitter coating stack. The model enabled quantitative calculation of wavelength-dependent polarization parameters， including diattenuation and phase retardation， for both reflected and transmitted channels under forward and reverse incidence conditions. The simulations covered the visible spectral range and assumed identical angles of incidence for both illumination directions to isolate the effect of direction reversal. To validate the simulation results， high-precision experimental measurements were conducted using Mueller matrix ellipsometer. Commercial non-polarizing beam splitter samples （models CCM1-BS013/M and CCM5-BS016/M） were selected as representative specimens. The complete 4×4 Mueller matrices of the samples were measured over a wavelength range from 380 nm to 800 nm under both forward and reverse illumination. Subsequently， the Lu-Chipman decomposition method was applied to the measured Mueller matrices to extract key polarization parameters， specifically diattenuation and phase retardation， for the reflected and transmitted channels. Multiple measurements were performed to ensure repeatability and to assess sample-to-sample consistency.

The simulation results reveal a pronounced dependence of polarization characteristics on the direction of incident light， particularly for the reflected channel of the non-polarizing beam splitter. Under forward and reverse incidence， substantial discrepancies were observed in both diattenuation and phase retardation of the reflected beam. Specifically， the maximum change in phase retardation between the two incidence conditions reached approximately 53.64°， with an average variation on the order of 29.49°， while the maximum difference in diattenuation was approximately 0.321， with an average difference of about 0.027 3. These findings indicate that reversing the illumination direction significantly alters the polarization behavior of the reflected channel. In contrast， the transmitted channel exhibited negligible variation in both diattenuation and phase retardation across the same conditions. Experimental measurements corroborated these trends with strong qualitative and quantitative agreement. Mueller matrix ellipsometry data showed that， for the reflected channel， the maximum difference in diattenuation between forward and reverse incidence was approximately 0.11， with an average difference of around 0.03， while the maximum difference in phase retardation reached approximately 51.5°， with an average difference of about 28.76°. Importantly， repeated experiments on different non-polarizing beam splitter samples consistently demonstrated the same directional dependence： significant polarization variation in the reflected channel and nearly identical polarization behavior in the transmitted channel under both illumination directions.

The accurate and efficient calculation of the Beam Shape Coefficients （BSCs） is one of the key issues in researching the interaction between a structured or shaped beam and the particles. For this reason， different techniques have been established， such as the quadrature method， the Localized Approximation （LA） or its variants， the Finite Series （FS） method， the Angular Spectrum Decomposition （ASD）， and the others. Among these methods， the Localized approximation has been widely used due to its advantages including mainly the efficiency in numerical calculation， the conciseness of the expressions and the straightforwardness in deducing the BSCs for the beams in both the on-axis and off-axis scenarios. However， this method， just as it is named， is an approximate one. The beam remodeling takes place when the beam field is reconstructed from the BSCs， i.e. the reconstructed beam field deviates from the originally given field. Up to date， the remodeling of the beam field has not been studied systematically.

In this work， the two-step indirect method is employed to study the remodeling effects of the localized approximation method for the Gaussian beams. In the first step， the expression of the BSCs is obtained， by using the localized approximation， for the Gaussian beam which is centered in the coordinate system （called beam system） and is described by using a scalar potential function （therefore the BSCs are called scalar BSCs）. Subsequently， the scalar translational addition theorem is used to transform the BSCs into another coordinate system whose axes are parallel to those of the beam system. The second coordinate system in which the spherical particle is centered is called particle system. In the second step of the indirect method， the electric and magnetic （EM） fields of the Gaussian beam are described by using the scalar potential function together with a polarization parameter. Based on this relation， the BSCs of the EM field （called vector BSCs or EM BSCs） are expressed as a linear combination of the scalar BSCs. In this way， the EM BSCs for the off-axis located Gaussian beam are obtained indirectly from the scalar BSCs of the centered beam. The two-step indirect method simplifies the analytical derivation of the BSCs. The expressions of the EM BSCs which are directly deduced in the localized approximation for the off-axis located Gaussian beam are used in the numerical calculations for making a comparison. It is found that the indirect method is at least eight times faster than the direct method in numerical calculation of the BSCs.

