Master equation for misaligned cavities

Research output: Contribution to journalArticle

Abstract

Misaligned cavities can be described by a 3 x 3 extension of the well-known ABCD matrix approach to aligned cavities. There is a corresponding Huygens integral (HI) formulation for the evolution of the field within such a cavity. We derive a differential 'master' equation (ME) formulation which yields identical eigenmodes and eigenvalues to this HI. This ME is fully equivalent to the HI for linear problems, while providing a more convenient route to the analysis of nonlinear behaviour in such cavities.

LanguageEnglish
Pages2005-2010
Number of pages6
JournalJournal of Modern Optics
Volume53
Issue number14
DOIs
Publication statusPublished - 20 Sep 2006

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cavities
formulations
differential equations
eigenvalues
routes
matrices

Keywords

  • generalized beam matrices
  • mode-locking
  • propagation

Cite this

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title = "Master equation for misaligned cavities",
abstract = "Misaligned cavities can be described by a 3 x 3 extension of the well-known ABCD matrix approach to aligned cavities. There is a corresponding Huygens integral (HI) formulation for the evolution of the field within such a cavity. We derive a differential 'master' equation (ME) formulation which yields identical eigenmodes and eigenvalues to this HI. This ME is fully equivalent to the HI for linear problems, while providing a more convenient route to the analysis of nonlinear behaviour in such cavities.",
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Master equation for misaligned cavities. / Firth, William J.; Yao, Alison M.

In: Journal of Modern Optics, Vol. 53, No. 14, 20.09.2006, p. 2005-2010.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Firth, William J.

AU - Yao, Alison M.

PY - 2006/9/20

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N2 - Misaligned cavities can be described by a 3 x 3 extension of the well-known ABCD matrix approach to aligned cavities. There is a corresponding Huygens integral (HI) formulation for the evolution of the field within such a cavity. We derive a differential 'master' equation (ME) formulation which yields identical eigenmodes and eigenvalues to this HI. This ME is fully equivalent to the HI for linear problems, while providing a more convenient route to the analysis of nonlinear behaviour in such cavities.

AB - Misaligned cavities can be described by a 3 x 3 extension of the well-known ABCD matrix approach to aligned cavities. There is a corresponding Huygens integral (HI) formulation for the evolution of the field within such a cavity. We derive a differential 'master' equation (ME) formulation which yields identical eigenmodes and eigenvalues to this HI. This ME is fully equivalent to the HI for linear problems, while providing a more convenient route to the analysis of nonlinear behaviour in such cavities.

KW - generalized beam matrices

KW - mode-locking

KW - propagation

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M3 - Article

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EP - 2010

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