title: Generalized Bessel beams in modified axially symmetric graded index structures.
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 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.
authors: Department of Engineering Physics and Mathematics, Faculty of Engineering, Ain Shams University, Cairo 11517, Egypt. a_fathallah@aucegypt.edu
authors: Ashraf
authors: A
authors: Fathallah
authors: Mohamed
authors: M
authors: Shalaby