The Wigner distribution function of a super Lorentz–Gauss SLG11 beam through a paraxial ABCD optical system

doi:10.1088/1674-1056/22/10/104201

Abstract An orthonormal beam family of super Lorentz–Gauss (SLG) beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG₀₀, SLG₀₁, SLG₁₀, and SLG₁₁ beams. The SLG₀₀ beam is just the Lorentz–Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function (WDF) of an SLG₁₁ beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG₁₁ beam propagating in free space are demonstrated. The normalized WDFs of an SLG₁₁ beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLG₁₁ beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG₁₁ beam in free space are also examined. This research reveals the propagation properties of an SLG₁₁ beam from another perspective. The WDFs of SLG₀₁ and SLG₁₀ beams can be easily obtained by using the WDFs of Lorentz–Gauss beam and the SLG₁₁ beam.

Keywords: Wigner distribution function super Lorentz–Gauss beam paraxial ABCD optical system

Received: 04 January 2013
Revised: 07 February 2013
Accepted manuscript online:

PACS:	42.25.Bs	(Wave propagation, transmission and absorption)
	42.55.Px	(Semiconductor lasers; laser diodes)
	42.60.Jf	(Beam characteristics: profile, intensity, and power; spatial pattern formation)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10974179) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y1090073).

Corresponding Authors: Zhou Guo-Quan
E-mail: zhouguoquan178@sohu.com

Cite this article:

Zhou Yi-Min (周益民), Zhou Guo-Quan (周国泉) The Wigner distribution function of a super Lorentz–Gauss SLG₁₁ beam through a paraxial ABCD optical system 2013 Chin. Phys. B 22 104201

[1]	Naqwi A and Durst F 1990 Appl. Opt. 29 1780
[2]	Yang J, Chen T T, Ding G L and Yuan X 2008 Proc. SPIE 6824 68240A
[3]	Gawhary O E and Severini S 2006 J. Opt. A: Pure Appl. Opt. 8 409
[4]	Gawhary O E and Severini S 2007 Opt. Commun. 269 274
[5]	Torre A, Evans W A B, Gawhary O E and Severini S 2008 J. Opt. A: Pure Appl. Opt. 10 115007
[6]	Zhou G Q 2009 Chin. Phys. B 18 2779
[7]	Zhou P, Wang X L, Ma Y X, Ma H T, Xu X J and Liu Z J 2010 J. Opt. 12 015409
[8]	Zhou P, Wang X L, Ma Y X and Liu Z J 2010 Appl. Opt. 49 2497
[9]	Yu H, Xiong L L and Lü B D 2010 Optik 121 1455
[10]	Jiang Y F, Huang K K and Lu X H 2011 Opt. Express 19 9708
[11]	Zhou G Q 2010 J. Opt. Soc. Am. A 27 563
[12]	Zhou G Q 2010 J. Opt. 12 05570
[13]	Zhou G Q 2010 Appl. Phys. B 101 371
[14]	Zhou G Q 2012 Chin. Phys. B 21 054104
[15]	Wigner E P 1932 Phys. Rev. 40 749
[16]	Dragoman D 1997 Prog. Opt. 37 1
[17]	Bastiaans M J 2000 J. Opt. Soc. Am. A 17 2475
[18]	Zhang Y C and Lü B D 2004 Opt. Lett. 29 2710
[19]	Hansson T, Anderson D, Lisak M, Semenov V E and Österberg U 2005 J. Opt. Soc. Am. B 25 1780
[20]	Duan K L and Lü B D 2005 J. Opt. Soc. Am. B 22 1585
[21]	Wu P, Lü B D and Chen T L 2005 Chin. Phys. 14 1130
[22]	Lü B D, Chen T L and Wu P 2005 Acta Phys. Sin. 54 658 (in Chinese)
[23]	Sun D and Zhao D M 2005 J. Opt. Soc. Am. A 22 1683
[24]	Oh S B and Barbastathis G 2009 Opt. Lett. 34 2584
[25]	Gao H H, Tian L, Zhang B L and Barbastathis G 2010 Opt. Lett. 35 4148
[26]	Chen R P, Zheng H P and Dai C Q 2011 J. Opt. Soc. Am. A 28 1307
[27]	Zhou G Q and Chen R P 2012 Appl. Phys. B 107 183
[28]	Schmidt P P 1976 J. Phys. B: At. Mol. Opt. Phys. 9 2331
[29]	Gradshteyn I S and Ryzhik I M 1980 Table of Integrals, Series, and Products (New York: Academic Press)

[1]	Nonclassicality of photon-modulated spin coherent states in the Holstein—Primakoff realization Xiaoyan Zhang(张晓燕), Jisuo Wang(王继锁), Lei Wang(王磊),Xiangguo Meng(孟祥国), and Baolong Liang(梁宝龙). Chin. Phys. B, 2022, 31(5): 054205.
[2]	Wigner function and the entanglement of quantized Bessel–Gaussian vortex state of quantized radiation field Zhu Kai-Cheng (朱开成), Li Shao-Xin (李绍新), Tang Ying (唐英), Zheng Xiao-Juan (郑小娟), Tang Hui-Qin (唐慧琴 ). Chin. Phys. B, 2012, 21(8): 084204.
[3]	Decoherence of elliptical states in phase space Wang Yue-Yuan (王月媛), Liu Zheng-Jun (刘正君), Liao Qing-Hong (廖庆洪), Wang Ji-Cheng (王继成), Liu Shu-Tian (刘树田). Chin. Phys. B, 2011, 20(5): 054201.
[4]	A new finite-dimensional thermal coherent state and its Wigner distribution function Meng Xiang-Guo(孟祥国), Wang Ji-Suo(王继锁), and Liang Bao-Long(梁宝龙) . Chin. Phys. B, 2011, 20(1): 014204.
[5]	Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform Shi Peng(石鹏) , Cao Guo-Wei(曹国威), and Li Yong-Ping(李永平). Chin. Phys. B, 2010, 19(7): 074201.
[6]	The Wigner function and phase properties of superposition of two coherent states with the vacuum state Wang Yue-Yuan (王月媛), Wang Ji-Cheng (王继成), Liu Shu-Tian (刘树田). Chin. Phys. B, 2010, 19(7): 074206.
[7]	Fractional Fourier transform of flat-topped multi-Gaussian beams based on the Wigner distribution function Wu Ping (吴平), Lü Bai-Da (吕百达), Chen Tian-Lu (陈天禄). Chin. Phys. B, 2005, 14(6): 1130-1135.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

The Wigner distribution function of a super Lorentz–Gauss SLG₁₁ beam through a paraxial ABCD optical system

Cite this article:

Online attention