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

中国物理B ›› 2013, Vol. 22 ›› Issue (10): 104201-104201.doi: 10.1088/1674-1056/22/10/104201

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

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

周益民, 周国泉

School of Sciences, Zhejiang Agriculture & Forestry University, Lin’an 311300, China

收稿日期:2013-01-04 修回日期:2013-02-07 出版日期:2013-08-30 发布日期:2013-08-30
基金资助:
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).

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

Zhou Yi-Min (周益民), Zhou Guo-Quan (周国泉)

School of Sciences, Zhejiang Agriculture & Forestry University, Lin’an 311300, China

Received:2013-01-04 Revised:2013-02-07 Online:2013-08-30 Published:2013-08-30
Contact: Zhou Guo-Quan E-mail:zhouguoquan178@sohu.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Wigner distribution function, super Lorentz-Gauss beam, paraxial ABCD optical system

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.

Key words: Wigner distribution function, super Lorentz–Gauss beam, paraxial ABCD optical system

中图分类号: (Wave propagation, transmission and absorption)

42.25.Bs

42.55.Px (Semiconductor lasers; laser diodes) 42.60.Jf (Beam characteristics: profile, intensity, and power; spatial pattern formation)

周益民, 周国泉. The Wigner distribution function of a super Lorentz–Gauss SLG₁₁ beam through a paraxial ABCD optical system[J]. 中国物理B, 2013, 22(10): 104201-104201.

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[J]. Chin. Phys. B, 2013, 22(10): 104201-104201.

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

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

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