Orthonormal mode sets for the two-dimensional fractional Fourier transformation

T. Alieva, M.J. Bastiaans

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23 Citations (Scopus)
3 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)1226-1228
Number of pages3
JournalOptics Letters
Volume32
Issue number10
DOIs
Publication statusPublished - 2007

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Fourier transformation
transformers
rays
eigenvectors
orbitals
output

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abstract = "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 Poincar{\'e} sphere are studied.",
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Orthonormal mode sets for the two-dimensional fractional Fourier transformation. / Alieva, T.; Bastiaans, M.J.

In: Optics Letters, Vol. 32, No. 10, 2007, p. 1226-1228.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Orthonormal mode sets for the two-dimensional fractional Fourier transformation

AU - Alieva, T.

AU - Bastiaans, M.J.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

U2 - 10.1364/OL.32.001226

DO - 10.1364/OL.32.001226

M3 - Article

VL - 32

SP - 1226

EP - 1228

JO - Optics Letters

JF - Optics Letters

SN - 0146-9592

IS - 10

ER -