基于随机并行梯度下降算法的相干合成动态相差控制与带宽分析
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摘要
分析随机并行梯度下降(SPGD)算法用于多路大型固体激光装置相干合成中校正动态相差的能力。首先介绍了SPGD算法实现相干合成的基本理论,利用数值模拟方法对算法进行了优化,实现了两路基于SPGD算法的波长为800nm、带宽为30fs光束的相干合成实验,验证了在外加10,15,20,25Hz动态相差条件下算法的特性,并进一步模拟了动态活塞相差和指向性相差的校正过程,分析了不同相位噪声强度和频率对校正能力的影响,计算了控制带宽与光束路数、算法执行速度之间的关系。结果表明:远场强度分布的平方和是高能短脉冲激光相干合成的最佳性能评价函数;采用自适应增益的方式时,在保证算法稳定性的前提下,提高了算法的收敛速度;随着相位噪声强度和频率的提高,算法的有效控制带宽减小;算法执行速度越快,光束路数越少,则算法控制带宽越大;受限于器件性能,SPGD算法不适用于4路以上带宽为30fs激光阵列的相干合成。
The correction ability of dynamic phase error in coherent beam combination for multi-channel large solid laser device is analyzed by stochastic parallel gradient descent(SPGD)algorithm.The fundamental theory of coherent beam combination by SPGD algorithm is introduced.The algorithm is optimized by numerical simulation method.Coherent beam combination of two beams with the wavelength of 800 nm and the bandwidth of 30 fs is experimentally achieved and the performances of SPGD algorithm under the 10,15,20,25 Hz dynamic phase error conditions are tested.Moreover,the processes of dynamic piston and point phase error correction are simulated.The influence of phase noises with different intensities and frequencies on the correction ability is analyzed.The relationships among the control bandwidth,number of beams and iteration rate are computed.The results show that the quadratic sum of far-field intensity is the optimal performance evaluation function of coherent beam combination for high-power short-pulse laser.The adaptive gain can guarantee the stability and improve the convergence speed of the algorithm.The effective control bandwidth decreases with increasing intensity or frequency of phase noise,and increases with increasing iteration rate and decreasing of beam number.Limited by the performance of device,SPGD algorithm cannot be applied to the coherent beam combination for more than four beams laser array with the bandwidth of 30 fs.
The correction ability of dynamic phase error in coherent beam combination for multi-channel large solid laser device is analyzed by stochastic parallel gradient descent(SPGD)algorithm.The fundamental theory of coherent beam combination by SPGD algorithm is introduced.The algorithm is optimized by numerical simulation method.Coherent beam combination of two beams with the wavelength of 800 nm and the bandwidth of 30 fs is experimentally achieved and the performances of SPGD algorithm under the 10,15,20,25 Hz dynamic phase error conditions are tested.Moreover,the processes of dynamic piston and point phase error correction are simulated.The influence of phase noises with different intensities and frequencies on the correction ability is analyzed.The relationships among the control bandwidth,number of beams and iteration rate are computed.The results show that the quadratic sum of far-field intensity is the optimal performance evaluation function of coherent beam combination for high-power short-pulse laser.The adaptive gain can guarantee the stability and improve the convergence speed of the algorithm.The effective control bandwidth decreases with increasing intensity or frequency of phase noise,and increases with increasing iteration rate and decreasing of beam number.Limited by the performance of device,SPGD algorithm cannot be applied to the coherent beam combination for more than four beams laser array with the bandwidth of 30 fs.
引文
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[24]Li Z L,Wang X,Mu J,et al.High pricision time jitter measurement for large multi-beam laser facility[J].High Power Laser and Particle Beams,2015,27(11):111001.李志林,王逍,母杰,等.大型激光装置束间同步抖动的高精度测量[J].强激光与粒子束,2015,27(11):111001.
[2]Leshchenko V E.Coherent combining efficiency in tiled and filled aperture approaches[J].Optics Express,2015,23(12):15944-15970.
[3]Leshchenko V E,Trunov V I,Frolov S A,et al.Coherent combining of multimillijoule parametricamplified femtosecond pulses[J].Laser Physics Letters,2014,11(9):095301.
[4]Homoelle D,Utterback E,Baker K L,et al.Phasing rectangular apertures[J].Optics Express,2009,17(22):19551.
[5]Miyanaga N,Azechi H,Tanaka K A,et al.Technological challenge and activation of high-energy PW laser LFEX[C].Conference on Lasers and Electro-Optics-Pacific Rim,2007:10020671.
