Objective Optical systems (OSs) that produce bottle beams (BBs) are increasingly diversifying in the literature, according to recent studies. However, the practicability of most OSs is relatively limited, and it has been difficult to meet the increasingly flexible application requirements. Therefore, under the premise of satisfying the properties of the bottle light field, it is necessary to design a controllable OS to obtain a multifunctional BB. In the traditional axicon-lens OS, the incident light that produces the BB is generally a circular Gaussian beam (GB). With the diversification of BB systems and applications, the initial beam with a special shape has important research significance for the regulation of BBs. Therefore, in this study, we design an OS for BBs and use the polygonal aperture to control the light field and analyze its characteristics. The circular GB was modulated by the polygonal aperture into a polygonal beam with a special shape. The BB produced after passing through the axicon-lens OS carries multiple notches. This has potential application value for multiparticle capture and precise capture and is of great significance for the multifunctional application of BBs.

Methods In this study, the axicon-lens structure was an OS, and polygonal apertures were placed before the axicon, so the BB with multiple notches was generated after the focusing lens. Polygonal apertures, including regular triangles, regular quadrilaterals, and regular hexagonal, were taken as the research objects. First, we theoretically analyzed and derived their transmission aperture functions, and used the Collins formula to calculate the light field distribution formula after the BB passes through the axicon-lens. Then, we used MATLAB software to analyze the theoretical formula and obtain the diffraction spot pattern after the axicon-lens via simulation and studied the relationship between the polygonal aperture shape and central diffraction spot. Finally, an experimental device of the OS was developed by replacing the polygonal aperture and using the charge-coupled device camera to observe the BB with multiple notches behind the focusing lens. Further, the influence of the number and position of the sides of the polygonal aperture on the notch of the bottle optical trap was studied.

Results and Discussions First, compared with the circular GB, the special shape beam could be adjusted by the polygonal aperture to form a BB with multiple notches (Fig. 2). The number of sides of the polygonal aperture was the same as that of the BB. In addition, the spot image obtained in the experiment showed that the notch position of the BB corresponded to the polygonal aperture. When the side number of the polygonal aperture was odd, the notch position of the BB was complementary to the side position, the angular position was the same. When the number of sides of the polygonal aperture was even, the notch position of the BB was the same as the side position, complementary to the angular position. Therefore, we could qualitatively analyze the notch position of the BB generated according to the odd and even number of apertures (Fig. 5). Finally, we found that as the number of sides of the polygonal aperture increased, the notch size of the BB gradually decreased. It has important research significance of the capture of particles with different sizes.

Conclusions A circular GB was regulated by the polygonal aperture (regular triangle, regular quadrilateral, and regular hexagon), and the diffracted beam and BB formed by the axicon system were studied. In the research process, to ensure the generation of the BB, the focusing lens was placed at 46, 78, and 63 mm, respectively, and the formed BBs carried multiple notches. After the research, we found that the number of the notches of the formed BBs corresponded to the number of sides of the polygonal aperture. The notch position of the BB generated by the even-numbered side aperture was the same as the position of the side, whereas that of the BB generated by the odd-numbered side aperture was complementary to the position of the side, and the local area could be analyzed according to the number of sides of the aperture. In addition, the analysis showed that the notch size of the BBs decreased with the increase in the number of sides of the polygonal aperture. The notch of the BB of different sizes was the key to high-quality capture and stable trapped particles. The radius of the largest focal plane hollow spot of the BB was 0.41 mm. The hollow spot size of the bottle optical trap was in the order of hundreds of microns, which was more suitable for capturing and manipulating large-sized particles.

Objective The developments in adaptive optics, image stabilization, fast laser scanning, and optical communications have resulted in the increasing demand for high-performance fast steering mirrors (FSMs). In some optical systems, such as laser metrology, projection system, and inter-satellite optical communication, FSM size is crucial. In integrated optical systems, there is an urgent application demand for portable FSM systems. However, the existing FSM design does not consider the volume, especially height size, which is not conducive to miniaturization of optical systems. To meet the requirements of a portable FSM system for small-size FSMs, a compact piezoelectric driven FSM structure was designed. We expect the FSM not only to be portable but also to have excellent performance.

Methods There are two types of FSM driving actuators: voice coil actuator and piezoelectric ceramic stack actuator (PCSA). Voice coil actuator is a direct drive motor based on Lorentz force, its size is generally larger than PCSA, and its environmental adaptability is also poor. For the miniaturization of FSM, we chose a PCSA with a height of only 17 mm. Because the displacement of the PCSA is small, we set a lever displacement amplification mechanism in the FSM structure. In the structural design of FSM, a decoupled flexure hinge was parallel to the PCSA. Through a reasonable layout of driving elements, displacement amplification mechanism, and decoupling support of the mirror, the overall dimension of the FSM, especially the height dimension, can be significantly reduced. We established a theoretical model for FSM and analyzed its angular stroke and resonance frequency. The theoretical results show that the angular stroke and resonance frequency of FSM reach 4.714 mrad and 707 Hz, respectively, which are consistent with our expected performance.

Results and Discussions The overall dimension of the mechanical structure of 75-mm diameter transparent mirror is 90 mm×90 mm×33 mm. We tested the angular stroke and resonant frequency of the FSM. The experiment results show that the angular stroke of the compact FSM is 4.2 mrad (Fig. 6). There is an error of 12.23% between the experiment and theory results; the main reason for this error is that the deformation of the flexure hinge in the theoretical model is considered a pure rotation, but there is a small lateral displacement in practice. The mechanical resonance frequency is 671 Hz (Fig. 7), the error between the theoretical value and the measured value of resonance frequency is 5.36%. The main causes of the errors are machining errors and PCSA stiffness errors. The experiment results show that the FSM has a good performance and can meet the application requirements of a portable FSM system.

Conclusions We design a compact FSM that is portable and has high performance based on the application requirements of portable FSM for small-size and integrated optical systems. We choose PCSA with small stroke and height and use a one-stage amplification mechanism in the FSM structure. PCSAs and decoupling support hinges are in parallel position. This design is the first example in FSM with a lever amplification mechanism. Through reasonable structure design, the size of FSM is significantly reduced. In this article, a theoretical model for FSM is established, and the angular stroke and resonant frequency of FSM are derived. The experiment results are consistent with the theoretical results. Finally, based on the experiment, the established FSM is not only portable but also exhibits excellent performance. Compared with the same caliber product S-340 of PI company, the compact FSM has similar performance, smaller volume, and good engineering application value.

Objective Although the acquisition of single-molecule localization microscopy (SMLM) includes various noises and background information, completely removal of structural noise is difficult for current denoising algorithms (e.g., the spatial wavelet algorithm and the extreme value-based emitter recovery algorithm) employed in the preprocessing of the reconstruction, thus decreasing the quality of reconstructed super-resolution images. To address this challenge, we develop a new background denoising algorithm based on the time-domain iterative wavelet transform (TDIWT), which can process a batch of SMLM datasets with different signal-to-noise ratios (SNRs) by adaptively selecting the appropriate levels and iterations. This algorithm can provide a new approach for adaptive batching SMLM data structural background.

Methods This denoising algorithm based on TDIWT includes two main parts. First, the appropriate level and iteration parameters of TDIWT are adaptively selected for different datasets to balance the time consumption and signal-noise separation effects by calculating the SNR of the dataset. Consequently, time-varied values of each pixel are calculated using TDIWT with selected parameters to separate the signal and background structural noise. The main steps of TDIWT calculation are described by (1) extracting the intensity of the signal from each pixel in a stack in the time domain; (2) acquiring the approximate coefficient via wavelet decomposition and then using it for wavelet reconstruction to fit the background curve; (3) estimating the reconstructed signal that is higher than the background curve and employing wavelet decomposition again; (4) repeating the process until the background fitting data is acquired; (5) outputting separated signal and background image according to the image size (Fig. 1).

Results and Discussions The simulated results demonstrate that the separation of signal and background using the TDIWT algorithm is more efficient than that using the other denoising algorithms (i.e., extreme value-based emitter recovery, Gaussian filter, background estimation based wavelet transform, median filter, and rolling filter) by evaluating the direct visualization and the quantitative parameters including structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR), as shown in Figs. 3 and 4. The SSIM and PSNR of the TDIWT algorithm are 29.9%, 68.5%, 226%, and 33.3%, 34%, 50.8% higher than that of the spatial wavelet algorithm (i.e., background estimation based wavelet transform) using SNR10, SNR6, and SNR2 datasets, respectively. This can be explained by the fact that the intensity of the signal varies rapidly, but the background structural noise varies gradually in the time domain. This advantage of the TDIWT algorithm is more noticeable under the low SNR with a strong structural background. The normalized intensity of signal near strong structural noise is calculated, as shown in Fig. 3, illustrating that the separated signal using the TDIWT algorithm is the closest to the simulated signal compared with the other algorithms and demonstrating the improved accuracy of signal extraction. In addition, the experimental data acquired using our easySTORM system and the real reference data from an open single-molecule localization website are employed to further evaluate the developed algorithms. The reconstructed tubulin images show a continuous state using the TDIWT algorithm and a discontinuous state using the other algorithms from the same dataset with strong structural noise, as shown in Fig. 5. Figure 7 also demonstrates that the TDIWT algorithm could more effectively remove the structural noise.

Conclusions In this study, we have developed a new denoising algorithm based on a time-domain iterative wavelet algorithm, which can process a batch of SMLM datasets with different SNRs by adaptively selecting the appropriate levels and iterations. This algorithm can provide an accurate signal extraction from the noisy background, thus improving super-resolution image reconstruction. Under the simulation datasets, the results have demonstrated that the structural similarity index and peak SNR of processed datasets using the TDIWT algorithm are increased by 226%, 50.8%, and 58.5%, 16.6% compared with that using the spatial wavelet and time extremum emitter recovery algorithm, respectively. In addition, the experimental data acquired using our easySTORM system and the data from the open single-molecule localization website have been employed to evaluate the algorithms. The reconstructed tubulin images have shown a continuous state using the TDIWT algorithm and a discontinuous state using the other algorithms from the same dataset, verifying the superiority of the algorithm. This denoising algorithm based on TDIWT can provide a new approach for adaptive batching SMLM data structural background.

Objective The demodulation algorithm based on the 3×3 coupler is one of the most widely used interferometric demodulation algorithms. It relies on the physical characteristics of the coupler to achieve symmetrical output signal, and is independent on external loading wave modulation and feedback control to achieve signals with high sensitivity and large dynamic range. Its cost and noise have additional advantages. The homodyne symmetric (NPS) demodulation method based on the 3×3 coupler was put forward for the symmetry condition of the 3×3 coupler to give full play to its advantages. However, the NPS method based on the 3×3 coupler is affected by the deviation of the splitter ratio of the coupler and difference in the light intensity coefficient of the photodetector. The three-channel light intensity direct current (DC) component coefficient and alternating current (AC) component coefficient produces real-time deviation. This leads to the residual DC component in the operation of eliminating the DC component for the original NPS algorithm, which destroys the differential cross-multiplication operation. Additionally, the uneven coefficient of the AC component causes the automatic gain control (AGC) operations failure to eliminate the influence on the optical signal from fluctuations, such as the light source. Eventually, the demodulated phase becomes inaccurate, which affects the sensitivity of the hydrophone. However, existing methods for compensating amplitude deviation cannot satisfy long-term stable balance and real-time correction. To solve the influence of real-time deviation of the AC component coefficients of the three output signals in the NPS system on the demodulation, a method of real-time correction of NPS is applied to the demodulation of distributed feedback (DFB) fiber laser hydrophone, which makes it easy to realize independent and stable demodulation on unmanned platforms.

Methods Wrap the single arm of the interferometer in the NPS demodulation system on a piezoelectric ceramic (PZT), and apply a sinusoidal signal with an amplitude greater than π rad to initiate full amplitude signals of the three outputs. Obtain the maximum and minimum values of the three output signals in the current PZT vibration period, calculate the eigenvalues of the DC component coefficients of each path, and obtain the average value of current eigenvalue and the sum of the DC component coefficients of all previous PZT vibration periods as the current period DC component coefficient; calculate the characteristic value of the AC component coefficient of each channel, and obtain the average value of current characteristic value and the sum of the AC component coefficients of all previous PZT vibration periods as the AC component coefficient of the current period. The three output signals of each period minus the respective periods. The DC and AC components are divided by their respective AC component coefficients to obtain the normalized three-channel AC component signals in real-time and NPS subsequent operations are performed. Finally, the measured phase signal is obtained, and demodulation is completed.

