Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: Analysis

H. Adachihara; D. W. McLaughlin; J. V. Moloney; A. C. Newell

doi:10.1063/1.528136

Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: Analysis

H. Adachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell

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41 Scopus citations

Abstract

The transverse behavior of a laser beam propagating through a bistable optical cavity is investigated analytically and numerically. Numerical experiments that study the (one-dimensional) transverse structure of the steady state profile are described. Mathematical descriptions of (i) an infinite-dimensional map that models the situation, (ii) the solitary waves that represent the transverse steady state structures, (iii) a projection formalism that reduces the infinite-dimensional map to a finite-dimensional one, and (iv) the theoretical analysis of this reduced map are presented in detail. The accuracy of this theoretical analysis is established by comparing its predictions to numerical observations.

Original language	English (US)
Pages (from-to)	63-85
Number of pages	23
Journal	Journal of Mathematical Physics
Volume	29
Issue number	1
DOIs	https://doi.org/10.1063/1.528136
State	Published - 1988

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "The transverse behavior of a laser beam propagating through a bistable optical cavity is investigated analytically and numerically. Numerical experiments that study the (one-dimensional) transverse structure of the steady state profile are described. Mathematical descriptions of (i) an infinite-dimensional map that models the situation, (ii) the solitary waves that represent the transverse steady state structures, (iii) a projection formalism that reduces the infinite-dimensional map to a finite-dimensional one, and (iv) the theoretical analysis of this reduced map are presented in detail. The accuracy of this theoretical analysis is established by comparing its predictions to numerical observations.",

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AB - The transverse behavior of a laser beam propagating through a bistable optical cavity is investigated analytically and numerically. Numerical experiments that study the (one-dimensional) transverse structure of the steady state profile are described. Mathematical descriptions of (i) an infinite-dimensional map that models the situation, (ii) the solitary waves that represent the transverse steady state structures, (iii) a projection formalism that reduces the infinite-dimensional map to a finite-dimensional one, and (iv) the theoretical analysis of this reduced map are presented in detail. The accuracy of this theoretical analysis is established by comparing its predictions to numerical observations.

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Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: Analysis

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