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

M.J. Bastiaans, T. Alieva

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

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.
Original languageEnglish
Title of host publicationProceedings of the 16th ProRISC, Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2005) 17 - 18 November 2006, Veldhoven, the Netherlands
Place of PublicationUtrecht, the Netherlands
PublisherTechnology Foundation
Pages589-593
ISBN (Print)90-73461-50-2
Publication statusPublished - 2005
Event2005 Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2005) - Veldhoven, Netherlands
Duration: 17 Nov 200518 Nov 2005
Conference number: 16

Conference

Conference2005 Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2005)
Abbreviated titleProRISC 2005
CountryNetherlands
CityVeldhoven
Period17/11/0518/11/05

Fingerprint Dive into the research topics of 'A general class of bi-orthonormal sets of Gaussian-type modes'. Together they form a unique fingerprint.

  • Cite this

    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 (pp. 589-593). Utrecht, the Netherlands: Technology Foundation.