Orthonormal mode sets for the two-dimensional fractional Fourier transformation | Zendy

Tatiana Alieva | Zendy; Martin J. Bastiaans | Zendy

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Orthonormal mode sets for the two-dimensional fractional Fourier transformation

Author(s) -

Tatiana Alieva,

Martin J. Bastiaans

Publication year - 2007

Publication title -

optics letters

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.524

H-Index - 272

eISSN - 1071-2763

pISSN - 0146-9592

DOI - 10.1364/ol.32.001226

Subject(s) - orthonormal basis , physics , fourier transform , mathematical analysis , eigenfunction , antisymmetric relation , mathematics , laguerre polynomials , eigenvalues and eigenvectors , hermite polynomials , quantum mechanics , mathematical physics

A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincaré sphere are studied.

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