准无衍射Lommel-Gauss光束非傍轴传输的解析
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摘要
为研究准无衍射Lommel-Gauss光束的非傍轴传输,根据光束传播的独立性和叠加性原理,先将Lommel-Gauss光束展开为无穷项Bessel光束的叠加,然后利用虚源法和格林函数法引入一组能够产生Lommel-Gauss光束的虚光源点,利用Fourier-Bessel变换理论,通过建立对应的非齐次亥姆霍兹方程,计算得到Lommel-Gauss光束传输的非傍轴严格积分表达式.利用该积分表达式推导给出了Lommel-Gauss光束轴上光场分布的非傍轴修正解析表达式,这为定量计算Lommel-Gauss光束的传输特性提供了方便.
According to the principle of independence and superposition of beam propagation, it was expanded the Lommel-Gauss beams into the superposition of an infinite number of Bessel beams when analyzing the nonparaxial propagation of the quasi-diffraction-free Lommel-Gauss beams. By using the virtual source point technique and the method of Green function, it was introduced a group of virtual sources for generating the Lommel-Gauss beams, and the corresponding inhomogeneous Helmholtz equation was established. The nonparaxial integral representation of Lommel-Gauss beams was obtained. Accordingly, the analytic expressions of nonparaxial corrections for the onaxis field of Lommel-Gauss beams were obtained. The expression could be used to calculate the propagation characteristics of Lommel-Gauss beams quantitatively.
According to the principle of independence and superposition of beam propagation, it was expanded the Lommel-Gauss beams into the superposition of an infinite number of Bessel beams when analyzing the nonparaxial propagation of the quasi-diffraction-free Lommel-Gauss beams. By using the virtual source point technique and the method of Green function, it was introduced a group of virtual sources for generating the Lommel-Gauss beams, and the corresponding inhomogeneous Helmholtz equation was established. The nonparaxial integral representation of Lommel-Gauss beams was obtained. Accordingly, the analytic expressions of nonparaxial corrections for the onaxis field of Lommel-Gauss beams were obtained. The expression could be used to calculate the propagation characteristics of Lommel-Gauss beams quantitatively.
引文
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[19]刘佳伟,李海英,吴振森,等.矢量贝塞尔涡旋波束在均匀单轴各向异性介质中的传输[J].光学学报,2018,38(2):0226001.
[2]KOVALEV A A,KOTLYAR V V,SOIFER V A.Asymmetric Bessel modes[J].Opt Lett,2014,39(8):2395-2398.
[3]KOVALEV A A,KOTLYAR V V.Lommel modes[J].Optics Communications,2015,338:117-122.
[4]GUTIERREZ-VEGA J C,BANDRES M A.Helmholtz-Gauss waves[J].Journal of the Optical Society of America A-optics Image Science and Vision,2005,22(2):289-298.
[5]SESHADRI S R.Virtual source for the Bessel-Gauss beam[J].Optics Letters,2002,27(12):998-1000.
[6]ZHANG Y C,SONG Y J,CHEN Z G,et al.Virtual sources for a cosh-Gaussian beam[J].Optics Letters,2007,32(3):292-294.
[7]LI D,REN Z J,DENG S Y.Virtual source for a Mathieu-Gauss beam[J].Journal of Optics,2017,19(5):055608.
[8]BANDRES M A,GUTIERREZ-VEGA J C.Higher-order complex source for elegant Laguerre-Gaussian waves[J].Optics Letters,2004,29(19):2213-2215.
[9]SESHADRI S R.Virtual source for a Hermite-Gauss beam[J].Optics Letters,2003,28(8):595-597.
[10]SESHADRI S R.Virtual source for a Laguerre-Gauss beam[J].Optics Letters,2002,27(21):1872-1874.
[11]KOVALEV A A,KOTLYAR V V.Family of three-dimensional asymmetric nonparaxial Lommel modes[J].Proceedings of the SPIE,2015,9448:944828.
[12]BELAFHAL A,EZ-ZARIY L,HRICHA Z.A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers[J].Journal of Quantitative Spectroscopy & Radiative Transfer,2016,184:1-7.
[13]FRANK W J O,DANIEL W L,RONALD F B,et al.NIST handbook of mathematical functions[M].New York:Cambridge University Press,2010.
[14]奚定平.贝塞尔函数[M].北京:高等教育出版社,1998:161-164.
[15]波恩,沃耳夫.光学原理[M].杨葭荪,译.北京:电子工业出版社,2006.
[16]GOODMAN J W.Introduction to Fourier optics[M].3rd.Colaorado:Roberts & Company,2005.
[17]苏显渝.信息光学[M].北京:电子工业出版社,1997.
[18]胡润,吴逢铁,朱清智,等.离轴像散对高阶贝塞尔光束的影响[J].光学学报,2017,37(8):0826002.
[19]刘佳伟,李海英,吴振森,等.矢量贝塞尔涡旋波束在均匀单轴各向异性介质中的传输[J].光学学报,2018,38(2):0226001.