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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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