Abstract

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 $\mathrm{E}(r)$ 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.

© 2011 Optical Society of America

Modified Bessel nondiffracting beams

S. Ruschin
J. Opt. Soc. Am. A 11(12) 3224-3228 (1994)

Propagation of a Bessel–Gaussian beam in a gradient-index medium

Shixin Pei, Shanshan Xu, Fenping Cui, Qingwei Pan, and Zhaolou Cao
Appl. Opt. 58(4) 920-926 (2019)

Bessel-like beam generation by superposing multiple Airy beams

Chi-Young Hwang, Kyoung-Youm Kim, and Byoungho Lee
Opt. Express 19(8) 7356-7364 (2011)

Hybrid metamaterials combining zero-index and graded-index materials for multi-directional Bessel beam generation

Jie Jiang, Fusheng Deng, Zhiwei Guo, Yuqian Wang, Yuntai Wu, Yong Sun, Yunlong Shi, and Hong Chen
Opt. Mater. Express 14(4) 1085-1093 (2024)

Laser ablation of silicon using a Bessel-like beam generated by a subwavelength annular aperture structure

Yuh-Yan Yu, Chin-Kai Chang, Ming-Wei Lai, Long-Sun Huang, and Chih-Kung Lee
Appl. Opt. 50(34) 6384-6390 (2011)