2023/11/16 by I. Ramos-Prieto, Ramos-Prieto, I., David Sánchez-de-la-Llave +9 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Optics (physics.optics)
paper · pdf · doi:10.48550/arxiv.2311.09541
openalex publication_date 2023/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the propagation characteristics of Cauchy-Riemann beams in gradient-index media. Our study reveals two key findings: a) the preservation of their form during propagation, and b) surprisingly, the feasibility of obtaining the fractional Fourier transform for any arbitrary entire function. We provide an explicit and straightforward expression for this transform. Additionally, our results contribute to a deeper understanding of the behavior of Cauchy-Riemann beams in complex media, offering insights that may have implications for various applications in optics and wave propagation.