A general class of bi-orthonormal sets of Gaussian-type modes

M.J. Bastiaans, T. Alieva

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

Samenvatting

Based on the recently introduced orthonormal Hermite-Gaussian-type modes, a general class of sets of nonorthonormal Gaussian-type modes is introduced, along with their associated bi-orthonormal partner sets. The conditions between these two bi-orthonormal sets of modes have been derived, expressed in terms of their generating functions, and the relations with W¨unsche’s Hermite two-dimensional functions and the two-variable Hermite polynomials have been established. A closed-form expression for Gaussiantype modes is derived from their derivative and recurrence relations, which result from the generating function. It is shown that the evolution of non-orthonormal Gaussiantype modes under linear canonical transformations can be described by the same mechanism as used for the evolution of orthonormal Hermite-Gaussian-type modes, when, simultaneously, the associated bio-orthonormal modes are taken into account.
Originele taal-2Engels
TitelProceedings of the 16th ProRISC, Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2005) 17 - 18 November 2006, Veldhoven, the Netherlands
Plaats van productieUtrecht, the Netherlands
UitgeverijTechnology Foundation
Pagina's589-593
ISBN van geprinte versie90-73461-50-2
StatusGepubliceerd - 2005
Evenement2005 Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2005) - Veldhoven, Nederland
Duur: 17 nov 200518 nov 2005
Congresnummer: 16

Congres

Congres2005 Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2005)
Verkorte titelProRISC 2005
LandNederland
StadVeldhoven
Periode17/11/0518/11/05
AnderProRISC 2005, Veldhoven, the Netherlands

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Citeer dit

Bastiaans, M. J., & Alieva, T. (2005). A general class of bi-orthonormal sets of Gaussian-type modes. In Proceedings of the 16th ProRISC, Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2005) 17 - 18 November 2006, Veldhoven, the Netherlands (blz. 589-593). Utrecht, the Netherlands: Technology Foundation.