Analysis of fast calculation about eigenvector method of laser resonator modes

WANG Wei; XIAO Yu; TANG Xiahui; QIN Yingxiong; WU Chao; WANG Zhen

doi:10.7510/jgjs.issn.1001-3806.2016.05.001

When eigenvector method was used to perform numerical simulation on laser resonator with big Fresnel number, the calculation efficiency was low by using trapezoidal integral method. In order to solve the problem, the minimum sampling numbers for numerical simulation were determined by analyzing the space-bandwidth product of resonators output mode and Gaussian quadrature was used to calculate the transmission matrix. This method not only ensured the calculation accuracy of chirp function but also reduced the transmission matrix size.Through numerical simulation of plane-concave resonator with square mirrors which Fresnel number is 10,the results show that, transmission matrix size of trapezoidal integration is 1000010000 and computation time of laser resonator modes is 412.47s. Transmission matrix size of Gaussian quadrature is 36003600 and computation time is 51.34s. These results indicate that the new method greatly improves computational efficiency of eigenvector method and reduces the consumption of computer memory at the same time.

Analysis of fast calculation about eigenvector method of laser resonator modes

Corresponding author: TANG Xiahui, txh1116@mail.hust.edu.cn;

1. College of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China

Received Date: 2015-08-25

Accepted Date: 2015-10-19

Available Online: 2016-09-25

Abstract: When eigenvector method was used to perform numerical simulation on laser resonator with big Fresnel number, the calculation efficiency was low by using trapezoidal integral method. In order to solve the problem, the minimum sampling numbers for numerical simulation were determined by analyzing the space-bandwidth product of resonators output mode and Gaussian quadrature was used to calculate the transmission matrix. This method not only ensured the calculation accuracy of chirp function but also reduced the transmission matrix size.Through numerical simulation of plane-concave resonator with square mirrors which Fresnel number is 10,the results show that, transmission matrix size of trapezoidal integration is 1000010000 and computation time of laser resonator modes is 412.47s. Transmission matrix size of Gaussian quadrature is 36003600 and computation time is 51.34s. These results indicate that the new method greatly improves computational efficiency of eigenvector method and reduces the consumption of computer memory at the same time.

HTML

Reference (17)

[1]	CHENG Y Y,WANG Y Q,HU J,et al.A novel eigenvector method for calculation of optical resonator modes and beam propagation[J].Acta Physica Sinica,2004,53(8):2576-2582(in Chinese).
[2]	CHENG Y Y,WANG Y Q,HU J,et al.An eigenvector method for optical field simulation[J].Optics Communications,2004,234(1):1-6.
[3]	QIN Y X,TANG X H,XIAO Y,et al.Toric concave mirror laser resonator with a big Fresnel number[J].Optics Letters,2009,34(7):1120-1122.
[4]	CHEN K,ZHU D X,ZHANG P C.Mode analysis of laser resonator based on finite element matrix[J].Laser Technology,2014,38(3):352-356(in Chinese).
[5]	LIU W B,ZHONG M,XIA H J,et al.Study on output modes of a corner cube array resonator[J].Laser Technology,2011,35(6):745-747(in Chinese).
[6]	QIN Y X,XIAO Y,LI G,et al.Numerical simulation of a laser resonator with an in-phase doughnut-like output beam[J].Journal of Modern Optics,2009,56(16):1804-1811.
[7]	WANG D,QIN Y,TANG X H,et al.Eigenvector method for unstable resonator simulations[J].Optics Communications,2012,285(10):2682-2687.
[8]	FOX A G,LI T.Resonant modes in a maser interferometer[J].Bell System Technical Journal,1961,40(2):453-488.
[9]	SIEGAMAN A E,SZIKLAS E A.Mode calculations in unstable resonators with flowing saturable gain.1:Hermite-Gaussian expansion[J].Applied Optics,1974,13(12):2775-2792.
[10]	SIEGAMAN A E,SZIKLAS E A.Mode calculations in unstable resonators with flowing saturable gain.2:Fast Fourier transform method[J].Applied Optics,1975,14(8):1874-1889.
[11]	CAO S S.Study on the transverse modes in stable optical resonators[J].Laser Technology,2010,34(1):135-137(in Chinese).
[12]	LOHMANN A W,DORSCH R G,MENDLOVIC D,et al.Space-bandwidth product of optical signals and systems[J].Journal of the Optical Society of America,1996,A13(3):470-473.
[13]	HEALY J J,SHERIDAN J T.Space-bandwidth ratio as a means of choosing between Fresnel and other linear canonical transform algorithms[J].Journal of the Optical Society of America,2011,A28(5):786-790.
[14]	HENNELLY B M,SHERIDAN J T.Generalizing,optimizing,and inventing numerical algorithms for the fractional Fourier,Fresnel,and linear canonical transforms[J].Journal of the Optical Society of America,2005,A22(5):917-927.
[15]	HEALY J J,SHERIDAN J T.Reevaluation of the direct method of calculating Fresnel and other linear canonical transforms[J].Optics Letters,2010,35(7):947-949.
[16]	XIAO Y.Research on optimization of numerical method for diffraction beam propagation in free space[D].Wuhan:Huazhong University of ScienceTechnology,2013:22-26(in Chinese).
[17]	GERALD C F,WHEATLEY P O.Applied numerical analysis[M].Beijing:China Machine Press,2006:244-253(in Chinese).

Analysis of fast calculation about eigenvector method of laser resonator modes

Abstract

References

Proportional views

通讯作者: 陈斌, bchen63@163.com

Proportional views