The remodeling of the localized approximation is studied， based on a comparison between the originally given field of the Gaussian beam and the fields which are reconstructed from the directly and/or indirectly calculated EM BSCs. The numerical results reveal that， in the direct LA method， the axisymmetric structure of the Gaussian beam is broken in the reconstructed beam field， exhibiting spurious-peaks in the electric field. When the off-axis distance becomes sufficiently large， a ring structure is produced in the field. The deviation of the reconstructed beam field from the given one increases gradually along the increase of the off-axis distance. However， in the indirect method， the reconstructed field is always axisymmetric and the discrepancy between the reconstructed and given fields is independent of the off-axis distance. In both the direct and indirect methods， the reconstructed beam fields deviate from the given one， showing a close dependence on the beam waist radius. Namely， the reconstructed beam fields agree much better with the given field when the beam waist radius is large， but the quality of the remodeled fields become poorer when the beam waist radius decreases， especially when the beam waist radius is close to or less than the wavelength of the light beam.

It is concluded that， compared with the direct localized approximation method， the two-step indirect method has advantages in analytical derivation of the BSCs， in conciseness of the expressions， in efficiency of numerical calculation， and in quality of reconstructed beam field. Besides， the work presented here suggests a warning against the use of the direct/indirect LA methods for strongly focused Gaussian beams and the use of the direct LA for large off-axis located beams.

Single-frequency continuous-wave lasers are critically important for advanced applications in quantum information science， high-precision metrology， and lidar systems. These applications demand laser sources that combine a narrow linewidth， low amplitude and frequency noise， and high temporal coherence. A significant challenge in the field is scaling the output power of such lasers while simultaneously preserving their superior spectral purity and high stability. Conventional techniques for achieving single-frequency operation often face limitations in power scaling due to thermal effects and nonlinearities.

This research demonstrates a high-power， single-frequency Nd∶YVO₄ laser system utilizing the seed injection-locking technique. A stable， narrow-linewidth fiber laser operating at 1 064 nm serves as the master oscillator. The slave laser is configured as an “8”-shaped ring resonator， which is pumped by an 888 nm diode laser. A composite Nd∶YVO₄ crystal is used as the gain medium to mitigate thermal lensing effects. Active frequency stabilization is implemented using the Pound-Drever-Hall （PDH） method. An error signal， derived from the cavity transmission， feeds back to a piezoelectric transducer to control the slave cavity length， thus locking it to the seed laser frequency.

Under optimal injection-locking conditions and at a pump power of 38.12 W， the laser delivers a maximum output power of 13.5 W in a single longitudinal mode. The linewidth of the amplified output is measured to be 7.0 kHz. This represents only a minor broadening compared to the 5.6 kHz linewidth of the original seed laser. The system exhibits excellent power stability， with a root-mean-square power instability of less than 0.18% over a continuous 60-minute period. Furthermore， the frequency stability is significantly enhanced through injection locking. The long-term wavelength drift is reduced to 132.4 MHz， a substantial improvement over the 300 MHz drift observed for the free-running seed laser. A detailed frequency noise characterization reveals effective suppression of noise at low Fourier frequencies （1~100 Hz） in the locked state compared to the free-running slave laser. A slight increase in noise is observed at higher frequency offsets， which is attributed to residual mechanical vibrations from the locking actuator. These results confirm that the seed injection-locking technique successfully amplifies the optical power while maintaining the spectral characteristics of the seed. Crucially， this high stability is achieved without the need for active frequency stabilization of the seed laser itself. This work contributes by achieving a compelling combination of high power （13.5 W）， narrow linewidth （7.0 kHz）， and high stability at the important 1 064 nm wavelength. A key finding is that this high stability is accomplished without requiring active stabilization of the seed laser itself. The results robustly demonstrate that the seed injection-locking technique is a highly effective method for amplifying optical power while simultaneously preserving and even enhancing the frequency stability and spectral characteristics of the original seed source.