Results and Discussions According to the experiment, comparing the demodulation effect of real-time correction NPS and the unmodified demodulation effect, it is found that the real-time correction demodulation can effectively compensate for the deviation of DC and AC component coefficients, and its demodulation can truly reflect the measured physical quantity, as shown in Figs. 7(a), 7(b), 8(a), and 8(b). When the experimental system works continuously for 15 h, the overall demodulation effect is stable, as shown in Fig. 9. In the underwater vibrating liquid column test experiment, the algorithm can effectively restore the vibration signal even though noise is introduced from an external source and other factors.

Conclusions A signal demodulation method for real-time correction of NPS for fiber laser hydrophone is proposed. This method is used to test 200 Hz--4 kHz vibration signals, and the system runs continuously for 15 h. The demodulation results can restore the vibration signal. Theoretical and experimental results show that this method can effectively compensate for the deviation of DC and AC component coefficients, improve the demodulation accuracy of DFB fiber laser hydrophone, and decrease the hardware costs. The calculation amount is not large, and it is expected to realize real-time high-speed miniaturization demodulation.

Objective The coexistence of rain and fog is a common atmospheric phenomenon in winter. When laser is transmitted in rain and fog weather, the attenuation is not only affected by rain but also by fog. Because of the small rainfall rate, fog attenuation is usually greater than rain. Globally, numerous studies have been conducted on the transmission characteristics of laser in rain and fog individually, but research on laser transmission characteristics in rain and fog coexisting weather is inadequate. To the best of our knowledge, the interaction between raindrops and fog droplets has not been considered. In this study, based on the mechanism of rain clearing fog, we improve the existing models and propose a prediction model of atmospheric attenuation in rain and fog coexisting weather, which dynamically shows the changes of atmospheric attenuation and transmittance with time in rain and fog coexisting weather. We believe that the findings of this study will have reference significance for the estimation and evaluation of atmospheric attenuation in wireless optical communication and related fields.

Methods In rain and fog coexisting weather, the precipitation process has a significant effect on fog removal. As fog is removed by raindrops, the scale distribution of fog will change. In this article, we employ the general dynamic equation considering wet deposition to study the dynamic change of fog with the removal of raindrops. Then, we use the lognormal scale distribution model of raindrops and Gamma distribution model of radiation fog and advection fog to calculate the total attenuation of rain and fog after clearing. Further, we employ Lambert-Beer law to reckon the transmittance of laser after a certain distance. Finally, the numerical results are compared with the Monte-Carlo simulation results to verify the rationality of the proposed model to a certain extent.

Results and Discussions The rainfall intensity positively correlates with the fog removal effect. Since the rainfall in rain and fog coexisting weather is small, the attenuation of fog gradually decreases with the removal of fog by rain (Fig. 1). When the rainfall rate is 1 mm/h, the transmittance of advection fog tends to be stable after 5 h of rainfall, whereas, the radiation of fog takes a longer time (Fig. 2). The water content of advection fog is higher than that of radiation fog, so the albedo of advection fog is higher than that of radiation fog. Owing to the obvious removal of advection fog by rain, the density of advection fog decreases, the proportion of raindrops per unit volume increases, the absorption increases, the scattering weakens, and the albedo of particle swarm increases (Tables 4 and 5). When the transmission distance is 1000 m and transmittance is less than 5%, the transmittance calculated using the Monte-Carlo method is larger than that calculated using the Lambert-Beer law, and vice versa in other cases.

Conclusions In this article, we employed the lognormal scale distribution model of raindrops and Gamma distribution model of radiation fog and advection fog to study dynamic change of fog with raindrop removal using the general dynamic equation considering wet deposition. Based on the basic principle of atmospheric attenuation, the attenuation of laser propagation in the atmosphere changes with the fog scale distribution model. Because most of the radiation fog droplets are medium-sized aerosols, they are difficult to be wet removed by rainfall, so the transmittance increases slowly with time. The droplet size of the advection fog is large and quickly removed in the case of moderate and heavy rain, and then the transmittance is at a fixed value. Through Monte-Carlo simulation analysis of laser transmission in the atmosphere, in the case of small attenuation, the photon moving step is larger, the scattering times in a fixed distance range are less, the particles hardly reach the receiving plane after the collision, and the calculation results of the Monte-Carlo method are minute. With the increase in particle number density and transmission distance, the number of scattering increases, and the transmittance calculated using the Monte-Carlo method is slightly higher than that calculated using the Lambert-Beer law. Over time, owing to the removal of fog by rainfall, the droplet number density decreases, and the numerical difference between the two methods increases.

Objective Under the action of long-term fatigue loading, the metal structures of the spacecraft, high-speed train, ship, and other large equipment are prone to fatigue crack in the stress concentrated part. Under the repeated action of alternating loading, the structure will be further extended, resulting in failure and fracture, causing major production safety hazards. In the fatigue crack monitoring field, the commonly used technical means are sound emission, ultrasonic guided wave, and strain monitoring. With the development of strain sensors, the strain monitoring method plays an important role in fatigue crack identification and life monitoring. Among them, the fiber Bragg grating (FBG) sensor is characterized by high precision, sensitivity, stability, and portability along with long monitoring range, promoting further development of strain monitoring technology toward higher accuracy, higher sensitivity, higher reliability, and better convenience. In this paper, a real-time continuous crack monitoring method based on the FBG sensor array is proposed for the fatigue crack monitoring of aluminum alloy structures in service.

Methods The research method of this paper is shown in a flow chart (Fig. 1), which is mainly divided into the following four parts: parameter selection, experiment and data processing, prediction and evaluation, and model building. First, fatigue loading test parameters and crack-propagation characteristics are obtained via tensile tests. The strain field distribution characteristics during crack propagation are obtained via extended finite element simulation. Based on the strain field analysis and fatigue loading experiment results of different crack-propagation stages, a reasonable layout of the FBG sensor array is designed. Through fatigue loading and strain monitoring experiments, the relationships among fatigue loading times, wavelength response, and crack length are obtained. Values of peak-peak wavelength are extracted as characteristic values to exclude the interference of temperature and deformation during the stretching process. The three-parameter exponential method is used to fit the a-N (a is the crack length, and N is the loading times) curve of fatigue expansion. Then, based on the experiment, the gradient boosting regression tree (GBRT) algorithm is used to build the prediction model, and the comparison is made using linear regression and support vector regression (SVR) methods. The three models are evaluated based on various indicators, such as explain variance score (EVS), mean absolute error (MAE), mean square error (MSE), R-squared (R²), and five-fold cross-validation. Finally, the best performing method is selected as the final prediction model on the basis of the evaluation results.

Results and Discussions Combined with the finite element simulation, fatigue loading experiment, and machine learning algorithm, this paper presents a method of fatigue crack strain field inversion prediction based on the FBG sensor array. To study the strain field change in the crack-propagation process, the crack extension strain field change is obtained in the cloud via finite element simulation (Fig. 3). Simulation experiment results show that the crack tip is singularity and the strain center will shift with the growing crack tip. Based on the simulation results, a sensor layout method was designed with six FBG sensors equally spaced on both sides of the crack (Fig. 7). The experimental results show that this design can effectively monitor the strain field changes at various stages of crack growth.

After filtering the experimental results of fatigue loading and strain monitoring, peak-peak wavelength values are extracted as the characteristic values. The response curves of loading times, crack length, and wavelength peak-to-peak values can be obtained (Figs. 11--12). The simulation results can be verified via direct analysis of the graph. The direction of crack propagation can be determined by placing sensors in the crack-propagation position.

Based on the strain response data collected in the experiment, the GBRT algorithm was used to invert the strain field in the stable expansion stage. In total, 31000 data with six features were imported into the GBRT model for five-fold cross-validation. The learning rate was 0.1, and the maximum iterations was 150 times. The regression results were consistent with the real value (Fig. 16). To verify the predictive performance of the GBRT method, it is compared with the linear regression and SVR methods. The results of cross-validation show that the SVR and GBRT methods are stable. In the evaluation of EVS, MAE, MSE, and R², the results of the GBRT model were closest to the ideal value best.

Conclusions The study is aimed at the safety monitoring requirements of large equipment in long-term service state and realizes the full-life fatigue crack monitoring of the metal structure parts in its key parts, which is important from the practical application perspective. Based on theoretical analysis, numerical simulation, and strain experiment, using strain field data to invert the crack length is proved to have a reliable theoretical basis and practical feasibility. The proposed FBG sensor array is a good strain monitoring method, which makes the collected local strain show regularity and gradation at different stages of crack growth, and realizes the prediction of crack growth degree and the identification of crack cracking direction. Based on the prediction method of fatigue crack length from experimental data, the GBRT algorithm is compared with linear regression and SVR methods. The results show that the GBRT algorithm performs better in strain field inversion by the evaluation of EVS, MAE, MSE, R², and cross-validation.

Objective The optical frequency comb generation schemes mainly include mode-locked laser, electro-optic modulation comb, nonlinear Kerr micro-resonator comb, and nonlinear supercontinuum-based comb. For the nonlinear supercontinuum-based comb scheme, flat optical frequency comb generation has been extensively studied, which is based on self-phase modulation and optical wave breaking in silica-based high nonlinear fibers (HNLFs) with near-zero flattened normal dispersion. The dispersion of the silica-based HNLFs needs to be near zero in the normal dispersion regime to generate the flattened and broadened spectrum. Furthermore, several hundred meters long silica HNLFs are required because of their relatively low nonlinearity coefficients. However, such a long fiber causes dispersion variation along the fiber owing to the fabrication inaccuracy. Herein, high repetition rate flat optical frequency comb generation based on normal dispersion lithium niobate (LiNbO₃) optical waveguides is proposed and numerically analyzed. The 3.6-m-long cavity-less nonlinear LiNbO₃ optical waveguide with normal dispersion can be used to solve the dispersion variation problem in the HNLFs. The repetition rate of the proposed optical frequency comb can reach 10--50 GHz owing to the electro-optic modulator tunable optical pulse source, and the waveguide structure and parameters used in the simulation are achievable using current technologies. The proposed optical frequency comb has potential applications in astronomy, optical communication, and microwave photonics. The parameters influencing optical frequency comb performances, time-frequency evolution mechanism, and spectral coherence are also analyzed, which provides a detailed guideline for flat optical frequency comb generation.

Methods Firstly, the dispersion and nonlinear coefficient of the LiNbO₃ waveguide are obtained using the finite element method mode solver. Then, the time-frequency evolution process of the pulse in the waveguide is simulated with the generalized nonlinear Schr?dinger equation. By simulating the pulse evolution process in time and frequency domains, a flat broadband optical frequency comb is obtained after a 3.6 m propagation length. Next, the time-frequency evolutions of a hyperbolic secant pulse, a Gaussian pulse, and a super-Gaussian pulse are simulated using the X-Frog technology. The pulse time-frequency evolution mechanism is analyzed. X-Frog spectrograms connect the time and frequency domains of the pulse, which clearly shows the change of pulse chirp during the propagation. In addition, the effects of several parameters, such as the second-order dispersion, initial peak power, initial pulse width, third-order dispersion, initial pulse chirp, loss, and initial pulse waveform, on the performance of the optical frequency comb are analyzed. Finally, the spectral coherence of the optical frequency comb is obtained by simulating 100 individual spectra, where the input chirp-free hyperbolic secant pulses are seeded with different random simulated quantum-limited shot noises. It is verified that the optical frequency comb has good spectral coherence in the whole bandwidth.

Results and Discussions Firstly, the LiNbO₃ waveguide structure with optimized normal dispersion and nonlinear coefficient is obtained through dispersion engineering (Fig. 1). Figure 2 shows a schematic diagram of optical frequency comb generation. A flat optical frequency comb with a 3 dB bandwidth of about 32 nm is obtained with a suitable propagation length (Fig. 3). It is found that for an optical frequency comb with a repetition rate of 10--50 GHz, the pulse-overlapping effect for adjacent pulses can be ignored in a short propagation length (3.6 m herein), which verifies that studying the spectral envelope of single-shot pulse and spectral envelope of optical frequency comb has certain commonalities (Fig. 4). Second, based on the X-Frog technology, the mechanisms of spectral broadening and flattening due to normal dispersion, self-phase modulation, and optical wave breaking are analyzed. The time-frequency evolution processes of the hyperbolic secant and Gaussian pulses are identical. The optical wave breaking effect occurs during propagation. However, for the energy transfer from the central wavelength of the front edge (back edge) to the long wavelength (short wavelength), the Gaussian pulse is more effective than the hyperbolic secant pulse (Figs. 5 and 6). For the super-Gaussian pulse, there is almost no optical wave breaking during propagation. However, comparing with the hyperbolic secant pulse and Gaussian pulse, the super-Gaussian pulse can produce a flatter optical frequency comb (Fig. 7). Third, based on the empirical formula for the propagation length of optical wave breaking and flat bandwidth, the parameters influencing the performances of the optical frequency comb are analyzed (Fig. 8). Finally, it is verified that the proposed optical frequency comb exhibits good spectral coherence, beneficial for its applications (Fig. 9).

