Coherent beam combination of two slab laser amplifiers based on stochastic parallel gradient descent algorithm

Coherent beam combination(CBC) of laser arrays is an efficient way to scale brightness.We demonstrate CBC of two slab laser amplifiers based on active phase locking.Instead of the complex phase detection system,intensity detection is used and the feedback control signal is calculated based on the stochastic parallel gradient descent(SPGD) algorithm.The experimental investigation on a 101.5-W CBC of two slab amplifiers shows that the entire system in a closed loop performs well for long-time observation.A combination efficiency of nearly 81% is realized.The slab amplifier laser arrays are the coherent beams efficiently combined by active phase locking based on the SPGD.     

Coherent beam combining of fiber amplifier based on adaptive polarization and active phase control

Coherent beam combining (CBC) of a polarization-maintaining fiber amplifier and a non-polarization-maintaining fiber amplifier is presented. The experiment is based on adaptive polarization control and active phase control. The stochastic parallel gradient decent (SPGD) algorithm is used for the adaptive polarization control in the non-polarization-maintaining fiber amplifier and the active phase control is realized by single frequency dithering (SFD) algorithm. When the adaptive polarization control system and the phase control system go into closed loop, the fringe contrast of far-field intensity pattern is improved to more than 87.7%. A scalable architecture for CBC of two styles fiber amplifiers is also proposed.     

Coherent beam combination of an optical array using adaptive fiber optics collimators

A novel adaptive-fiber-optics-collimator (AFOC) compensating both piston-type and tip/tilt-type phase errors of output beam is introduced, and has been employed in experiments of coherent beam combination (CBC) of a delta distributed fiber array. Feedback control is realized using stochastic parallel gradient descent (SPGD) algorithm. Excellent CBC effect has been achieved when piston and tip/tilt errors among beamlets corrected. The necessity of wavefront tip/tilt control in CBC is verified. Experimental results exhibit great potential applications of this kind of AFOC in fiber amplifier arrays.     

Coherent beam combining of 137 W 2 × 2 fiber amplifier array

We demonstrate coherent beam combining of two-dimensional fiber amplifier arrays with a total of 137 W output power using stochastic parallel gradient descent (SPGD) algorithm. Compact all-fiber polarization-maintained single frequency fiber amplifier chains are developed and four fiber amplifiers are arranged to 2 × 2 laser array with a fill factor of 70% in the near-field. Active phase control is implemented by a digital signal processor (DSP) based SPGD controller. The fringe visibility of the coherent combined beam profile is as high as 81% when the system is closed-loop controlled despite perturbations of the environment.     

The 260-W coherent beam combining of two compact fibre amplifier chains

Coherent beam combining of two fibre amplifier chains with a total power of 260 W in a compact system using the stochastic parallel gradient descent (SPGD) algorithm is demonstrated. A 150 MHz linewidth fibre laser is built and introduced for high-power amplification to mitigate stimulated Brillouin scattering (SBS). Compact high-power amplifier chains are built with low power all-fibre system and high-power bulk free-optics fibre amplifiers. When the total power is about 260 W, active phase-locking of two high-power amplifiers is demonstrated using the SPGD algorithm. In closed-loop, the power in the main lobe increases 1.68 times, the visibility is increased from 0 to 0.62, and the phase residual error is less than λ/10.     

Bandwidth analysis and improvement of the beam phasing of fiber amplifiers using the stochastic parallel gradient descent algorithm

We present the numerical analysis and improvement of the bandwidth of the beam phasing of fiber amplifiers using the stochastic parallel gradient descent (SPGD) algorithm. Time-varying phase distortions are incorporated into the dynamic simulation. It is shown by numerical calculation that the bandwidth of the standard SPGD algorithm is dependent on the phase distortions and on the number of lasers. The time-averaged cost function will decrease with an increase in the amplitude and frequency of phase distortions, and in the number of lasers. A cross-grouped SPGD algorithm is proposed, which offers attractive performance due to its robustness to various time-varying phase distortions and faster convergence rate for beam phasing of larger number of lasers. Dynamic simulation shows that the control bandwidth can be improved using the cross-grouped SPGD algorithm.     

基于偏振自适应和主动相位控制的相干合成的实验研究

进行了非保偏放大器与保偏放大器的相干合成的实验研究。通过随机并行梯度下降（SPGD）算法对非保偏放大器进行偏振自适应控制,使非保偏放大器输出激光的消光比达到11.5 dB,与保偏放大器在同一偏振方向上的光功率占总功率的93.4%。利用单抖动法进行非保偏放大器与保偏放大器的主动相位控制,实现相干合成。实验结果表明:SPGD算法能够有效实现偏振自适应控制,偏振自适应控制前后相干合成远场的条纹对比度从80.1%提高到87.2%,相干合成的效果提升明显;通过增加参与合成的放大器路数,并在各路激光中引入多级功率放大器,能够得到更高的合成功率输出。     

