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对像散椭圆高斯光束, 传统的M2因子测量采用Mx2和My2来描述光束质量. 当光束绕z轴旋转, Mx2和My2会随之变化, 单纯采用Mx2和My2来评价激光光束质量并不唯一. 为此采用了像散椭圆高斯光束的M2因子矩阵, 理论推导出了在同一坐标系下光场绕z轴旋转不同角度后的M2因子矩阵, 找出了光场旋转前后的M2因子矩阵元的不变量关系. 数值模拟、 实验测量得到M2因子矩阵主对角元随光斑旋转角度的变化轨迹曲线, 及反对角元随旋转角度的变化规律. 理论推导与实验结果相符. 结果表明, 像散椭圆高斯光束在主方向上时Mx2与My2之和最小; 在其他方向上的Mx2, My2之和大于在主方向上的Mx2, My2之和; 反对角元随旋转角度呈周期变化, 在主方向上为零.Mx2 and My2 are provided for characterizing and measuring the beam quality of an astigmatic elliptical Gaussian beam. The value undergoes certain changes when the beam is not at an arbitrary azimuth angle . Accordingly, problem arises: merely using Mx2 and My2 cannot characterize beam quality effectively. So in this paper M2 factor matrix is introduced. The M2 factor matrix for the beam at an azimuth angle is theoretically derived. It is found that elements of the matrix for the original field are related to that beam at azimuth angle . The matrix elements, including diagonal and off-diagonal elements, versus azimuth angle have been presented on the basis of calculation results. Theoretical results are in agreement with experimental ones. Results imply that the sum of Mx2 and My2 for an astigmatic elliptical Gaussian beam is to be minimum as the principal axes correspond to the laboratory coordinate axes; off-diagonal elements, however, vary periodically with the variation in , and are to be zero as the principal axes correspond to the laboratory coordinate axes.
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Keywords:
- M2 factor matrix /
- astigmatic elliptical Gaussian beam /
- measurement /
- matrix optics
[1] Siegman A E 1990 Proc. SPIE 1224 7
[2] L B D 1992 Laser Optics-Laser Beam Propagation and Beam Quality Control second edition (Chengdu: Sichuan University Press) p9 (in Chinese) [吕百达 1992 激光光学-激光束的传输变换和光束质量控制 第二版 (成都: 四川大学出版社) 第9页]
[3] Duncan M D, Mahon R 1989 Appl. Opt. 28 4570
[4] Johnston T F 1998 Appl. Opt. 37 4845
[5] Bouafia M, Bencheikh A, Bouamama L, Weber H 2004 Proc. SPIE 5456 135
[6] Kang X P, L B D 2006 Acta Phys. Sin. 55 4563 (in Chinese) [康小平, 吕百达 2006 55 4563]
[7] Ruff J A, Siegman A E 1992 Appl. Opt. 31 4907
[8] Lambert R W, Cortés-Martínez R, Waddie A J, Shephard J D, Taghizadeh M R, Greenaway A H, Hand D P 2004 Appl. Opt. 43 5037
[9] Luo S R, L B D 2004 Acta Phys. Sin. 53 82 (in Chinese) [罗时荣, 吕百达 2004 53 82]
[10] Feng G Y, Zhou S H 2009 Chinese J. Lasers 36 1643 (in Chinese) [冯国英, 周寿桓 2009 中国激光 36 1643]
[11] ISO 2005 ISO 11146-1. Part 1
[12] ISO 2004 ISO/TR 11146-3. Part 3