Conclusions Herein, a new generation scheme for high repetition rate flat optical frequency comb generation based on a normal dispersion LiNbO₃ optical waveguide was proposed. By optimizing the LiNbO₃ ridge waveguide structure and dispersion engineering, a flat optical frequency comb with a 3 dB bandwidth of about 32 nm was realized via simulation. The time-frequency evolution processes of hyperbolic secant, Gaussian, and super-Gaussian input pulses during propagation were analyzed. From the simulation results, a flat broadband optical frequency comb is generated in the normal dispersion LiNbO₃ waveguide owing to the combined effects of normal dispersion, self-phase modulation, and optical wave breaking. In addition, the effects of several parameters, such as the second-order dispersion, initial peak power, initial pulse width, third-order dispersion, initial pulse chirp, loss, and initial pulse waveform, on the performance of the optical frequency comb were studied. The proposed optical frequency comb exhibits good spectral coherence in the whole spectral range. This study shows that the LiNbO₃ waveguide has a potential benefit for the 1550-nm broadband flat optical frequency comb based on a normal dispersion integrated nonlinear optical waveguide.

Objective Laser-matter interaction research using nanosecond pulse lasers has resulted in industrial applications, such as laser processing, laser marking, and laser cleaning, because of its advantages of moderate cost and high reliability. The repetition rate is an important indicator to describe the number of laser pulses per unit time. The higher the repetition frequency, the more the number of working pulses per unit time. Thus, high-quality processing results can be obtained via high-speed and high-precision processing using nanosecond pulse lasers. Therefore, development efforts in this field focus on achieving a narrow pulse width, high average power, and high repetition rate. With the increase in pump power, traditional lasers such as fiber lasers have strong nonlinear effects, such as stimulated Brillouin scattering and backscattering, resulting in a wider output pulse width; however, the peak power obtained is limited. Because of the radial distribution of the heat generated by the laser rod and the uneven temperature distribution, the radial temperature gradient will cause a serious thermal lens effect, which will affect the high power output and beam quality of the nanosecond laser. The emergence of thin-disk lasers has effectively improved this situation, wherein multipass pump technology is used to compensate for the considerably low single-pass absorption of the gain medium. The ingenious pump method improves its pump absorption efficiency, while the single-sided pumping back cooling method further reduces the thermal lens effect of the crystal, making it widely used in continuous and nanosecond pulse fields.

Methods A cavity-dumped laser based on an independently developed 24-pass thin-disk pump module was investigated with a high repetition rate, narrow pulse duration, and high beam quality. First, the relationship between media absorption and the number of pump passes was calculated according to the Beer-Lambert law. Then, using the quasi-three-level rate equations, the dependence of the threshold pump power and continuous output power on the transmittance of the output coupler was analyzed. Subsequently, to achieve the balance among absorption efficiency, thermal lens effect, and processing difficulty, the thickness of the thin crystal of the multipass pump module was selected to be 200 μm and the multipass number N was 24. Finally, to obtain the continuous and pulsed output of the linearly polarized laser, a Z-shaped cavity in which the thin film polarizer acts as both a polarizer and a high reflectivity mirror in the cavity, was designed.

Results and Discussions The continuous output performance of the Yb∶YAG quasi-three-level thin-disk laser is shown in Fig. 11, and the spot of the output laser and the measured beam quality M² are shown in Fig. 12. Figure 11 shows that when the pump power reaches 30 W, the laser output starts. The pump power is close to the pump threshold power calculated theoretically (Fig. 5). Simultaneously, the output power increases linearly with the increase in pump power, the slope efficiency is 62.1%, the maximum output power is 94.1 W, and the maximum light-to-light conversion efficiency is 52.84%. Figure 12 shows that the output laser intensity distribution is Gaussian and the beam quality M² is close to the diffraction limit. In addition, the cavity-dumped nanosecond pulse performance is shown in Fig. 13. Figure 13 shows that the pulse output power increases with an increase in the pump power and the slope efficiency is 45.3%. It can be seen from the right axis of Fig. 13 that the optical-optical conversion efficiency also increases with an increase in the pump power and gradually stabilizes. When the pump power reaches 180 W, the average pulse output power is 65.4 W, the peak power is 88.02 kW, and the optical-optical conversion efficiency is as high as 36.33%. The Yb∶YAG cavity-dumped thin-disk laser pulse sequence and waveform are shown in Fig. 14. Figure 14(a) shows that at a repetition frequency of 100 kHz, the pulse output sequence is stable, further, only some pulse amplitudes are lower than the average pulse amplitude. Air ionization can be observed in the experiment; therefore, it is speculated that the reason for the irregular pulse sequence may be that the entire resonant cavity is placed in an air environment. The excessive peak power causes the air to ionize, and finally, air disturbance affects the stability of the pulse output. It can be seen from Fig. 14(b) that the leading edge of the output pulse is very narrow and the trailing edge is wide, which is considerably consistent with the cavity-dumped waveform obtained from the theoretical calculation in Fig. 6, which proves the accuracy of the theoretical calculation results of the previous cavity dumping.

Conclusions Based on the Beer-Lambert-law and the quasi-three-level rate equations, the performance of the continuous and pulse outputs of the Yb∶YAG thin-disk laser is theoretically calculated and the effect of the multipass number, crystal thickness, and transmittance of the output coupling mirror on the laser output is also analyzed. Based on the 24-pass pump module independently designed by the laboratory and optimized cavity design, the maximum continuous output power can reach 94.1 W and the optical-optical conversion efficiency is 52.8% when the pump power is 180 W. At a repetition rate of 100 kHz, the maximum average output power of the pulse output is 65.4 W, the pulse output sequence is stable, and the pulse width is as narrow as 7.425 ns. The theoretical predictions are verified experimentally, and the experimental results are significantly higher than those reported in the previous literature, which has important reference significance for related research work. Because of the high peak power density in the cavity, air ionization occurs in the cavity. Therefore, to obtain high optical-optical conversion efficiency, better beam quality, and pulse stability, the next step is to place the cavity in a vacuum environment.

Objective Semiconductor lasers have the advantages of high efficiency, easy integration, high reliability, and easy tuning; hence, they are used in various applications such as fiber coupling, seed laser sources, medical equipment, and communication systems. To increase the output power of semiconductor lasers, a wide-ridge waveguide structure is usually employed; however, in such lasers, the lateral mode is poor and the energy distribution is uneven. These observations are mainly reflected in the “multilobe” phenomenon of the near-field spot, thereby limiting the wide applications of semiconductor lasers. To improve the lateral mode performance of semiconductor lasers, researchers have proposed many solutions including an external cavity laser structure, tapered waveguide structure, and curved waveguide structure. These approaches can improve the lateral mode and quality of the lateral beam. However, they have the disadvantages of low output power, complicated process, and high threshold. In this study, a wide-ridge waveguide semiconductor laser with a lateral microstructure (LMWR-LD) was proposed. Results show that the output power, slope efficiency, and electro-optic conversion efficiency of LMWR-LD were improved, while the mode competition inside the cavity was reduced. Moreover, the lateral microstructure and wide-ridge waveguide structure were formed in the same step of photolithography, which is beneficial to simplify the process and reduce the cost.

Methods Based on the threshold gain theory, the influence of the mode loss on the mode threshold gain was analyzed. As the mode loss increased, the threshold gain of the mode increased. The lateral mode characteristics of wide-ridge waveguide semiconductor laser (WR-LD) were simulated using PIC3D, and the optical field distribution of each order lateral mode was shown (Fig. 2). The fundamental mode optical field was a single spot with a Gaussian distribution, and the energy was mainly concentrated at the center of the optical field. A broken line was observed in the middle of the first-order lateral mode optical field, which was divided into two spots. Thus, the energy distribution of the laser was uneven. When the order index of the lateral mode increased, the number of broken lines in the corresponding lateral mode optical field increased and the energy distribution became more uneven. Based on the characteristics of the optical field distribution of each order lateral mode in WR-LD, the suppression mechanism of the lateral microstructure on lateral modes (Fig. 3) was observed using FDTD simulation software. The influence of the microstructure width on the mode loss of each order lateral mode was investigated [Fig. 4(a)]. When the microstructure width was fixed, each order lateral mode exhibited different losses. By analyzing the loss difference between the fundamental and high-order lateral modes [Fig. 4(b)], the optimal lateral microstructure width can be obtained. In this case, the loss of the fundamental mode was small and that of the high-order lateral mode was large. Thus, the lateral mode characteristics of LMWR-LD were improved owing to the introduction of microstructure.

Results and Discussions Experimental results show that owing to the fierce competition among each order lateral mode, the near-field spot showed a “mutilobe” appearance in WR-LD [Fig. 5(a)]. After introducing the lateral microstructure, the near-field spot “mutilobe” phenomenon of the LMWR-LD was clearly eliminated [Fig. 5(b)]. Comparing the near-field optical distribution of these two devices, the intensity at the edge of near-field optical distribution for LMWR-LD was observed to decrease significantly [Fig. 5(c)]. This proves that the lateral microstructure had a good inhibition effect on the high-order lateral mode. Because the “multilobe” phenomenon of the near-field optical distribution of LMWR-LD was eliminated, the far-field optical distribution presented a “single-lobe” phenomenon and the full width at half-maximum divergence angle of LMWR-LD decreased from 2.07° to 2.05° (Fig. 6). At 0.5 A input current, the LMWR-LD achieved an output power of 130 mW, showing an improvement of 58.5% compared with WR-LD [Fig. 7(a)]. Moreover, the slope efficiency and electro-optic conversion efficiency of LMWR-LD were 0.27 W/A and 14.5%, respectively, which are 80% and 55.9% higher than those of WR-LD [Fig. 7(b)]. The improvement in slope efficiency and electro-optic conversion efficiency was mainly attributed to the introduction of lateral microstructure. Because the high-order lateral mode was suppressed in the LMWR-LD cavity, the mode competition in the cavity decreased to a certain extent and the optical field distribution of the output laser became more uniform. Therefore, the matching degree of the optical field and injection current was improved.

Conclusions A LMWR-LD structure was proposed in this study. The diffraction loss of the high-order lateral mode was increased by introducing microstructures on both sides of the wide ridge, leading to the suppression of high-order lateral modes. Moreover, the “multilobe” phenomenon in the output laser of LMWR-LD was eliminated. After the fabrication and packaging of LMWR-LD, the test and analysis were conducted. Experimental results show that compared with WR-LD at 0.5 A, the output power of LMWR-LD increased from 82 mW to 130 mW, slope efficiency increased from 0.15 W/A to 0.27 W/A, and the electro-optic conversion efficiency increased from 9.3% to 14.5%. Additionally, the lateral microstructure of LMWR-LD was simultaneously formed with the wide-ridge waveguide structure in ultraviolet lithography. Further, LMWR-LD offers the advantages of simple process and low cost. Based on this research, by optimizing the structure of the device, high-power semiconductor laser devices with good lateral mode characteristics can be achieved.

Objective With their high sensitivity to Ge and InGaAs and excellent transparency in the atmosphere, eye-safe lasers emitting in the 1.5--1.6 μm spectral range have great application prospects in the lidar, rangefinder, and three-dimensional imaging. Vehicular lidars operating at 1.5 μm have attracted wide attention in the recent development of unmanned aerial vehicles (UAVs). Therefore, high-performance 1.5-μm lasers with high repetition rate, high pulse energy, and narrow pulse duration are commercially valuable. Passively Q-switched lasers operating at 1.5 μm in different gain media, such as Er ³⁺/Yb ³⁺co-doped borated crystals and phosphate, have been often reported. Owing to their high thermal conductivity, high Yb ³⁺→ Er ³⁺ energy-transfer efficiency, and weak up-conversion loss, Er, Yb∶YAB crystals are considered as an excellent 1.5 μm laser material. However, all previous reports on Er, Yb∶YAB lasers have employed c-cut Er, Yb∶YAB crystals. This paper reports a passively Q-switched microchip laser with an a-cut Er, Yb∶YAB crystal.

