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Chin. Phys. B, 2012, Vol. 21(3): 034201    DOI: 10.1088/1674-1056/21/3/034201
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

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

Zhu Kai-Cheng(朱开成)a)†, Li Shao-Xin(李绍新)b), Tang Ying(唐英)a), Yu Yan(余燕)a), and Tang Hui-Qin(唐慧琴)a)
a. School of Physical Science and Technology, Central South University, Changsha 410083, China;
b. Physical Staff Room, Guangdong Medical College, Dongguan 523808, China
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

Cite this article: 

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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