In conclusion， this research successfully realizes a high-power， narrow-linewidth， low-noise single-frequency Nd∶YVO₄ laser. The system exhibits outstanding power and frequency stability， making it suitable for demanding applications. The approach provides a viable and practical pathway for developing high-performance single-frequency lasers. Future work will focus on refining the feedback control system to achieve even lower frequency noise. Additionally， the integration of intracavity nonlinear frequency conversion techniques， such as second harmonic generation， could be implemented to produce high-power， single-frequency radiation at other strategically important wavelengths， further expanding the utility of this laser architecture.

Accurate monitoring of atmospheric CO₂ and CH₄ column concentrations is crucial for understanding greenhouse gas source-sink processes， assessing the effectiveness of emission reduction measures， and formulating climate change mitigation strategies. Fourier Transform Infrared （FTIR） spectroscopy， known for its high spectral resolution and sensitivity， is a key ground-based remote sensing technique. The portable EM27/SUN FTIR spectrometer， developed by KIT and Bruker， features a compact and robust design suitable for long-term field observations. Its core is an interferometer： incoming solar radiation is split， reflected by fixed and moving mirrors， and recombined to generate interference signals. Subsequently， the PREPROCESS program and the PROFFAST retrieval algorithm are applied to retrieve the column concentrations of the target gases.

To further improve the retrieval accuracy and reliability of EM27/SUN， this paper evaluates the reliability of the EM27/SUN by comparing its retrieval results in the Hefei area with those from the TCCON high-resolution FTIR spectrometer. Calibration formulas were developed to optimize the EM27/SUN retrieval performance. After calibration， the daily average deviation of the column-averaged dry-air mole fraction of carbon dioxide （XCO₂） between the EM27/SUN and TCCON was 1.259 0 ppm， while that of methane （XCH₄） was 0.003 7 ppm. Furthermore， the observation precision of XCO₂ and XCH₄ was calculated based on continuous observation data from the Dalian observation site during the midday period （11∶00~13∶00） on October 23rd. The observation precision for XCO₂ was found to be 0.12 ppm， and for XCH₄， it was 0.9 ppb， which meets the precision requirements for ground-based remote sensing of greenhouse gas monitoring.

Using the PROFFAST retrieval algorithm， time series of atmospheric XCO₂ and XCH₄ were obtained for selected dates in February， March， September， October， and November 2023 in the Dalian Changxing Island region. The mean XCO₂ was （422.41±0.34） ppm （parts per million by volume）， while the mean XCH₄ was （1.915 2±0.001 8） ppm. The observational data were divided into two periods： the late winter to early spring transition period （late February to March） and the mid-to-late autumn period （late September to early November）. The mean XCO₂ during the late winter to early spring period （422.99 ppm） was higher than that during the mid-to-late autumn period （421.55 ppm）. In contrast， XCH₄ showed an opposite trend， with a lower mean during the late winter to early spring transition period （1.909 9 ppm） compared to the mid-to-late autumn period （1.923 2 ppm）. Although CO₂ and CH₄ have different source-sink mechanisms， their concentration variations exhibited certain correlations in specific months， implying common influences on their variations. The correlation coefficient was 0.73 in the late winter to early spring period and 0.69 in the mid-to-late autumn period. By analyzing the characteristics of CO₂ and CH₄ concentration variations during the observation period and combining this with a backward trajectory model， possible source-sink processes were investigated.

Furthermore， a comparison was conducted between the EM27/SUN observation data and the corrected data from the Japanese GOSAT satellite. The results showed high consistency， with correlation coefficients of 0.87 for XCO₂ and 0.76 for XCH₄， respectively. Additionally， GOSAT satellite data （monthly averages） from December 2021 to November 2024 were analyzed， revealing distinct seasonal variations for both gases： XCO₂ peaked in spring and winter and reached its lowest in summer （spring>winter>autumn>summer）， whereas XCH₄ was lower in spring and higher in summer and autumn （autumn>summer>winter>spring）. Both gases exhibited a clear increasing trend over the years. This study provides important data support for greenhouse gas source-sink analysis in the Dalian region. The portable FTIR spectrometer EM27/SUN can accurately observe atmospheric CO₂ and CH₄ column concentrations and their variations， making it suitable for validating satellite remote sensing data in remote areas.

