Propagation of Tricomi beams in a gradient-index medium

Abstract

Based on the generalized Huygens-Fresnel diffraction theory and ABCD transfer theory, analytical expression for a newly proposed Tricomi beam propagating through a gradient-index medium is derived. The targeted beam’s propagation trajectory, intensity profile, and phase distribution are investigated. Impact of the beam’s complex parameters α and β, and topological charge n on the propagation properties are discussed in detail. It is shown that by selecting appropriate complex parameters α and β, Tricomi beams can degenerate into standard, asymmetric, off-axis Bessel beams, or sheet beams. While propagating in a gradient-index medium, Tricomi beams would be focused at two singularities within one period L, and go through periodic propagation. After passing the singularity, the transverse intensity pattern reconstructs itself and experiences symmetric inversion. Furthermore, propagation trajectory of the superimposed beam becomes visible and the main lobe splits. As the topological charge n increases, the peak intensity gradually diminishes, and meanwhile, the peak intensity position undergoes a shift. These findings presented in this article are of significant importance for prospective applications in the field of optical control, trapping, and optical communication.