Coherent beam combining of hybrid phase control in master oscillator-power amplifier configuration

A novel scalable architecture for coherent beam combining with hybrid phase control involving passive phasing and active phasing in master oscillator-power amplifier configuration is presented. Wide-linewidth mutually injected passive phasing fibre laser arrays serve as master oscillators for the power amplifiers, and the active phasing using stochastic parallel gradient descent algorithm is induced. Wide-linewidth seed laser can suppress the stimulated Brillouin scattering effectively and improve the output power of the fibre laser amplifier, while hybrid phase control provides a robust way for in-phase mode coherent beam combining simultaneously. Experiment is performed by active phasing fibre laser amplifiers with passive phasing fibre ring laser array seed lasers. Power encircled in the main-lobe increases1.57 times and long-exposure fringe contrast is obtained to be 78% when the system evolves from passive phasing to hybrid phasing.     

Coherent beam combining of two fiber amplifiers using stochastic parallel gradient descent algorithm

We demonstrate the coherent beam combining of fiber amplifiers using a stochastic parallel gradient descent (SPGD) algorithm, producing a total output power of 23 W. Active phase control on each amplifier is performed by running the SPGD algorithm on a DSP chip with updating rate of almost 100 kHz. Experimental results show that power encircled in the target pinhole in closed-loop mode is 1.85 times more than that in open-loop mode, which is 92% of the ideal case. The fringe contrast of the far-field fringe pattern is as high as 92% when the system is in closed-loop mode. The whole system in closed-loop mode performs well in a long-time observation.     

Powerful, diffraction-limited semiconductor laser using photorefractive beam coupling

We use semiconductor laser amplifiers and a photorefractive crystal to generate a high-power, diffraction-limited laser beam at 860 nm. Using a single flared amplifier, we obtain 1.09 W in a diffraction-limited beam from 2.2 W of pump power. Using an array of flared amplifiers, we also demonstrate efficient beam coupling, showing that this technique is easily extended to semiconductor amplifier arrays.     

倾斜相差对光纤激光相干合成的影响与模拟校正

选取不同路数和不同填充因子的合成光束模型,模拟并分析了倾斜相差对相干合成的影响.介绍了倾斜校正的关键器件--自适应光纤光源准直器.在主振荡功率放大器结构的光纤激光相干合成系统中,模拟了随机并行梯度下降(SPGD)算法校正七路激光阵列间时变倾斜相差的动态过程,分析了不同倾斜相差幅值和频率对校正能力的影响.实验表明,要提高相干合成的效果,必须校正倾斜相差;而SPGD算法校正倾斜相差的能力随着倾斜相差幅值和频率的增加而降低.文章为在实际大气环境中实现多路高功率光纤激光的相干合成提供了参考. 关键词： 光纤激光 相干合成 倾斜相位差 动态分析     

Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique

Coherent beam combination of a 1.08?kW fiber amplifier array has been demonstrated for the first time, to our knowledge. In the experiment, nine fiber amplifiers are tiled into a 3×3 array, and the output power of each amplifier is approximately 120?W. A single frequency dithering algorithm is used to compensate the phase noises between the elements, which runs on a signal processor based on field programmable gate array for phase control on the fiber amplifiers. When the phase control system goes into closed loop, the fringe contrast of the far-field intensity pattern is improved to more than 85%, and the residual phase error is less than λ/15.     

Numerical and experimental study on coherent beam combining of fibre amplifiers using simulated annealing algorithm

We present the numerical and experimental study on the coherent beam combining of fibre amplifiers by means of simulated annealing (SA) algorithm. The feasibility is validated by the Monte Carlo simulation of correcting static phase distortion using SA algorithm. The performance of SA algorithm under time-varying phase noise is numerically studied by dynamic simulation. It is revealed that the influence of phase noise on the performance of SA algorithm gets stronger with an increase in amplitude or frequency of phase noise; and the laser array that contains more lasers will be more affected from phase noise. The performance of SA algorithm for coherent beam combining is also compared with a widely used stochastic optimization algorithm, i.e., the stochastic parallel gradient descent (SPGD) algorithm. In a proof-of-concept experiment we demonstrate the coherent beam combining of two 1083~nm fibre amplifiers with a total output power of 12~W and 93% combining efficiency. The contrast of the far-field coherently combined beam profiles is calculated to be as high as 95%.     

Coherent Beam Combining of Three Watt-Level Fiber Amplifiers Using a DSP-Based Stochastic Parallel Gradient Descent Algorithm

We present an experimental study on coherent beam combining of three watt-level fiber amplifiers using a stochas- tic parallel gradient descent （SPGD） algorithm. Phase controlling is performed by running the SPGD algorithm on a digital-signal-processor （DSP） chip with a voltage updating rate of 16500 times per second. Energy encircled in the target pinhole is 2.62 times more than that in an open loop. The combining efficiency is as high as 87%.     

