Fathallah Ashraf, Shalaby Mohamed
Department of Engineering Physics and Mathematics, Faculty of Engineering, Ain Shams University, Cairo 11517, Egypt.
Appl Opt. 2011 Jul 1;50(19):3128-34. doi: 10.1364/AO.50.003128.
We explore a general type of stable Bessel beams in graded index media. The proposed axially symmetric medium is characterized by an "α" index profile. Explicit solutions for the radial envelope of the field E(r) are derived in terms of generalized Bessel functions. Emphasis is given on illustrating how far the conditions of the proposed modified structure permit only a Bessel function of the first kind to be uniquely retained in the solution. This paper considers both the optical and mathematical aspects. Some numerical examples corroborating our theoretical results are included, showing the stability, propagation, and diffraction of such Bessel beams.
我们研究了渐变折射率介质中一种通用类型的稳定贝塞尔光束。所提出的轴对称介质由“α”折射率分布来表征。根据广义贝塞尔函数推导出了场E(r)径向包络的显式解。重点在于说明所提出的修改结构的条件在多大程度上仅允许在解中唯一保留第一类贝塞尔函数。本文兼顾了光学和数学方面。包含了一些证实我们理论结果的数值示例，展示了此类贝塞尔光束的稳定性、传播和衍射。
