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 inOptik (Stuttgart) Vol. 309; p. 171864
Main Authors Ramos-Prieto, I., Sánchez-de-la-Llave, D., Ruíz, U., Arrizón, V., Soto-Eguibar, F., Moya-Cessa, H.M.
Format Journal Article
LanguageEnglish
Published Elsevier GmbH 01.08.2024
Subjects
Beam propagation
Cauchy–Riemann beams
Fractional Fourier transform
GRIN media
Paraxial equation
Quadratic GRIN media
Beam propagation
Cauchy–Riemann beams
GRIN media
Paraxial equation
Fractional Fourier transform
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