Methods This paper explores a passively Q-switched microchip laser with an a-cut Er, Yb∶YAB laser crystal as the gain medium. The experimental setup is shown in Fig. 2(b). The detailed performance of a laser with an a-cut Er (atomic fraction of 1.5%)∶Yb (atomic fraction of 12%)∶YAB crystal was reported in our previous work. In the present experiment, a Co ²⁺∶MgAl₂O₄ crystal with an initial transmission of 96% at 1.5 μm was employed as the saturable absorber. An input mirror and an output coupler were separately coated on the surfaces of two sapphire crystals, which acted as heat sinks in the microchip laser. The input-mirror material was antireflective in the 800--1000 nm range and reflected 99.8% of the light in the 1500--1600 nm range. Meanwhile, the output coupler transmitted 2.5% of the light in the 1500--1600 nm range. The input mirror and output coupler were tightly attached to the surfaces of the Er∶Yb∶YAB and Co ²⁺∶MgAl₂O₄ crystal, respectively. The resonator length was 2.7 mm. The pump source was a 976-nm diode laser with a central wavelength of 975.5 nm, a core diameter of 105 μm, and a numerical aperture of 0.22. After passing the lens assembly, the pump beam was focused into the laser crystal (with approximate radius of 60 μm). The microchip laser was maintained at 19 ℃ by water-cooling.

Results and Discussions Pumped by the 976 nm diode laser, the microchip laser successfully generated 1.5-μm pulses. The output power of the laser was measured by a PM 100D power meter with an S314C thermal power head. The pulse profile was recorded by an InGaAs photodiode connected to a digital oscilloscope with a 1.0-GHz bandwidth, and the laser spectrum was recorded by a wavescan laser-spectrometer. From the plotted dependence of average output power on the incident power (Fig. 3), the laser threshold was determined as 4 W. The average output power increased as the incident pumped power increased from 4 to 6 W. At higher incident powers (> 6 W), the average output power was not obviously increased and bends appeared in the output characteristics. The average output power was maximized at 275 mW. The repetition rate increased with incident pump power, and was maximized at 127 kHz. The pulse train [Fig. 4(a)] was stable and the pulse-amplitude variations and time jittering remained at 5%. The pulse duration [Fig. 4(b)] was 12 ns, narrower than that in previous reports. The laser wavelength was 1530 nm, consistent with previously reported emission spectra of Er, Yb∶YAB crystals. The pulse energy and pulse duration remained at approximately 2 μJ and 13 ns, respectively. As the Er∶Yb∶YAB crystal is optically uniaxial, it was characterized for two principal light polarizations, E∥c(π) and E^c(σ) (in which the optical axis is parallel and perpendicular to the c axis, respectively). The emission coefficient was much higher in σ-polarization than that in π-polarization, implying linear polarization of the pulses generated from the a-cut Er, Yb∶YAB microchip laser. In pulse-polarization tests (Fig. 5), the extinction ratio of the pulse laser was 44∶1. The spatial profile of the output beam presented high ellipticity and an even energy distribution. Therefore, a high-repetition-rate linear polarization laser was successfully fabricated from the microchip.

Conclusions This paper reports a microchip laser based on an a-cut Er, Yb∶YAB crystal. A Co ²⁺∶MgAl₂O₄crystal with an initial transmission of 96% was employed as the saturable absorber. The cavity length and maximum repetition rate of the microchip laser were 2.7 mm and 127 kHz, respectively, corresponding to the pulse energy and duration of 1.8 μJ and 12 ns, respectively. The emission coefficient was much larger in σ-polarization than that in π-polarization, indicating linear polarization of the pulse laser. In summary, a high-repetition-rate linearly polarized 1.5-μm pulse laser was fabricated by a simple and reliable method.

Objective Owing to the advantages of being highly transmitted in the atmosphere, being safe to human eyes, being in the absorption spectrum band of water molecules, and being an efficient pump source for 3--5-μm laser, solid-state lasers emitting around 2 μm have been widely employed in many areas, including the medical field, high-precision ranging, environmental monitoring, and photoelectric counter-measurement. Laser source emitting at 2 μm with high energy and high beam quality output performance is a paramount component of the remote wind-measuring light radar. In addition, more than one hundred nanosecond pulse duration and narrow spectral linewidth are required. Therefore, the Q-switched 2-μm solid-state laser with a high energy output at room temperature has been a research hotspot for the space-borne lidar. Usually, the laser source used in the ground-based wind lidar system adopts the traditional liquid-cooling method, whereas those used in the air- or space-borne lidar system should adopt the conductive cooling design. To meet the special application requirement of the space-borne lidar, in this study, a laser diode (LD) side-pumped (Tm, Ho)∶YLF laser with a conductive cooling structure is developed by optimizing the key parameters of four-mirror ring cavity, such as the length of the cavity, the pump beam size inside the gain medium, output coupler mirror. As a result, high energy output with high energy efficiency and good beam quality are achieved.

Methods The special eight-shaped ring cavity comprising two concave mirrors and two plane mirrors is designed (Fig. 1). The pulse width of the Q-switched laser is calculated as a function of cavity length (Fig. 2). To obtain a Q-switched pulse output of more than one hundred pulse width, the length of the ring cavity is chosen about 2580 mm. In theory, there are two waist positions inside the ring cavity, one placed with acousto-optic modulation (AOM) and another with (Tm, Ho)∶YLF crystal. In experiments, the driving signal waveform of the AOM is a square wave pulse with a pulse duration of 4 μs. In addition, the LD side-pumped arrangement with a novel wedge waveguide lens is specially designed (Fig. 4). The crystal rod is side-pumped by two banks of five radically arranged LD modules, each is capable of outputting a maximum of 200-W pump power. The size of the lens duct is designed by ZEMAX software, and the energy distribution is calculated by MATLAB (Fig. 5). Almost 48% of the absorbed pumping energy by the gain crystal (the crystal radius is r=2 mm) is centralized in the central area of the rod (r<1.1 mm).

Results and Discussions At a repetition rate of 1 Hz, pulse energy and pulse width variation are recorded as functions of the pump energy input in the free-running and Q-switched modes (Fig. 6). A maximum output pulse energy of 340 mJ is obtained in the free-running mode with 3.3 J of pump energy input; the optical-optical efficiency is approximately 10.3%, and the slope efficiency is 22.2%. Meanwhile, the maximum output pulse energy of 141 mJ is obtained in the Q-switched mode with pump energy of 3.3 J; the optical-optical efficiency is 4.3%, and the slope efficiency is 8.3%. The output ratio of Q-switching to free-running reached up to 0.41. The Q-switched pulse waveform is detected by a photodetector with a 12.5-GHz sampling rate, and a pulse width of about 103 ns is detected (Fig. 7). Obviously, multilongitudinal mode lasing is demonstrated. The spectral linewidth is almost 0.82 nm (Fig. 8). The laser beam quality is measured using a lens with a focal length of 1 m and a CCD(Charge Coupled Device) camera; the spot diameter of the laser beam is recorded at different positions along the optic axis. Fitted by the Gaussian beam propagation equation, the beam quality factors of Mx2 and My2 are achieved as 1.22 and 1.08, respectively (Fig. 9). The inlet in Fig. 9 shows the far-field intensity distribution of the laser beam, indicating the output pulse is near the fundamental transverse mode.

Conclusions To meet the requirements of high pulse energy output at 2-μm spectral range for remote wind measurement in space-borne lidar, an acousto-optic Q-switched, conductively cooled (Tm, Ho)∶YLF laser emitting at 2051 nm is developed in this study. In a specially designed eight-shaped ring cavity, using an LD side-pumped arrangement with a novel wedge waveguide lens-coupling system, a Q-switched laser pulse output with more than one hundred nanosecond pulse width is achieved. At a repetition of 1 Hz and maximum pump energy of 3.3 J, a 141-mJ Q-switched laser with around 103-ns pulse width is obtained. The optical-optical and slope efficiencies are 4.3% and 8.3%, respectively. The central wavelength is 2051.4 nm, and beam quality factors of Mx2 and My2 are detected as 1.22 and 1.08, respectively. The experiment results are helpful to develop a high pulse energy of about 2-μm laser pulse output with a narrow linewidth by adopting a seeder injection method, which is needed to develop the high-performance coherent wind lidar for remote detection.

Objective Solid-state lasers have attracted extensive attention because of their advantages of high efficiency and high beam quality. Solid-state tube lasers with zigzag beam paths (SSZTLs) combine the outstanding characteristics of rod and slab lasers, such as compact structure and light weight, and overcome the shortcoming of insufficient thermal load capacity, providing a potential approach to realize high-power lasers. These advantageous characteristics have resulted in some attractive applications in the fields of military defense and industrial manufacturing. However, the beam quality of SSZTLs is extremely sensitive to alignment and fabrication errors of the gain medium owing to their unique tubular structure. To improve the beam quality of SSZTLs, we propose a novel self-correction method to eliminate annular off-axis aberrations of the laser beam in SSZTLs.

Methods Taking neodymium-doped yttrium aluminum garnet (Nd∶YAG) two-stage tube laser amplifiers as an example, a novel beam-correction method based on a right-angled conical reflector was proposed for the self-correction of annular off-axis aberrations in high-power two-stage thin-walled tube laser amplifiers. A right-angled conical reflector makes the laser beam propagate through two conjugate beam paths successively, which compensates the off-axis aberrations. First, based on a numerical simulation, the validity of this method to correct fabrication and alignment errors of a single tube was verified. Then, the correction effect of this method on matching errors of two-stage tubes was further analyzed. Finally, the influence of the structural parameters of the right-angled conical reflector on the aberration correction effect was discussed and the wavefront aberration caused by alignment and fabrication errors of the right-angled conical reflector was quantitatively analyzed using the annular Zernike polynomial decomposition theory.

Results and Discussions The proposed self-correction method can effectively correct alignment and fabrication errors induced by a single tube medium. For tube media with concentricity, parallelism, and alignment errors, the output beam quality of SSZTLs with planar mirrors degrades rapidly and almost linearly with an increase in these errors. The output beam quality after correction is significantly improved, and the energy concentration of the focal spot becomes better (Fig. 3). In addition, for alignment error, although the focal spot distribution is well focused after correction, its off-axis tendency is not corrected. When the alignment error is large, the focal spot distribution shows an obvious off-axis tendency, but the ideal focal spot distribution can still be obtained. The self-correction method can only correct the off-axis aberration induced by two-stage tubes and contributes little to the correction of input beam inclination angles [Figs. 3(c6)--(c8) and Fig. 4]. To further illustrate beam quality degradation characteristics, laser beam aberrations were analyzed using the annular Zernike polynomial decomposition theory of wavefront aberration. As shown in Fig. 5, irrespective of the type of error considered, the main aberrations are tilt and coma and the peak valley (PV) of off-axis aberrations decreases by about two orders of magnitude compared with those in two-stage tubes without self-correction (Fig. 5). In addition, the proposed method can effectively correct the matching errors of two-stage tubes. When concentricity and parallelism matching errors exist in the two-stage tubes, the PV of the wavefront distortion decreases dramatically (Tables 1 and 2).

Since achieving perfect assembly of the right?angled conical reflector and two?stage tubes in actual corrections is difficult, analyzing the key parameters of the right?angled conical reflector and their effects is necessary. Taking the sensitive concentricity error as an example, the correction effects of a non?ideal right?angled conical reflector were analyzed. When the right?angled conical reflector has translation, rotation, and taper errors tolerance for the translation and rotation errors can reach tens of microns and milliradians, respectively, while that for taper error is only microradians. Therefore, the proposed method has high tolerance for alignment errors and is highly sensitive to fabrication errors (Fig. 8). To further illustrate the effects of alignment and fabrication errors of the right?angled conical reflector on wavefront phase, laser beam aberrations were analyzed using the annular Zernike polynomials decomposition theory. Results show that the main components of translation error are tilt and coma, rotation error mainly induces astigmatism, and taper error primarily results in defocus (Fig. 9).

