Cauchy–Riemann beams in GRIN media

We investigate the propagation characteristics of Cauchy–Riemann beams in gradient-index media. Our study reveals two key findings: first, the preservation of their form during propagation; and second, the surprising feasibility of obtaining the two-dimensional fractional Fourier transform for any a...

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Bibliographic Details
Published in:Optik (Stuttgart) 2024-08, Vol.309, p.171864, Article 171864
Main Authors: Ramos-Prieto, I., Sánchez-de-la-Llave, D., Ruíz, U., Arrizón, V., Soto-Eguibar, F., Moya-Cessa, H.M.
Format: Article
Language:English
Subjects:
Beam propagation
Cauchy–Riemann beams
Fractional Fourier transform
GRIN media
Paraxial equation
Quadratic GRIN media
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Summary:We investigate the propagation characteristics of Cauchy–Riemann beams in gradient-index media. Our study reveals two key findings: first, the preservation of their form during propagation; and second, the surprising feasibility of obtaining the two-dimensional fractional Fourier transform for any arbitrary entire function. We elucidate an explicit and straightforward expression for this transform. Additionally, our results contribute to a deeper understanding of the behavior of Cauchy–Riemann beams in inhomogeneous media, offering insights that may have implications for various applications in optics and wave propagation.
ISSN:0030-4026
1618-1336
DOI:10.1016/j.ijleo.2024.171864