[13] ISO 2005 ISO 11146-2. Part 2
[14] Wang X Q, L B D 2002 Acta Phys. Sin. 51 247 (in Chinese) [王喜庆, 吕百达 2002 51 247]
[15] Su Z P, Lou Q H, Dong J X, Zhou J, Wei Y R 2007 Acta phys. Sin. 56 5831 [苏宙平, 楼祺洪, 董景星, 周军, 魏运荣 2007 56 5831]
[16] Du Y Z, Feng G Y, Li H R, Cai Z, Zhao H, Zhou S H 2013 Opt. Commun. 287 1
[17] Schmidt O A, Schulze C, Flamm D, Brning R, Kaiser T, Schröter S, Duparré M 2011 Opt. Express 19 6742
[18] Schulze C, Flamm D, Duparré M, Forbes A 2012 Opt. Lett. 37 4687
[19] Li W, Feng G Y, Huang Y, Li G, Yang H M, Xie X D, Chen J G, Zhou S H 2009 Acta Phys. Sin. 58 2461 [李玮, 冯国英, 黄宇, 李刚, 杨火木, 谢旭东, 陈建国, 周寿桓 2009 58 2461]
[20] Feng G Y, Huang Y Z 1997 High Power Laser and Particle Beams 9 491 (in Chinese) [冯国英, 黄永忠 1997 强激光与粒子束 9 491]
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[1] Siegman A E 1990 Proc. SPIE 1224 7
[2] L B D 1992 Laser Optics-Laser Beam Propagation and Beam Quality Control second edition (Chengdu: Sichuan University Press) p9 (in Chinese) [吕百达 1992 激光光学-激光束的传输变换和光束质量控制 第二版 (成都: 四川大学出版社) 第9页]
[3] Duncan M D, Mahon R 1989 Appl. Opt. 28 4570
[4] Johnston T F 1998 Appl. Opt. 37 4845
[5] Bouafia M, Bencheikh A, Bouamama L, Weber H 2004 Proc. SPIE 5456 135
[6] Kang X P, L B D 2006 Acta Phys. Sin. 55 4563 (in Chinese) [康小平, 吕百达 2006 55 4563]
[7] Ruff J A, Siegman A E 1992 Appl. Opt. 31 4907
[8] Lambert R W, Cortés-Martínez R, Waddie A J, Shephard J D, Taghizadeh M R, Greenaway A H, Hand D P 2004 Appl. Opt. 43 5037
[9] Luo S R, L B D 2004 Acta Phys. Sin. 53 82 (in Chinese) [罗时荣, 吕百达 2004 53 82]
[10] Feng G Y, Zhou S H 2009 Chinese J. Lasers 36 1643 (in Chinese) [冯国英, 周寿桓 2009 中国激光 36 1643]
[11] ISO 2005 ISO 11146-1. Part 1
[12] ISO 2004 ISO/TR 11146-3. Part 3
[13] ISO 2005 ISO 11146-2. Part 2
[14] Wang X Q, L B D 2002 Acta Phys. Sin. 51 247 (in Chinese) [王喜庆, 吕百达 2002 51 247]
[15] Su Z P, Lou Q H, Dong J X, Zhou J, Wei Y R 2007 Acta phys. Sin. 56 5831 [苏宙平, 楼祺洪, 董景星, 周军, 魏运荣 2007 56 5831]
[16] Du Y Z, Feng G Y, Li H R, Cai Z, Zhao H, Zhou S H 2013 Opt. Commun. 287 1
[17] Schmidt O A, Schulze C, Flamm D, Brning R, Kaiser T, Schröter S, Duparré M 2011 Opt. Express 19 6742
[18] Schulze C, Flamm D, Duparré M, Forbes A 2012 Opt. Lett. 37 4687
[19] Li W, Feng G Y, Huang Y, Li G, Yang H M, Xie X D, Chen J G, Zhou S H 2009 Acta Phys. Sin. 58 2461 [李玮, 冯国英, 黄宇, 李刚, 杨火木, 谢旭东, 陈建国, 周寿桓 2009 58 2461]
[20] Feng G Y, Huang Y Z 1997 High Power Laser and Particle Beams 9 491 (in Chinese) [冯国英, 黄永忠 1997 强激光与粒子束 9 491]
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