Conclusions In this paper, we proposed a self-correction method for the annular aberrations of high-power two-stage tube laser amplifiers. The simulation results validate the self-correction method in correcting alignment and fabrication errors of a single tube as well as matching errors of two-stage tubes. The proposed method can significantly eliminate the distortion wavefront caused by concentricity and parallelism errors of a single tube and the matching errors of two-stage tubes. However, the proposed method fails to compensate for the tilt aberration caused by alignment error. In conclusion, the proposed method not only dramatically improves the beam quality of two-stage tube laser amplifiers but also expands the range of incident angles for the input beam. Moreover, the right-angled conical reflector used in this work has a large tolerance for alignment errors, which is beneficial for engineering applications. In practical applications, to ensure the availability of the self-correction method, controlling fabrication errors of the right-angled conical reflector is necessary.

Objective Since the development of Yb-doped fiber laser, increasing the output of a single fiber has been one of the most important directions. The output of a single fiber has now been able to attain 10 kW-level or above. However, these results are mainly laboratory reports, and few fibers have been adopted in practical applications because the coating material of these double cladding fibers age quickly due to the injected high pump power and large amount of quantum defect heating. To minimize the impact of high pump power on coating materials, triple-clad Yb-doped fibers, with an addition of fluorine-doped fused silica between silica and low-index coating, have been suggested. For a given fiber, high brightness of the tandem-pumping can not only reduce the quantum defect heating, but also further increase the pump injection and output-power scaling. To achieve a more reliable and higher laser output, a highly Yb-doped triple-clad fiber used for tandem-pumping is proposed.

Methods The Yb-doped fiber preform has been prepared by modified chemical vapor deposition (MCVD) in combination with sol-gel solution-doping method to improve the Yb-doped concentration without clusters. The doped preform was overcladded and shaped via grinding in an octagonal shape to form the pump cladding. The preform was further surrounded by the second highly fluorine-doped synthetic fused silica cladding with a depressed refractive index to form the out cladding. Then, the preform was drawn and coated as conventional double cladding fiber to obtain the triple-clad fiber (Fig. 1). The fiber was characterized by refractive index profiling, electron probe microanalysis (EPMA), loss, and absorption. Finally, the fiber laser performance was characterized.

Results and Discussions The fiber is 50/350/400 μm core-clad diameter, 0.06/0.22/0.46 NA, and approximately 0.6 dB/m inner cladding absorption at 1018 nm. The EPMA results showed that the homemade triple-clad fiber has a much higher Yb-doped concentration than the commonly used 20/400 μm double cladding fiber (Fig. 2). The reduced core numerical aperture was achieved by higher fluorine-doped silica, and laser performance of the fiber was demonstrated by an all-fiber master oscillator power amplifier at 1080 nm. Figure 3 shows the experimental setup; the seed laser is about 600 W, generated via a 20/400 μm Yb fiber laser oscillator. The triple-clad fiber was used as a gain medium in the power amplifying stage, and the pump sources are 1018 nm fiber lasers. When about 11606 W pump power was absorbed, up to 9010 W laser output with a slope efficiency of 80.5% was achieved (Fig. 4). Further power scaling was limited by the unabsorbed helical light in the fluorine-doped fused silica cladding, which is round-shaped. Thus, in the high-power laser experiment, only the forward pump was on. In future studies, we will improve the design of fiber laser setup and reduce the pump power in the fluorine-doped silica to further increase the fiber laser output.

Conclusions A maximum 9010 W laser output was achieved by the 1018 nm tandem-pumping using the homemade 50/350/400 μm large-mode-area Yb-doped triple-clad fiber. This is an important progress in the field of high-power fiber laser materials. Compared with double cladding fiber, the triple-clad fiber design, which deliveries most of the pump light inside the fluorine-doped fused silica, can greatly minimize the aging effect of the pump light on the coating material. This is of great significance for the long-term operation reliability of high-power laser fiber.

Objective High-power blue-green laser light sources are widely applied in the welding of highly reflective materials (e.g., copper and its alloys), pumping Ti:sapphire lasers, deep ultraviolet laser generation, semiconductor processing, and underwater optical communication and detection. High-power blue-green lasers are mainly derived from blue semiconductor lasers, disk laser frequency doubling, and narrow-linewidth fiber laser frequency doubling. Compared to blue LDs and disc lasers, a fiber laser has the advantages of all-fiber structure, high efficiency, easy heat dissipation, and flexibility. A fiber laser with a 1-μm band kW-level near-diffraction-limit narrow linewidth and full polarization maintenance is an ideal fundamental-frequency light source for high-efficiency frequency doubling and high output power. This paper introduces a high-efficiency green laser based on single-pass frequency doubling of a polarization-maintaining fiber laser.

Methods Figure 1 shows experimental principle. Based on the master oscillator power amplifier cascaded amplification technology, we achieved a fundamental light source with an approximate output power of 1.1 kW and a beam quality at the near-diffraction-limit. The linewidth was ~20 GHz (~0.077 nm) and the polarization extinction ratio was better than 15 dB. We selected a non-critical phase-matched lithium triborate (LBO) crystal as the frequency doubling crystal cut at angles of θ=90° and φ=0°. The acceptance linewidth and matching temperature of the non-critical phase matching LBO crystal for the fundamental-frequency light were theoretically calculated. High-efficiency frequency multiplication can be obtained by optimizing the focal length of the focusing lens and the crystal control temperature.

Results and Discussions The calculated acceptance linewidths of the 40-mm and 60-mm LBO crystals were inversely proportional to crystal length. The focal length of the focusing lens and the crystal working temperature were selected as 400 mm and ~150 ℃, respectively. The difference between the experimental and theoretical optimal temperatures can mainly be explained by the incident angle of the fundamental-frequency light. When the maximum output power of the fundamental-frequency light was 1084 W, the laser output continuous green light at 610 W, and the efficiency of second-harmonic generation was 56.27% (Fig. 2). The beam-quality factor M² of the green light was 1.05, and the output far-field spot presented a fundamental transverse-mode shape (Fig. 3).

Conclusions Based on the narrow-linewidth linear polarization fiber laser and the single-pass frequency doubling scheme, a 610 W single-mode green laser output was obtained. The efficiency of frequency doubling reached 56.27%, and the beam quality M² was 1.05. To the best of our knowledge, we present the most efficient generation of hundreds of watts of continuous-wave green laser using the single-pass frequency doubling scheme. Furthermore, two green-light polarization beams can be combined to realize a kilowatt-level high-brightness green laser output.

Objective A picosecond pulse at 780 nm has played an important role in practical applications and scientific researches. A Ti: sapphire laser is a famous light source at this wavelength range. However, due to its bulk design and complex architecture, the Ti: sapphire laser is sensitive to its environment. Compared with Ti: sapphire lasers, fiber lasers have the advantages of compact structure, high beam quality, and high stability. An alternative way to generate a picosecond pulse at 780 nm is to utilize frequency doubling of the pulse output from an Er-doped fiber laser. In this study, we experimentally demonstrated a frequency doubling efficiency as high as 55.7% based on an all-polarization-maintaining Er-doped fiber laser. Moreover, this scheme favors the advantages such as compact structure and good stability, and can be further applied in many fields such as ultrafast spectroscopy and semiconductor testing.

Methods In this study, a passively mode-locked fiber oscillator and a cascaded fiber amplifier, including a single mode fiber pre-amplifier and a double-cladding fiber amplifier, were used to produce a picosecond pulse at 1550 nm. The fiber oscillator was mode-locked by a semiconductor saturable absorber mirror (SESAM). A segment of Er-Yb co-doped double-cladding fiber with a 12 μm fiber core was used in the main amplifier to provide a laser gain and suppress nonlinear effects at a watt-level average power. The frequency conversion was achieved in a periodically poled lithium niobate (PPLN) crystal with 10 mm×3 mm×1 mm size and a 19.34 μm poling period. The fundamental-wave was focused on the PPLN crystal by a lens with a 19 mm focal length. A temperature-controlled oven was used to achieve the thermal phase matching condition for frequency doubling. A collimating lens and two dichroic mirrors were used for splitting the two beams at 775 nm and 1550 nm.

Results and Discussions The average power from the oscillator was 30 mW at a 100-MHz repetition rate. Subsequently, the pulsed laser was amplified to 1.3 W by the cascaded Er-doped fiber amplifiers. The amplified pulse had a spectral bandwidth of 1.01 nm centered at 1549.6 nm, and a pulse duration of 11.6 ps [Fig. 2(a) and Fig. 2(b)]. The polarization extinction ratio of the pulse was measured to be 13 dB. In order to avoid optical damage on the end facet of the crystal, the maximum incident power of the fundamental-wave was controlled below 1.1-W average power. The optimum temperature of this PPLN crystal was 34 ℃. In our experiment, the second harmonic average power increases monotonically with the fundamental-wave power. With an incident average power of 1.1 W, the second harmonic laser achieves a power as high as 613 mW, yielding a conversion efficiency of 55.7% [Fig. 3(a)]. The spectral bandwidth and pulse duration of the frequency doubled pulse are 0.68 nm and 11.4 ps, respectively [Fig. 2(c) and Fig. 2(d)]. Benefiting from the all-polarization-maintaining fiber architecture, the frequency doubled pulse exhibits an excellent long-term stability. As shown in Fig. 3(c), the average power instability is as low as 0.6% within 3 h.

Conclusions A picosecond laser architecture for 780-nm spectral range was demonstrated by using an all-polarization-maintaining Er-doped fiber laser and a PPLN frequency doubling crystal. As high as 613-mW average power and 55.7% conversion efficiency were achieved. The proposed laser scheme has the characteristics of compact structure and high stability, which is a good candidate to replace Ti:sapphire lasers in some circumstances.

Objective Gallium nitride (GaN) and its ternary alloys have drawn considerable attention because of their broad applications and promising market prospects for light-emitting devices. p-type doped GaN is an important part of GaN-based optoelectronic device structure. However, the applications of p-GaN are often limited by the low hole concentration and high resistivity. Until now, only Mg has been successfully employed as an effective and practical acceptor impurity in GaN for achieving useful p-type conduction. Post-growth treatment, such as thermal annealing, is required to activate the Mg acceptors in GaN in case of layers grown via metal-organic chemical vapor deposition (MOCVD). Further, there is convincing evidence that hydrogen passivates Mg acceptors in the as-grown state of the materials. An appropriate Mg doping concentration is required for obtaining high-quality GaN. The usage of a considerably high or low Mg doping concentration does not allow for a high hole concentration because of the self-compensation effect associated with heavy Mg doping. In addition, the dislocation density and the concentration of unintentionally doped impurities (e.g., carbon and oxygen) have an important effect on the resistivity of p-GaN. Overall, the compensation mechanisms and functions of the p-doped GaN and AlGaN materials must be clarified for their further development.

Methods A series of Mg-doped p-GaN films was grown in a vertical MOCVD system under different growth temperatures. An Aixtron 3×2 MOCVD system was used for growing p-GaN films. A 20-nm thick GaN buffer layer was initially grown at 540 ℃ on a sapphire substrate. Then, a 2-μm thick unintentionally doped GaN layer was grown by increasing the temperature to 1060 ℃. Subsequently, a series of 0.7-μm thick Mg-doped GaN layers was grown at 1000--1050 ℃. Each sample was annealed at 800 ℃ for 3 min under the same nitrogen environment for activating the Mg acceptors. Trimethylgallium (TMGa), ammonia (NH₃), and Cp₂Mg were used as sources of Ga, N, and Mg, respectively, when using MOCVD. All the conditions were maintained constant for each sample (A--E), except the growth temperature. X-ray diffraction was performed to confirm that the dislocation density in each sample was approximately identical. Further, the resistivity and hole concentration of each sample were measured using the room-temperature Hall method. In addition, the photoluminescence (PL) was measured and secondary-ion mass spectrometry (SIMS) was performed to study the compensation effect of the carbon impurities on p-GaN and its physical mechanism.

