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Generating function for Hermite–Gaussian modes propagating through first-order optical systems

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Martin J Bastiaans1 and Tatiana Alieva2

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LETTER TO THE EDITOR

We consider the field that appears at the output of a first-order optical system when its input field is a Hermite–Gaussian mode. The generating function for the output modes is determined. The orthonormality property of the output modes is confirmed, and derivative and recurrence relations for these modes are derived. Mode converters that generate Laguerre–Gaussian and Hermite–Laguerre–Gaussian modes are considered as examples.


PACS

42.30.Kq Fourier optics

02.30.Uu Integral transforms

02.30.Nw Fourier analysis

MSC

78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section)

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (See also 42C05 for general orthogonal polynomials and functions)

Subjects

Mathematical physics

Optics, quantum optics and lasers

Dates

Issue 6 (11 February 2005)

Received 24 October 2004, in final form 3 December 2004

Published 26 January 2005



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