The Wigner distribution functions of coherent and partially coherent Bessel–Gaussian beams

doi:10.1088/1674-1056/21/3/034201

Abstract Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function (WDF) for a coherent or partially coherent Bessel-Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.

Keywords: partially coherent Bessel-Gaussian beam Wigner function optical angular momentum

Received: 05 July 2011
Revised: 05 September 2011
Accepted manuscript online:

PACS:	42.25.-p	(Wave optics)
	42.60.Jf	(Beam characteristics: profile, intensity, and power; spatial pattern formation)
	42.25.Kb	(Coherence)

Corresponding Authors: Zhu Kai-Cheng,zhukaicheng@vip.sina.com
E-mail: zhukaicheng@vip.sina.com

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Zhu Kai-Cheng(朱开成), Li Shao-Xin(李绍新), Tang Ying(唐英), Yu Yan(余燕), and Tang Hui-Qin(唐慧琴) The Wigner distribution functions of coherent and partially coherent Bessel–Gaussian beams 2012 Chin. Phys. B 21 034201

[1]	Wigner E P 1932 Phys. Rev. 40 749
[2]	Bastiaans M J 1978 Opt. Commun. 25 26
[3]	Bastiaans M J 1979 J. Opt. Soc. Am. 69 1710
[4]	Simon R, Sudarshan E C G and Mukunda N 1984 Phys. Rev. A 29 3273
[5]	Simon R, Sudarshan E C G and Mukunda N 1985 Phys. Rev. A 31 2419
[6]	Bastiaans M J 1986 J. Opt. Soc. Am. A 3 1227
[7]	Dragoman D 1997 Prog. Opt. 37 1
[8]	Dragoman D 1994 J. Opt. Soc. Am. A 11 2643
[9]	Almeida J B and Lakshminarayanan V 2003 J. Comput. Appl. Math. 160 17
[10]	Rivera A L, Lozada-Cassou M, Rodriguez S and Castano V M 2003 Opt. Commun. 228 211
[11]	Gase R 1995 IEEE J. Quantum Electron. 31 1811
[12]	Simon S and Agarwal G S 2000 Opt. Lett. 25 1313
[13]	Bastiaans M J and van de Mortel P G J 1996 J. Opt. Soc. Am. A 13 1698
[14]	Sun D and Zhao D M 2005 J. Opt. Soc. Am. A 22 1683
[15]	Durnin J, Miceli J J and Eberly J H 1987 Phys. Rev. Lett. 58 1499
[16]	Gori F, Guattari G and Padovani C 1987 Opt. Commun. 64 491
[17]	Durnin J 1987 J. Opt. Soc. Am. A 4 651
[18]	Arlt J, Hitomi T and Dholakia K 2000 Appl. Phys. B 71 549
[19]	Seshadri S R 1999 J. Opt. Soc. Am. A 16 2917
[20]	Wang F and Cai Y 2010 Opt. Express 18 24661
[21]	Yuan Y, Cai Y, Qu J, Eyyubovglu H T, Baykal Y and Korotkova O 2009 Opt. Express 17 17344
[22]	Chen B and Pu J 2009 Chin. Phys. B 18 1033
[23]	Ji X L 2011 Acta Phys. Sin. 60 064207 (in Chinese)
[24]	Dattoli G and Torre A 1996 Theory and Applications of Special Functions (Rom: Arachne Editrice)
[25]	Rainville E D 1971 Special Functions (New York: Macmillan, Reprinted by Chelsea Publ. Co., Bronx)
[26]	Andrews L C 1985 Special Functions for Engineers and Applied Mathematicians (New York: Macmillan)

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The Wigner distribution functions of coherent and partially coherent Bessel–Gaussian beams

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