Results and Discussions The results obtained from the room-temperature Hall method (Table 1) indicate that the hole concentration increased and the resistivity decreased with the increasing growth temperature. To find possible causes for these phenomena, room-temperature PL spectra (Fig. 1) were obtained using a 325-nm laser beam excitation. The undulation of the PL spectral curves can be attributed to the interference caused by the Fabry-Perot effect owing to flat epitaxial films, which can be eliminated via a line-shape simulation treatment. Samples B, C, and D exhibited a blue luminescence (BL) band peak at approximately 430 nm (2.8 eV), whereas samples A and B did not exhibit such a peak. Detailed investigations have proven that the 2.8-eV BL is caused by donor-acceptor pair (DAP) recombination, where a strong BL peak indicates a high density of DAPs. A considerably high Mg doping concentration may induce a high concentration of DAPs, which can decrease the hole concentration and increase the resistivity. However, in this study, samples B, C, and D exhibited a high BL intensity but not the highest resistivity, implying that factors other than the self-compensation of Mg resulted in the high resistivity of GaN grown at low temperatures. By performing SIMS on samples B, C, and D (Fig. 2), we can observe that the carbon concentration in sample D was the lowest, implying that the concentration of carbon impurities considerably influences the resistivity of p-GaN by acting as a nonradiative recombination center and thereby decreasing the intensity of the BL band peak. Thus, the carbon impurities in p-GaN can form deep donors and compensate for the Mg acceptors, resulting in the deteriorated resistivity and poor mass of p-GaN. The experimental results presented in Table 2 indicate that the self-compensation effect of Mg in case of p-GaN growth was weaker at a lower growth temperature. However, a lower growth temperature can increase the density of carbon impurities, increasing the resistivity. Further, a higher growth temperature resulted in a stronger self-compensation effect and a lower carbon impurity concentration. The samples grown at high temperatures exhibited low resistivity despite the enhanced self-compensation effect of the Mg impurities, indicating that the compensation of carbon impurities played a more important role in p-GaN. Therefore, carbon impurities must be suppressed to obtain p-GaN materials with low resistivity and high hole concentrations. The p-GaN samples grown at high temperatures were of high quality because of their low concentrations of carbon impurities. High-quality p-GaN conduction layers are required for the growth of InGaN/GaN multiple quantum well optoelectronic devices. However, tradeoffs must be considered because the growth temperature of the top p-type GaN layer must not be considerably high to avoid thermal instability and the decomposition of the InGaN layers. It must be considerably lower than 1050 ℃ in a blue or green light-emitting device. Carbon impurities must be suppressed by regulating other growth conditions to obtain a high-quality p-type layer. Generally, the p-GaN layer in GaN/AlGaN multilayer devices must be grown at high temperatures.

Conclusions The effect of the growth temperature of heavily Mg-doped p-GaN films is studied based on the SIMS and PL measurements as well as the Hall method. Experimental results show that the self-compensation of the Mg impurity in p-GaN increased with the increasing growth temperature; however, its resistivity decreased. Further study indicated that the concentration of carbon impurity in the p-GaN sample grown at high temperatures was low. Carbon impurities can compensate for the Mg acceptor and increase the resistivity. The presented results indicate that the compensation of carbon impurities plays a more important role in the development of p-GaN films than the self-compensation of Mg. Thus, high-quality p-GaN films can be obtained by increasing the growth temperature appropriately to inhibit the incorporation of carbon impurities.

Objective The main dynamic performance indexes of the photoelectric theodolite are dynamic tracking accuracy and dynamic measuring accuracy. The target detection is to track the airborne flight targets, such as aircrafts, which usually consumes a lot of manpower and material resources. Therefore, the process detection and the final detection before this step are detected by the dynamic targets provided indoors. The dynamic targets are used to simulate objects in space with a long distance and can provide real-time spatial location information. This equipment can be used to carry out an indoor process detection and a final detection on a target tracking equipment such as photoelectric theodolite, so that can analyze the dynamic tracking performance of a target tracking equipment. With the development of science and technology, the performance of a photoelectric theodolite is improved, and the dynamic target has developed from the traditional simple rotary dynamic target to the high-precision one. The improvement from a tracking detection equipment to a tracking measurement equipment requires spatial positions with high precision.

The spatial position accuracy of a dynamic target includes static accuracy and dynamic accuracy. The static accuracy is measured by Leica theodolite, and the measuring accuracy is 0.5″. At present, the available dynamic accuracy detection methods include tracking method, video judging method and autocollimator detection method. The tracking method has low tracking speed, low accuracy, and high instrument price, so it is not suitable for the dynamic accuracy detection on target. In addition, the video judging method has low sampling speed, large reference position error, and low measurement accuracy. The autocollimator detection method can detect the dynamic errors caused by shafting shaking and rotating arm deformation, which has a certain reference value, but it cannot give the dynamic precision of the target comprehensively. Based on the above analysis, there is a lack of an effective method to measure the dynamic precision of dynamic targets.

Methods This article introduces a spatial target position measurement method to measure the accuracy of the target position when the target is in the state of high-speed movement. This method uses a computer vision technology to record the motion trajectory of a dynamic target captured by a high-speed camera in the whole field of view, and the recorded information is inverted into an actual space position to obtain the objective spatial position information of this target. A spatial position precision measurement system is designed based on this method. The measurement platform is composed of the system and the dynamic target equipment. By analyzing the relationship between the target and the measurement system,the state parameters of the measurement system could be calculated. Based on these parameters, the theoretical position of the target could be derived. By comparing the theoretical position with the actual position, the position accuracy of the dynamic target was able to be confirmed. After analyzing the error sources of the space target position measurement system, the total error of the whole system is less than 1.00″, which meets the design requirement of the measurement system.

Results and Discussions To measure the spatial position accuracy of a certain type of high-precision dynamic target, the static accuracy of the dynamic target was first measured, which was less than 0.59″, and then the dynamic accuracy of the dynamic target was measured with the spatial position accuracy measurement system. The measurement results are shown in Table 1. As shown in the table, the maximum dynamic error for different speeds and different positions is 4.01″. Combining the measurement error of the measuring system as described above, the total dynamic error of the dynamic target is 4.13″.

Generally, the dynamic measurement accuracy of photoelectric theodolite in China is not less than 20″. According to the principle of error transfer, the design requirement of the dynamic precision of the high-precision dynamic target is within 5″. The total dynamic error of the high-precision dynamic target measured by this measurement system is 4.13″, which is less than 5″. The dynamic target meets the dynamic precision index requirement.

This experiment confirmed that the spatial position accuracy measurement system can be widely used for dynamic precision parameter detection of dynamic targets, so that it can be used as a tracking measurement equipment.

Conclusions This article mainly studied the measurement method of the spatial position accuracy of the dynamic target based on the perspective geometry theory. The measurement method adopts the high-speed image processing method, and converts the three-dimensional spatial information into the two-dimensional image information through the imaging system. The advantages of the method are objective detection, non-contact and high precision. Based on the method, the article established one spatial position precision measurement system, and the dynamic precision of a high-precision dynamic target was measured by this measurement system. The experimental results show that the measurement system can complete the initial dynamic calibration of dynamic targets, so that it can be used as a tracking measurement equipment. The design of the spatial position precision measurement system lays a foundation for further solving the difficult problems in dynamic measurement precision detection of target tracking equipment such as photoelectric theodolite, and fills the gap in the field of dynamic detection of target tracking equipment.

Objective As an emerging technology, terrestrial laser scanners (TLSs) are used in various applications in forest resource surveys, reverse engineering, and measurement modeling. The original observations, distances, and angles of a TLS are easily affected by the external environment and instrument itself during acquisition, so the geometric information of a TLS often contains certain systematic errors in addition to random and gross errors. Thus, a TLS cannot completely reflect the real characteristics of the target objects directly related to the subsequent processing and applications. Therefore, it is necessary to effectively remove or correct the errors contained in the original observations of the point cloud data, which is also known as the calibration methodology. The traditional method usually separates the distance and angle, i.e., using a TLS to measure multiple fixed-length baselines or angles, solving the systematic error based on the theory of least squares. However, the above methods cannot completely remove the random and gross errors located in datasets. In this study, a new TLS self-calibration method was proposed by incorporating random and systematic errors into the function model as unknown parameters via the scanner observation principle and Gauss-Helmert model. The method can effectively consider all kinds of errors in the geometric information, and the results show that this method can efficiently remove random and gross errors with good robustness via simulation experiments and verification analysis of the measured data.

Methods In this study, a self-calibration function model was proposed based on the scanner observation principle and Gauss-Helmert model; the corresponding additional parameters (APs), random errors of the original observations, and exterior orientation parameters (EOPs) were rationally appended to this model. In addition, a stochastic model conforming to the normal distribution was implemented according to the nominal accuracy of the original observations. The functional model was nonlinear; hence, it was first linearized via the Taylor series, retaining the first-order terms, then the Lagrange objective function was constructed based on the weighted total least squares principle, and all unknown parameters, including the terms of systematic and random errors, were solved using the Newton-Gauss iterative method. Thus, considering the gross errors in the original observations, the IGGIII weighting factor function was constructed by normalizing the residuals to realize the reweighting of outliers, and the robust solution of the functional model was obtained.

Results and Discussions In the simulation experiments, the differences between the parameters and true values in schemes 2 and 3 are closer to 0 than those in scheme 1, which indicates the necessity of system error calibration (Fig. 2). The parameter values of the scheme 3 are closer to the true values than those of the scheme 2, which proves that the proposed model can obtain higher accuracy of APs and EOPs (Fig. 2). The root-mean-square error (RMSE) of the parameter estimation of the scheme 3 is the smallest, indicating that the scheme 3 has the strongest resistance to gross errors in the original observations (Fig. 2). The RMSE of the scheme 2 at the translation parameter Δz is greater than that of the scheme 1, indicating that the scheme 2 is sensitive to gross errors in the parameter estimation process (Fig. 2). In addition, the error of coordinate components and median error of point position in schemes 2 and 3 are smaller than those in the scheme 1, indicating that the observations corrected by systematic errors are closer to the real values (Fig. 3). Because the random and systematic errors (even, possibly, gross errors) in the original observations of checkpoints could not be removed in the adjustment process, the RMSE of coordinate components of individual checkpoints in the scheme 3 is larger than that in the scheme 2; however, the final point accuracy of the scheme 3 is optimal (Fig. 3). For the experiments on the measured data, at a common point, each coordinate component and the point median error of the scheme 2 are better than those of the scheme 1, and the point accuracy is improved from 10 ^-4 to 10 ^-11; the point accuracy of the checkpoint is improved by 23.8%. Apparently, the accuracy of the scheme 2 for the x-component of the checkpoint is reduced by 50% compared with that of the scheme 1, because the random error of the checkpoint cannot be removed in the adjustment process (Table 3).

Conclusions In this study, a novel model of scanner self-calibration function is proposed by combining the scanner observation principle and Gauss-Helmert model, and the IGGIII weighting factor function is used to derive its robust solution. Compared with the existing methods, the proposed model can effectively consider the random and gross errors in the original observations, which is more rigorous in theory. The experimental results prove that compared with the existing methods, the parameter solutions can be obtained with higher accuracy via a posteriori weighting of the observations with good robustness. After systematic errors’ correction, the point cloud coordinates are closer to the real ones. Moreover, since the proposed model is nonlinear, its variables need to be continuously updated in the iterative process; thus, how to improve the operation efficiency of the algorithm still needs further studies.

Objective When the binocular vision system is used to measure underwater targets, the refraction effect of water makes the measurements differ from the actual situation. The existing methods for reducing the refraction effect include the following. 1) A high-accuracy refraction model is established for calculating the refraction path of each pixel in the camera using the model and for obtaining the actual position of the pixel. 2) The refraction effect is assumed to be an aberration of the camera model. Furthermore, a new camera-calibration method is used to estimate the camera parameters in the underwater environment through which a new measurement model is established to reduce the refraction effect. 3) By improving the traditional epipolar line-based matching method, the traditional onshore epipolar line model can be applied to underwater situations for feature point matching. However, these three methods have certain limitations. 1) High-order parameters need to be introduced when establishing a high-accuracy refraction model, making the calculation process more complex. 2) Special calibration devices are used for camera calibration to compensate for the refraction effect of water. Although an accurate underwater refraction model can be obtained using this method, the calibration devices are usually complex. 3) Although the matching method of the traditional epipolar line exhibits good practicability, the refraction effect on the epipolar line is not considered. Herein, we propose a new modeling method of underwater epipolar line using a device containing multiple line-structured light and a binocular vision system. The discrete curve model of the underwater epipolar line is established based on the ray-tracing principle. In addition, the underwater epipolar line-matching method is improved for feature point matching. The method can effectively improve the matching accuracy of underwater feature points and further improve the measurement accuracy of underwater targets.