With the rapid development of cloud computing and large language models， global mobile data traffic has experienced exponential growth， imposing higher demands on data center interconnection technologies. To achieve high-speed data transmission at 800 Gbit/s， coherent optical communication with high spectral efficiency and support for advanced modulation formats has emerged as a key solution for short-reach optical interconnects. However， traditional coherent receivers are hindered by high Digital Signal Processing （DSP） complexity， which makes it difficult to meet stringent power and cost requirements. To address this， this paper proposes a low-complexity DSP scheme based on baud-rate sampling， which reduces computational complexity while maintaining performance for short-reach coherent optical communications.

The proposed DSP architecture integrates a baud-rate clock recovery module with a two-stage adaptive equalizer， both designed for low complexity. The clock recovery module employs a split-path design comprising four independent units， each utilizing a sign-MM Timing Phase Error Detection （TPED） algorithm. Operating at the symbol rate， this module uses a sign function to extract timing errors from signal polarity changes. This approach enables robust compensation of Sampling Clock Offsets （SCO） and In-phase/Quadrature （I/Q） skew without requiring carrier recovery. Subsequently， a Two-stage Real-valued Multiple Input Multiple Output （RV-MIMO） adaptive equalizer is applied. Its tap configuration is flexible： the first stage uses N_{\mathrm{1}} main taps to mitigate intra-polarization impairments， such as chromatic dispersion and inter-symbol interference， while the second stage includes N_{\mathrm{2}} cross-term taps and a 4×4 RV-MIMO with N_{\mathrm{3}} taps to handle residual inter-polarization crosstalk and polarization demultiplexing. This tunable structure allows the equalizer's complexity to be dynamically adjusted based on channel conditions， thereby optimizing the performance-complexity balance.

Simulation results under a 56 GBaud dual-polarization 16QAM transmission over 2 km standard single-mode fiber demonstrate the effectiveness of the proposed scheme. The sign-MM TPED exhibits robust performance against impairments such as carrier frequency offset and phase noise， with timing jitter remaining below -45 dB under various conditions. The two-stage equalizer reliably achieves Bit Error Rate （BER） performance below the hard-decision forward error correction threshold， even in the presence of IQ skew. Compared to conventional oversampling-based DSP schemes， the proposed approach reduces the number of real multipliers required in the equalizer by approximately 50%. This complexity reduction is achieved with only minor penalties of 0.4 dB in Optical Signal-to-Noise Ratio（OSNR） tolerance and 1.1 dB in Received Optical Power（ROP） sensitivity.

In summary， this work presents a low-complexity DSP solution for short-reach coherent optical interconnects， using baud-rate sampling to significantly reduce computational complexity while maintaining performance. The integrated architecture， which combines I/Q-independent clock recovery with a configurable-tap adaptive equalizer， enhances robustness against I/Q skew and sampling offsets， making it suitable for data center applications. These attributes collectively make the scheme a practical and efficient candidate for high-speed， power-and cost-sensitive applications such as intra-data center interconnects.

3D reconstruction techniques have been extensively applied across a wide range of fields in recent years， including medical imaging， robotic navigation， virtual and augmented reality， 3D animation modeling， and online product inspection. Among these techniques， Fringe Projection Profilometry （FPP） has attracted significant attention owing to its non-contact measurement capability， full-field acquisition， and high spatial resolution. These advantages have led to its widespread adoption in industrial inspection， cultural heritage preservation， biomedical applications， and reverse engineering. Within an FPP system， phase recovery constitutes a fundamental and indispensable step， as both the accuracy and computational efficiency of phase estimation directly determine the quality of the reconstructed 3D surface and the overall system performance. Consequently， the development of fast， accurate， and robust phase recovery methods remains a central research topic in fringe projection profilometry.