[6]Garrec B J L,Hernandez-Gomez C,Winstone T,et al.HiPER laser architecture principles[J].Journal of Physics:Conference Series,2010,244:032020.
[7]Augst S J,Fan T Y,Sanchez A.Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers[J].Optics Letters,2004,29(5):474-476.
[8]Liu L,Vorontsov M A,Polnau E,et al.Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners[C].Proceedings of SPIE,2007,6708:6708OK.
[9]Liu L,Vorontsov M A.Phase-locking of tiled fiber array using SPGD feedback controller[C].Proceedings of SPIE,2005,5895:138-146.
[10]Shay T M,Benham V,Baker J T,et al.Selfsynchronous and self-referenced coherent beam combination for large optical arrays[J].IEEE Journal of Selected Topics in Quantantum Electronics,2007,13(3):480-486.
[11]Michaille L,Taylor D M,Bennett C R,et al.Characteristics of a Q-switched multicore photonic crystal fiber laser with a very large mode field area[J].Optics Letters,2008,33(1):71-73.
[12]Corcoran C J,Durville F.Experimental demonstration of aphase-locked laser array using a self-Fourier cavity[J].Applied Physics Letters,2005,86(20):201118.
[13]Kong F,Liu L,Sanders C,et al.Phase locking of nanosecond pulses in a passively Q-switched twoelement fiber laser array[J].Applied Physics Letters,2007,90(15):151110.
[14]Zhou P,Liu Z,Wang X,et al.Coherent beam combining of two fiber amplifiers using stochastic parallel gradient descent algorithm[J].Optics and Laser Technology,2009,41(7):853-856.
[15]Zhou P,Wang X,Ma Y,et al.Generation of a hollow beam by active phasing of a laser array using a stochastic parallel gradient descent algorithm[J].Journal of Optics,2010,12(1):015401.
[16]Yang Y C,Luo H,Li F Q,et al.Coherent beam combination simulation of high-power solid state lasers using stochastic parallel gradient descent algorithm[J].High Power Laser and Particle Beams,2011,23(4):875-880.
[17]Mu J,Jing F,Wang X,et al.Error control of piston and tilt based on SPGD in coherent beam combination[J].Chinese Journal of Lasers,2014,41(6):0602002.母杰,景峰,王逍,等.相干合成中基于SPGD算法的平移误差和倾斜误差控制[J].中国激光,2014,41(6):0602002.
[18]Zhang J,Zhang S,Lin D,et al.Study on control strategy of structure stability for the Shenguang-IIIlaser facility[J].Fusion Engineering and Design,2017,120:27-33.
[19]Zhou P,Ma Y X,Wang X L,et al.Dynamical simulation and control bandwidth analysis on coherent beam combination of fiber amplifiers based on stochastic parallel gradient descent algorithm[J].Chinese Journal of Lasers,2009,36(11):2972-2977.周朴,马阎星,王小林,等.基于随机并行梯度下降算法光纤放大器相干合成的动态模拟与控制带宽分析[J].中国激光,2009,36(11):2972-2977.
[20]Chen B,Yang H Z,Zhang J B,et al.Performances index and convergence speed of parallel gradient gescent algorithm in adaptive optics of point source[J].Acta Optica Sinica,2009,29(5):1143-1148.陈波,杨慧珍,张金宝,等.点目标成像自适应光学随机并行梯度下降算法性能指标与收敛速度[J].光学学报,2009,29(5):1143-1148.
[21]Yang H Z,Chen B,Li X Y,et al.Simulation and analysis of stochastic parallel gradient descent algorithm for adaptive optics system[J].Acta Optica Sinica,2007,28(8):205-210.杨慧珍,陈波,李新阳,等.自适应光学系统随机并行梯度下降控制算法实验研究[J].光学学报,2007,28(8):205-210.
[22]Voronstov M A,Carhart G W,Ricklin J C.Adaptive phase-distortion correction based on parallel gradientdescent optimization[J].Optics Letters,1997,22(12):907-909.
[23]Weyrauch T,Vorontsov M A,Bifano T G,et al.Microscale adaptive optics:wave-front control with a mu-mirror array and a vlsi stochastic gradient descent controller[J].Applied Optics,2001,40(24):4243-4253.
[24]Li Z L,Wang X,Mu J,et al.High pricision time jitter measurement for large multi-beam laser facility[J].High Power Laser and Particle Beams,2015,27(11):111001.李志林,王逍,母杰,等.大型激光装置束间同步抖动的高精度测量[J].强激光与粒子束,2015,27(11):111001.