Methods Herein, the objects of measurement included a standard ball workpiece (Fig. 9), a standard cylinder workpiece (Fig. 9), and a three-ball workpiece (Fig. 13). Our multiple line-structured light and binocular vision system comprised two Aca1300-60gm gray-scale cameras produced by the German Basler Company, 25 blue line lasers, a blue dot laser, several lighting LEDs, and a switch (Fig.2). The abovementioned devices are strictly fixed in a sealed cabin. The included angle of principal axes and the spatial distance of optical centers between the two cameras are approximately 35° and 500 mm. The laser position is fixed, and all the light planes are approximately parallel to each other. The measured object is placed within the cameras’ public field of view, and the array line laser beams are projected on the object surface. The images are captured simultaneously by the binocular vision system. The feature points of the current target objects are obtained from these images (Fig.11). According to the above system’s underwater binocular stereo vision model and ray-tracing principle, we adopted an iterative optimization method to solve the underwater epipolar line model, which corresponded to a pixel on the left image plane. Then, we could achieve a higher precision underwater feature point selection and matching according to the epipolar line model. In the experiment, the standard ball and standard cylinder workpieces are, respectively, placed in still water for measurement. The feature points of the extracted object are the waiting-for-matched points. The waiting-for-matched points are screened and matched based on the minimum distance constraint and the epipolar line model. To evaluate the matching effect, we compared the matching precision of the model with that of the traditional epipolar line model in the experiments. Furthermore, we conducted a three-dimensional (3D) reconstruction of the matched feature points to verify the effect of using the epipolar line model for underwater target object measurement.

Results and Discussions Our multiple line-structured light exhibit good penetration capability and can capture the characteristic information of underwater targets more accurately. The experimental results showed that the established underwater discrete epipolar line model is more consistent with the actual distribution of feature points than the traditional epipolar line model. The distance between the feature points and the epipolar line model is closer, and the matching accuracy is higher (Table 1). In the measurement experiments on the three-ball workpiece, the maximum measurement radius errors obtained using the traditional epipolar line model are greater than 0.5 mm, whereas those obtained using the epipolar line model are less than 0.3 mm (Table 3). In the experiments of measuring the center distance of several standard ball workpieces, the maximum center distance error obtained using the traditional epipolar line model is greater than 0.6 mm, while that of the epipolar line model less than 0.2 mm. Thus, the epipolar line model can achieve higher spatial accuracy when it is applied to 3D underwater target measurement.

Conclusions Herein, we proposed a discrete epipolar curve model-based underwater multiple line-structured light binocular measuring method. According to the underwater refraction model of the measurement system, we established the underwater discrete epipolar curve model. Then, we selected the waiting-for-matched feature points using the epipolar line model to achieve effective feature matching. The experimental results showed that the method has high measurement accuracy for the standard underwater ball and cylinder workpieces. It solves the problem of large matching error of feature points in the underwater binocular system and exhibits a good 3D reconstruction effect. Moreover, it is suitable for underwater target measurement because of the simple operation of the measurement process.

Objective Atmospheric turbulence is a key research topic in the field of atmospheric and environmental science. It greatly influences the development of aerospace, aircraft safety control, and laser communication. Random fluctuations in the refractive index of the atmosphere along the laser propagation path cause a series of transmission effects. Therefore, a laser beam projected onto a large area microcrystalline reflective film appears as irregular dynamic speckles in the far-field plane. In addition, there are constant directional moving shadows in the laser speckle images, which are caused by the path integral effect of transverse wind. Theoretically, two-dimensional (2D) laser shadow images can be used to detect the path transverse averaged wind velocity. However, due to the deformation of laser shadows and uneven transverse wind distribution, it is uncertain whether the moving velocity of laser shadows calculated using a cross-correlation algorithm can accurately reflect the moving velocity of the flow field and how the sampling frequency of images affects the calculation results. To address these problems, a new method for simulating transverse wind in atmospheric turbulence based on the dynamic phase screen theory is developed for quantitative simulation analysis. In addition, simulation results are substantially verified by experiments. We hope that our study will be helpful in the remote sensing detection of wind and other engineering applications.

Methods A complete pixel search algorithm based on normalized cross-correlation is used to calculate the displacement of laser shadows. First, the transverse wind along the laser propagation path is simulated by moving infinitely long and nonstationary phase screens. Images of lasers transmitted through the atmosphere are obtained for uniform and nonuniform transverse wind distributions. Then, the relationships between the velocity of laser shadows and wind speed are analyzed separately when the wind flow field is distributed differently. In addition, the appropriate sampling frame rates of different wind speeds are calculated. Next, a laser propagation experiment on the horizontal path is conducted, and real-time laser shadow images are taken. Finally, the calculated displacement of laser shadow images and transverse wind speed obtained using an ultrasonic anemometer are fitted to obtain their quantitative relationship. The path transverse wind velocity can be calculated directly from laser shadow images using this relation.

Results and Discussions Simulation results show that there is a linear relationship between the moving speed of laser shadows and path transverse wind speed when the distribution is uniform. Although the path transverse wind blowing from different directions introduces errors, this linear relationship still exists (Fig. 5). The shadow displacement caused by the transverse wind near the emission end is greater than the average wind speed; whereas, it is less than the average wind speed near the receiving end, that is, the influence of transverse wind on shadow displacement has a different path weight (Fig. 6). In addition, the sampling frequency of the image has a great influence on the calculation results of shadow displacement. (Fig. 7). Finally, experimental results show that the correlation coefficient between the measured and fitted wind speeds based on shadow displacement reaches 0.949, demonstrating that 2D wind vector can be obtained using laser shadow images in actual measurements. (Fig. 10).

Conclusions Simulation analysis shows that when the path transverse wind is uniformly distributed, the movement speed of laser shadows and transverse wind speed have an approximately 1∶1 linear relationship, which means that the moving velocity of laser shadows accurately reflects the moving velocity of the flow field. If the path transverse wind is in an inconsistent direction, some fitting errors are introduced, but the linear relationship between the shadow movement speed and average transverse wind speed is maintained. Moreover, the influence of path transverse wind at different positions on the shadow displacement is slightly different, causing the proportionality coefficient not to be 1. In addition, the minimum sampling frequency of CCD is estimated to ensure sufficient spatial correlation between continuous images and the accurate calculation of laser shadow displacement. Laser propagation experimental results demonstrate that 2D wind vector can be obtained using laser shadow images in actual measurements. We can quantitatively observe the motion of a 2D field and the evolution of an atmospheric vortex on a laser propagation path using laser shadow images, which is difficult to obtain using traditional methods, such as ultrasonic anemometers and wind lidar. In addition, the transverse wind is closely related to the effect of laser atmospheric transmission heat halo, and the change in wind speed in the vertical direction near the ground is related to the surface heat flow, which can be studied as a potential application direction.

Objective Stable luminescent efficiency in inorganic halogen perovskite quantum dots (QDs) is difficult to achieve because of their degradation when exposed to air. In addition to stability, increased luminescence efficiency of QD composite films is an important factor for their future applications. Due to a sharp difference in refractive index between the air and flat QD film interface, some light is limited in the film, which has difficulty in crossing the interface and this decreases the luminescence efficiency of the QD film. This light is absorbed by the film and converted into thermal energy, which shortens the device’s lifetime. Therefore, improvement of luminescence efficiency and stability of halogen perovskite QDs is essential. In this study, we report the fabrication of a flexible QD polydimethylsiloxane (PDMS) film with a microlens array (MLA) pattern using PDMS polymer mixed with lead cesium bromide (CsPbBr₃) QDs to transfer the concave MLA master mold. The flexible MLA QD film effectively improves luminescence efficiency and stability of the CsPbBr₃ QDs. Additionally, we find that introducing the MLA structure on the surface of the film significantly enhances surface hydrophobicity.

Methods The preparation procedure of CsPbBr₃ QD film with a MLA pattern is divided into the following two steps. (1) CsPbBr₃ QDs are synthesized by a conventional and simple chemical synthesis method and then dissolved into n-hexane (Fig. 1). Next, PDMS prepolymer and its crosslink agent are successively poured into the n-hexane QD solution in a weight ratio of 10∶1, and the solution is ultrasonically oscillated for uniformity. Finally, the CsPbBr₃ QD PDMS system is obtained by removal of n-hexane using vacuum. During the preparation process, both PDMS and its crosslink agent, with a constant weight of 1.1 g, are added into the CsPbBr₃ QD n-hexane solution in different volumes. The volume of CsPbBr₃n-hexane solution is denoted by x (in mL) and the corresponding QD film is denoted as QD-x. (2) The second step of the preparation procedure is the transfer of the microlens array structure onto the surface of the CsPbBr₃ QD film (Fig. 2). First, a micropillar array is prepared by the laser direct writing technique and then the array is heated to melt and cooled to form a convex MLA master mold. Next, the convex MLA master mold is transferred onto the PDMS surface to form a concave MLA pattern using a soft lithography technique. The PDMS MLA pattern surface is modified by a plasma surface treatment and then immersed into ethyl alcohol for 4 h. Third, the CsPbBr₃ QD PDMS solution is poured onto the modified PDMS concave MLA surface, which is then followed by a degassing and curing process. Finally, a CsPbBr₃ QD film with the MLA pattern is obtained by separation from the PDMS concave MLA surface.

Results and Discussions The luminescence efficiencies of the prepared CsPbBr₃ QD films are measured using a fluorescence spectrometer (Fig. 3). With the increase of QD concentration, the number of QDs per unit volume of PDMS becomes large and the luminescence intensity of the QD film increases. However, the increase of QD concentration also increases the agglomeration of the QDs, which decreases the luminescence efficiency. In this experiment, QD-2.5 displays an optimum luminescence intensity and, thus, the QD PDMS system of QD-2.5 is selected as the prepared material for subsequent QD PDMS film fabrication. Moreover, this film displays stable luminescence intensity when repeatedly bent a thousand times or when immersed into water for ten days (Figs. 4 and 5). This demonstrates that the QD film is water-repellent and suitable for wearable flexible devices. The prepared MLA QD film shows about 10% increase in luminescence intensity compared to a flat QD film without any patterns (Fig. 6). This is mainly due to the antireflective property of the MLA pattern, which effectively avoids total reflection and decreases Fresnel reflection at the interface of air and the QD film (Fig. 7). When a 2 μL deionized water droplet is dropped on the surface of the prepared MLA QD film, the droplet shows a contact angle of 138.6°. By contrast, the contact angle is 96.7° when a 2 μL droplet is dropped on a flat QD film. The MLA pattern blocks the spreading of the water droplet and the three-phase contact line does not cross the obstacle, reaching a new thermodynamic equilibrium state. As a result, the droplet on the MLA pattern has a large contact angle. On a flat solid surface, the three-phase contact line will not encounter any retardation. The droplet reaches its corresponding thermodynamic equilibrium state and thus displays a small contact angle. The experimental results demonstrate that the MLA QD film is suitable for high-humidity environment because its hydrophobic surface is not conducive to water vapor accumulation.

Conclusions Inorganic CsPbBr₃ QDs were synthesized by a conventional and simple chemical synthesis method. The synthesized CsPbBr QDs were uniformly added to PDMS by ultrasonic mixing, which was followed by removal of the n-hexane in the QD solution by vacuum. The PDMS QD film shows good luminescence stability under repeated bending or after immersion into water. After introducing the MLA pattern on the surface of the flexible QD film, the luminescence efficiency and surface hydrophobicity are significantly improved.

Objective In 1979, Berry and Balazs provided the first theoretical derivation of Airy wave packets from quantum mechanics. Finite-energy Airy beams (FEABs) are achieved by an exponential aperture in an optical study by Siviloglou and Christodoulides in 2007. FEABs have since proven a valuable research tool and their potential applications are wide-ranging. Examples are light bullets, curved plasma channel generation, optical routing, optical interconnection, vacuum electron acceleration, and laser-assisted guiding of electric discharges. FEAB applications are based on light-field regulation theory. Therefore, controlling the propagation and interaction of FEABs in different nonlinear media has attracted great interest. Thus far, most of this research has focused on the propagation dynamics of a single FEAB and the interaction of two FEABs. It is found that breathing solitons or soliton pairs can be generated during the propagation. However, the interaction of solitons and FEABs has been little investigated. In the present study, we investigate the interaction of solitons and a single FEAB or two FEABs in a saturable nonlinear medium. This novel phenomenon is applicable to beam control and optical information processing.

Methods We first established the theoretical model and considered the one-dimensional case for convenience. A light wave propagating through saturated nonlinear medium satisfies the nonlinear Schr?dinger equation. For different initial incident beams, the beam evolution is simulated in the saturated nonlinear medium using the split-step Fourier method. In addition, the dynamic characteristics of the FEAB-soliton interaction are investigated by changing the model parameters: initial amplitude ratio R, initial interval b, phase shift Q, and saturable nonlinear strength β.

