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Based on the method of generalized truncated second-order moment, the analytical formula of the generalized beam propagation factor (M2G factor) of truncated partially coherent Hermite-Gaussian(H-G) beams is derived. The analytical results obtained from truncated fully coherent H-G beam, truncated Gaussian Shell Model (GSM) beam and truncated Gaussian beam are given as particular examples in this paper. It is shown that the M2G factor of truncated partially coherent H-G beam depends on truncated parameter δ, beam order m, and beam coherence parameter α. When the value of δ is very small, the odd-even groups happen to the M2G factor, i.e., the values of M2G factor with different values of the odd m are nearly the same, and so are they for the even m case. However, this phenomenon disappears as δ increases. For the truncated GSM beams with different values of δ, there exist the cross points between the curves of the M2G factor versus α. However, this phenomenon may disappear for truncated partially coherent H-G beams. In addition, the larger the m is, the more the M2G factor is affected by the δ, and the effect of aperture on M2G factor may be neglected when the δ is larger.
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Keywords:
- truncated partially coherent Hermite-Gaussian beam /
- generalized M2G factor /
- generalized truncated second-order moments
[1] Siegman A E 1990 Proc. SPIE 1224 2
[2] Johnston T F 1990 Jr. Laser Focus World 26 173
[3] Sasnett M W 1989 Propagation of multimode laser beams—the M2 factor (New York) p132
[4] Martinez-Herrero R, Mejias P M 1993 Opt. Lett. 18 1669
[5] Martinez-Herrero R, Mejias P M, Arias M 1995 Opt. Lett. 20 124
[6] Mei Z R, Zhao D M 2004 J. Opt. A: Pure Appl. Opt. 6 1005
[7] Mei Z R, Zhao D M 2005 Appl. Opt. 44 1381
[8] Zeng Q G, Wen Q, Zhang B 2004 Acta Phys. Sin. 53 1357(in Chinese)[曾庆刚、 文 侨、 张 彬 2004 53 1357]
[9] Lü B D, Luo S R 2000 Opt. Common. 178 275
[10] Wen J J, Breazeal M A 1988 J. Acoust. Soc. Am. 83 1752
[11] Chu X L, Zhang B, Wang G Q 2002 Acta Opt. Sin. 22 1051(in Chinese)[楚晓亮、 张 彬 2002 光学学报 22 1051]
[12] Zhang B,Chu X L, Wen Q 2002 J. Opt. Soc. Am. A 19 1370
[13] Chu X L, Zhang B, Wen Q 2003 Appl. Opt. 42 4280
[14] Zhou G Q 2010 Opt. Laser Technol. 42 489
[15] Zhou G Q 2010 J. Opt. 12 015701
[16] Lu Z D,Jiang H L, Du X Y, Zhao D M 2008 J. Mod. Opt. 55 2381
[17] Zhang Y, Guo X, Li K, Wen Q, Zhang B, Cai B W 2006 Acta Opt. Sin. 26 1057(in Chinese) [张 艳、 郭 欣、 李 琨、 文 侨、 张 彬、 蔡邦维 2006 光学学报 26 1057]
[18] Zhou G Q, Chen L, Chu X X 2007 Chin. Phys. 16 2709
[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]
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[1] Siegman A E 1990 Proc. SPIE 1224 2
[2] Johnston T F 1990 Jr. Laser Focus World 26 173
[3] Sasnett M W 1989 Propagation of multimode laser beams—the M2 factor (New York) p132
[4] Martinez-Herrero R, Mejias P M 1993 Opt. Lett. 18 1669
[5] Martinez-Herrero R, Mejias P M, Arias M 1995 Opt. Lett. 20 124
[6] Mei Z R, Zhao D M 2004 J. Opt. A: Pure Appl. Opt. 6 1005
[7] Mei Z R, Zhao D M 2005 Appl. Opt. 44 1381
[8] Zeng Q G, Wen Q, Zhang B 2004 Acta Phys. Sin. 53 1357(in Chinese)[曾庆刚、 文 侨、 张 彬 2004 53 1357]
[9] Lü B D, Luo S R 2000 Opt. Common. 178 275
[10] Wen J J, Breazeal M A 1988 J. Acoust. Soc. Am. 83 1752
[11] Chu X L, Zhang B, Wang G Q 2002 Acta Opt. Sin. 22 1051(in Chinese)[楚晓亮、 张 彬 2002 光学学报 22 1051]
[12] Zhang B,Chu X L, Wen Q 2002 J. Opt. Soc. Am. A 19 1370
[13] Chu X L, Zhang B, Wen Q 2003 Appl. Opt. 42 4280
[14] Zhou G Q 2010 Opt. Laser Technol. 42 489
[15] Zhou G Q 2010 J. Opt. 12 015701
[16] Lu Z D,Jiang H L, Du X Y, Zhao D M 2008 J. Mod. Opt. 55 2381
[17] Zhang Y, Guo X, Li K, Wen Q, Zhang B, Cai B W 2006 Acta Opt. Sin. 26 1057(in Chinese) [张 艳、 郭 欣、 李 琨、 文 侨、 张 彬、 蔡邦维 2006 光学学报 26 1057]
[18] Zhou G Q, Chen L, Chu X X 2007 Chin. Phys. 16 2709
[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]
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