光纤激光相干合成高速高精度相位控制器

基于随机并行梯度下降算法（SPGD）和现场可编程逻辑阵列（FPGA）设计制作了相干合成（CBC）相位控制器。理论分析表明,该控制器单次迭代速率大于1.125 MHz,对于2路和16路相干合成,其平均控制带宽的理论值分别大于70 kHz和9 kHz,与现有的SPGD算法相位控制器相比有了量级上的提高。利用该控制器进行了验证性实验,表明该控制器能够实现高速高精度相位控制。当利用相位控制器对两路激光的相位进行锁定时,目标圆孔内能量提高了1.51倍,远场光斑对比度提高了5.29倍。     

随机并行梯度下降光束净化实验研究

利用自适应光学技术进行光束净化是高能激光系统中一项重要的研究内容.为实现光束净化系统的小型化和低成本,基于系统性能评价函数无模型最优化的波前畸变校正方法是适合的技术方案.就随机并行梯度下降(SPGD)最优化算法在光束净化系统中的应用展开研究.针对高能激光束常见的像差分布进行了SPGD波前校正的数值模拟,在此基础上构建了37单元自适应光学光束净化实验平台,讨论了双边扰动梯度估计和迭代增益系数自适应变化对算法收敛特性的影响.数值模拟与实验结果验证了SPGD算法对不同程度波前畸变的校正能力,表明了SPGD光束净化方案的可行性.     

Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control

We present an experimental study on tilt-tip(TT) and phase-locking(PL) control in a coherent beam combination(CBC) system of adaptive fiber laser array.The TT control is performed using the adaptive fiber-optics collimator(AFOC),and the PL control is realized by the phase modulator(PM).Cascaded and simultaneous controls of TT and PL using stochastic parallel gradient descent(SPGD) algorithm are investigated in this paper.Two-fiber-laser-,four-fiber-laser-,and six-fiber-laser-arrays are employed to study the TT and PL control.In the cascaded control system,only one high-speed CMOS camera is used to collect beam data and a computer is used as the controller.In a simultaneous control system one high-speed CMOS camera and one photonic detector(PD) are employed,and a computer and a control circuit based on field programmable gate array(FPGA) are used as the controllers.Experimental results reveal that both cascaded and simultaneous controls of TT using AFOC and PL using PM in fiber laser array are feasible and effective.Cascaded control is more effective in static control situation and simultaneous control can be applied to the dynamic control system directly.The control signals of simultaneous PL and TT disturb each other obviously and TT and PL control may compete with each other,so the control effect is limited.     

Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm

We demonstrated active phase locking a nine-element 1.1 kW all-fiber master-oscillator power amplifier (MOPA) array using the stochastic parallel gradient descent (SPGD) blind optimization algorithm. Two spectrally combined single-frequency seed lasers, which provide potential ability to suppress the stimulated Brillouin scattering effect, are employed as a master oscillator for the nine MOPA channels. The nine laser beams are tiled side by side into a 3×3 laser array with a fill factor of 40% in the near field. When the SPGD controller is enabled, the metric function is increased 4.1 times, and a visibility more than 90% of the interference pattern at the receiving plane is obtained. The computed phase residual error is less than λ/15, despite the phase fluctuation of each channel.     

用于共孔径相干合成的衍射光学元件设计

分析了衍射光学元件实现共孔径相干合成的物理过程,建立了基于衍射光学元件的共孔径相干合成数学模型,推导了合成光束复振幅与入射光束和衍射光学元件相位分布之间的关系。提出用合成光束强度分布的均匀性作为评价函数的优化方法,获得了一维衍射合束器的相位分布。与文献报道的衍射光学元件分束器相比,可获得更高的合成效率。采用模拟退火算法结合随机并行梯度下降算法优化合束器设计,提高了计算效率,获得了多束衍射合束器的相位分布和合成效率。分析了单子束失效及合束器像差对合成效率的影响,结果表明:随着合束数量的增加,单子束失效对合成效率的影响逐渐减小;若使合成效率退化小于5%,衍射光学元件的波像差均方根值应控制在λ/28以内。     

基于随机并行梯度下降算法光纤激光相干合成的高精度相位控制系统

随机并行梯度下降(SPGD)算法是实现大功率主振荡功率放大器相干合成的有效手段之一.分析了SPGD算法用于相干合成的基本原理,设计了基于SPGD算法的相位控制系统,给出了基于该SPGD控制器的相干合成实验结果.理论分析表明,SPGD算法控制器的迭代速率为200kHz,对于两路相干合成的平均控制带宽大于12.5kHz,最优控制精度可达1/179个波长.实验表明,SPGD控制器能够实现高速的相位控制.在相位噪声幅度大于1/10个波长、频率为3kHz的情况下,有效地实现了两路激光的相位锁定,相位残差控制在1/25个波长内.