Results and Discussions When a weak-energy FEAB and a soliton interacted with a phase shift of 0 or π, the collision is followed by a breathing soliton (Fig. 2). The peak intensity of the breathing soliton is higher in the in-phase case than in the out-of-phase case (Fig. 4(a)). By adjusting the phase shift in the range -π<Q<0 or 0<Q<π, the tilt angle (angle from the longitudinal axis) is first increased and then decreased, and is maximized at approximately ±3.5° when Q=?π/2 (Fig. 3). This property is a useful reference for the fabrication of optical interconnection devices. In the in-phase case, enlarging the initial amplitude ratio and reducing the initial interval more strongly emphasized the linearly increasing trend of the average peak intensity of the breathing soliton. When the initial interval |b| is enlarged, the average peak intensity of the breathing soliton is almost unchanged in the in-phase case (Fig. 4(b)), but the reverse is true in the out-of-phase case (Fig. 4(c)). Meanwhile, increasing the nonlinear saturation parameter β increased the average peak intensity of the breathing soliton and decreased the breathing period, in both the in-phase and out-of-phase cases (Fig. 6). When two FEABs interacted with the soliton, changing the initial interval b altered the period of the breathing soliton (Fig. 8), and when R is sufficiently large, increasing its initial amplitude ratio gradually increased the peak intensity of the breathing soliton. Coexistence of solitons and soliton pairs is enabled by energy shedding from the Airy main and side lobes (Fig. 9).

Conclusions The interaction of FEABs and solitons is numerically studied in a saturated nonlinear medium, and the effects of a single FEAB and two FEABs on the soliton propagation are analyzed. For weak-energy FEABs, the post-collision propagation mode of the soliton became a damped oscillatory mode. The breathing soliton is tilted rightward at -π<Q<0 and leftward at 0<Q<π. The maximum tilt angle is ±3.5° at Q=?π/2. When the initial amplitude ratio increased and the initial interval decreased, a monotonic increase and decrease in the mean intensity of the breathing soliton is observed in the in-phase and out-of-phase cases, respectively. For strong energy FEABs, the peak position of the breathing soliton moved leftward in the in-phase case, but in the out-of-phase case, two solitons with different intensities are formed with a certain angle. When two FEABs interacted with a soliton for a given initial amplitude ratio, the mean peak intensity of the breathing soliton is linearly related to the initial interval in both the in-phase and out-of-phase cases. Increasing the initial amplitude ratio gradually enhanced the beam interaction, and a single soliton or soliton pair is formed. When the amplitude ratio is sufficiently large, the soliton and soliton pair could co-exist because energy is shed from the Airy main and side lobes.

Objective With the development of unmanned aerial vehicle(UAV) technology, the identification and ranging of small targets at long ranges have become an essential defense requirement. The Swedish defense research agency investigates a linear detected laser range lidar for target recognition and classification, such as small boats at sea and small UAV. However, to measure a small target at long range, the linear detected lidar requires a high-power laser so that the system will be very huge and harmful to the eyes. Alternatively, the time-correlated single photo-counting(TCSPC) technique has emerged as a candidate technology for lidar systems due to its high-sensitivity and excellent range resolution. The use of high-sensitivity single-photon detectors means that low average optical power levels and receive aperture can be used, even at long distances. In this study, we propose a photo-counting lidar, which can install on the theodolite platform to real-time obtain the distance and speed of a small moving target at long-rang.

Methods The light source of lidar is a fiber laser at 1545.3 nm, and the pulse width is 6 ns. The laser single pulse energy is 80 μJ, and the repetition frequency is 25 kHz. To track the small moving target more easily and steadily, the divergence angle of the laser beam and receiver field of view is set to 1.0 and 1.2 mrad, respectively. The InGaAs/InP avalanche photodiodes, which is Peltier cooled to 240 K, is adopted as the single-photon detector. The detection efficiency is 15% at 1545 nm, and the dark count rate is 30 kHz. A 1 nm bandpass fitter is selected to reduce the solar background noise. The lidar export a distance of the target by accumulating every 250-laser echo signal collected using the field-programmable gate array(FPGA) with a sampling rate of 400 MHz. Thus, the distance update rate is 100 Hz. However, the laser pulse width is wider than the echo signal-sampling resolution. Therefore, a Gaussian-fitting method is used to deal with the accumulated echo signal so that it can find the exact target distance. During the outfield test, a 0.99 reflectivity square target plate with a side length of 25 cm is designed so that it can be equivalent to a small target with a reflection cross-sectional area of 0.1 m ² and reflectivity of 0.6. The target plate is placed in five places with a known distance. The accuracy and precision of lidar are tested using lidar to range the five targets. Afterward, the target plate is placed 5 km away to test the lidar maximum range. Finally, the non-cooperative moving target ranging ability of the lidar is verified, the lidar system is installed on the theodolite platform for tracking and ranging a moving UAV fabricated by DJI corporation. The unscented Kalman filter algorithm is used to obtain the distance and velocity of UAV in real-time.

Results and Discussions During the entire outside experiment, the atmospheric visibility is 7 km. The target plate is detected at a distance of 5017.56 m(Fig.5) with the detected single-to-noise(SNR) of 5.86 dB. The precision is 0.165 m. The laser power is 1.42 W with a maximum power of 2 W. The maximum range is 5446.3 m through the extinction method. The lidar accuracy is 0.161 m when the detected SNR is around 6 dB(Table 2). Besides, the lidar system has tracked the moving UAV with a starting distance of 972.53 m(Fig. 8(a)). The laser power is 0.625 W, and the detected SNR is 20.2 dB during the tracing experiment. The Gaussian-fitting result showes that the distance is jittered so that it cannot calculate the velocity in real-time(Fig.8(b)). Thus, the polynomial fitting approach is used to smooth the distance obtained from a Gaussian-fitting method so that the speed of UAV can be precisely calculated by differentiating the polynomial fitting result(Figs. 8(c) and(d)). The distance and speed of the UAV are obtained using the unscented Kalman filter algorithm in real-time(Fig.9(a) and(c)). The unscented Kalman filter algorithm result, compared to the polynomial fitting approach, showes that the ranging deviation is within 0.11 m(Fig.9(b)), and the speed deviation is within 0.5 m/s(Fig.9(d)).

Conclusions A miniature lidar is designed, which is suitable for high-speed ranging of long-distance non-cooperative small targets. The theoretical analysis and experimental results show that the laser ranging system can achieve a maximum-detecting distance of 5446.3 m and an accuracy of 0.161 m for a small target with a reflection cross-sectional area of 0.1 m ² and reflectivity of 0.6 when the atmospheric visibility is 7 km. The system is installed on the theodolite platform to track and range the moving UAV. The distance and velocity of the UAV are obtained using the unscented Kalman filter algorithm in real-time. The ranging and speed deviations are within 0.11 m and 0.5 m/s, respectively. The photo-counting lidar design and unscented Kalman filter algorithm proved to be feasible for small moving targets ranging.

Significance With the rapid development of laser technologies, the number of laser weapon equipment is increasing. At the same time, human eyes, photoelectric detection equipment, and optical systems are being exposed to strong laser environment and are vulnerable to laser attacks. It is an urgent problem to ensure that these devices have anti-attack capability based on normal operation. Consequently, it is paramount to develop a laser protection technology.

Based on the working principle, the laser protection technology can be divided into two types. One is based on the linear optical principle, such as absorption-type filter, reflection-type filter, and coherent filter. The other is based on the nonlinear optical (NLO) principle—also known as optical limiting (OL)—such as nonlinear absorption-, scattering-, and refraction-type optical limiters. In addition, there are thermally induced phase-change materials and liquid-crystal materials, etc. The OL technology can combine high transmittance to weak light and low transmittance to strong light at the same wavelength. In addition, it has obvious advantages in the protection against high-energy, continuous broadband laser spectra, and ultrafast response time. Moreover, it is one of the materials with high practical application value in the field of laser protection.

Progress Various materials, such as graphene, transition metal dichalcogenide (TMDC), black phosphorus (BP), carbon nanotube, phthalocyanine, and porphyrin, can be used to fabricate optical limiters. This study focuses on the progress of two-dimensional (2D) nonlinear optical limiting materials, such as graphene, TMDC, and BP, applied in the aspect of laser protection.

In 2009, Wang et al. first reported the OL characteristics of high-quality graphene (Fig. 3). By dispersing graphite in organic solvents, they have successfully produced large numbers of graphene mono- and multilayers. A significant NLO response of graphene dispersions to nanosecond laser pulses at 532 nm and 1064 nm was observed, thereby implying a potential broadband OL application. Nonlinear scattering arising from the formation of solvent bubbles and micro-plasmas is the principal mechanism for OL. The surface tension of solvents has a strong influence on the OL performance of graphene dispersions. The OL effect of N,N-dimethylacetamide (DMA) dispersions is better than those of N-methyl-2-pyrrolidone (NMP) and γ-butyrolactone (GBL) dispersions.

Feng et al. investigated the NLO and OL properties of graphene families, including graphene oxide nanosheets, graphene nanosheets (GNSs), graphene oxide nanoribbons (GONRs), and graphene nanoribbons (GNRs), using 532 nm and 1064 nm nanosecond lasers (Fig. 4). GNSs, GONRs, and GNRs exhibit broadband NLO and OL properties. The reduced graphene samples exhibit stronger NLO and OL responses than their corresponding oxide precursors due to their increased crystallinity and conjugation. Nonlinear scattering and two-photon absorption are found to have strong effects on the NLO and OL responses of graphene nanostructures.

Dong et al. reported the NLO properties of TMDC nanosheet dispersions, including MoS₂, MoSe₂, WS₂, and WSe₂, using nanosecond laser pulses at 1064 nm and 532 nm (Fig. 5). The results demonstrate that the TMDC dispersions exhibit a significant OL response at 1064 nm due to nonlinear scattering, contrary to the combined effect of both saturation absorption and nonlinear scattering at 532 nm. Selenium compounds exhibit a better OL performance than sulfides at near-infrared. A liquid dispersion system-based theoretical model is proposed to estimate the number density of nanosheet dispersions, the relationship between the incident laser fluence and the size of laser-generated microbubbles, and the Mie scattering-induced broadband OL behavior in the TMDC dispersions.

Li et al. synthesized mono- and multilayer MoS₂ triangular islands using a seeding method via chemical vapor deposition (Fig. 6). Distinct NLO responses demonstrate that multilayer MoS₂ exhibits the SA effect. However, monolayer MoS₂ exhibits a remarkable two-photon absorption effect for a femtosecond laser pulse at 1030 nm. Notably, they observed two-photon pumped upconverted luminescence in monolayer MoS₂, another vital third-order NLO response in 2D semiconductors.

Huang et al.investigated the wavelength- and pulse-duration-dependent SA properties of BP by a femtosecond laser pulse at 1030 nm/515 nm and a nanosecond laser pulse at 1064 nm/532 nm (Fig. 8). The results reveal that BP exhibits a better NLO response in the visible range than that in the near-infrared range and stronger SA ability in 6 ns-pulsed excitation than in 340-fs-pulsed excitation. Finally, they reported the SA-induced optical transparency and NLS induced optical limiting in BP dispersions.

Conclusion and Prospect In this paper, we have introduced the basic concept of a laser protection technology, summarized several laser protection schemes, and illustrated the mechanism of laser protection technology based on the NLO principle. Moreover, we have introduced the research progress of three types of 2D NLO materials—graphene, TMDC, and BP—in term of laser protection. In summary, these materials exhibit OL characteristics in the range of visible to near-infrared bands. For ns-pulsed laser, laser protection is mainly induced by nonlinear scattering, while for fs-pulsed laser, it is dominated by two-photon absorption. Under the same experimental conditions, the OL properties of three materials from strong to weak orders are TMDC, graphene, and BP. In addition, the covalent modification can improve the dispersion of 2D nanomaterials as well as their OL and NLO properties. However, the development of laser protection devices based on these materials is still in the research stage, and they are yet to be practicalized. For 2D nanomaterials, many problems still remain, such as: 1) the materials have a strong aggregation effect, leading to poor dispersion; 2) the problem of realizing the precise control of the layer number and size of 2D materials makes it difficult to achieve low-cost and large-scale material fabrications. In the future, we need to focus on these materials to design and fabricate high-quality covalent chemically modified 2D nanomaterials as well as develop ideal OL devices with broad protective spectral bands, low input thresholds, high linear transmittance to weak radiation, fast responses, and large damage thresholds.