Traditional phase retrieval techniques mainly include Fourier Transform Profilometry （FTP） and multi-step Phase-Shifting Profilometry （PSP）. Multi-step phase-shifting methods achieve high phase accuracy by projecting and capturing multiple phase-shifted fringe patterns； however， their reliance on multiple frames significantly restricts their applicability in dynamic scenes or high-speed measurement scenarios. In contrast， Fourier transform-based methods can extract phase information from a single fringe image， offering improved measurement efficiency. Nevertheless， their performance tends to degrade considerably when dealing with complex surface geometries， depth discontinuities， severe noise， or strong surface reflectivity， resulting in reduced accuracy and robustness. In recent years， researchers have increasingly integrated deep learning with phase extraction and phase unwrapping processes， achieving high reconstruction accuracy while significantly reducing the number of required projection patterns. Compared with conventional analytical approaches， deep learning-based methods exhibit superior capability in handling noise， nonlinear distortions， and surface discontinuities. Despite these advantages， existing deep learning-based absolute phase recovery methods still suffer from several limitations. Existing deep learning-based absolute phase recovery methods mainly fall into two categories. The first predicts the numerator and denominator terms of wrapped phase at three different frequencies separately， then computes the absolute phase using multi-frequency or number-theoretic methods. The second employs either a dual-network or dual-decoding architecture to separately predict the numerator and denominator terms of the high-frequency wrapped phase along with the fringe order， thereby obtaining the absolute phase. The former suffers from error accumulation during multi-frequency unwrapping， leading to significant inaccuracies and poor stability. The latter incurs high computational complexity and low inference efficiency due to the multi-network or dual-decoder design.

Aiming to address the issues of error accumulation and high model complexity inherent in existing methods， this paper proposes a novel multi-task phase recovery framework based on GD-UNet （UNet with an Information Gather-and-Distribute Mechanism）. The proposed method enables simultaneous prediction of the wrapped phase and fringe order within a single network， thereby allowing direct recovery of the absolute phase. Built upon the classical UNet architecture， the proposed model incorporates residual modules to enhance feature extraction capability and improve training stability. In addition， by integrating an information gather-and-distribute mechanism， the network supports multi-task learning and directly outputs the numerator and denominator of the wrapped phase as well as the corresponding fringe order. This unified design eliminates the need for multiple networks， effectively reducing computational complexity and inference time. Furthermore， to enhance the robustness of fringe order prediction-particularly in challenging regions such as object boundaries， sharp depth discontinuities， and highly reflective surfaces-a fringe order correction strategy based on Connected Domain Segmentation （CDS） of the wrapped phase is introduced. The proposed CDS-based correction method exploits the spatial continuity of the wrapped phase， under the assumption that all pixels within the same connected domain theoretically share an identical fringe order. Since prediction errors tend to occur more frequently near domain boundaries， the final fringe order for each connected region is determined through majority voting， thereby effectively suppressing local misclassifications. This strategy significantly improves the stability and accuracy of fringe order estimation without introducing additional computational burden. Extensive experiments are conducted to evaluate the performance of the proposed method under various conditions， including different surface materials， complex geometries， and discontinuous scenes. Both quantitative and qualitative comparisons with state-of-the-art methods demonstrate that the proposed GD-UNet-based framework achieves superior phase recovery accuracy while maintaining lower model complexity and faster inference speed.

The experimental results indicate that the proposed approach effectively mitigates error accumulation， enhances robustness against noise and surface reflectivity， and exhibits strong generalization capability across diverse measurement scenarios. In conclusion， this paper aims to achieve stable and high-precision phase recovery from a single fringe image in complex scenes containing large surface discontinuities or isolated objects through a unified network model. A single-frame phase extraction method is presented， in which only one fringe image is required， and a single network simultaneously predicts the numerator and denominator of the wrapped phase as well as the fringe order map. The proposed approach demonstrates clear advantages in both accuracy and efficiency. Comprehensive experimental evaluations confirm that the method achieves excellent measurement accuracy and strong robustness in challenging scenarios， including complex surface reconstruction， high noise interference， and multi-material object measurement.