Non-lorentzian spectral lineshapes near a HOPF bifurcation

J. P. Gleeson; F. O'Doherty

doi:10.1137/040615146

Non-lorentzian spectral lineshapes near a HOPF bifurcation

J. P. Gleeson, F. O'Doherty

University College Cork

Research output: Contribution to journal › Article › peer-review

Abstract

The effects of additive white noise upon the dynamics of a system described by its Hopf normal form are investigated, with particular reference to the well-known model of a detuned single-mode laser. The power spectrum corresponding to the laser amplitude is determined by finite-difference solution of a partial differential equation, and analytical formulas are determined in the asymptotic limits of large parameters. The effect of the amplitude-phase coupling parameter in generating non-Lorentzian lineshapes is highlighted, and the regions of parameter space where accurate first-eigenvalue approximations of the Fokker-Planck equation exist are indicated.

Original language	English
Pages (from-to)	1669-1688
Number of pages	20
Journal	SIAM Journal on Applied Mathematics
Volume	66
Issue number	5
DOIs	https://doi.org/10.1137/040615146
Publication status	Published - 2006
Externally published	Yes

Keywords

Fokker-Planck equation
Hopf normal form
Oscillators
Semiconductor lasers
Stochastic differential equations
White noise

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10.1137/040615146

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title = "Non-lorentzian spectral lineshapes near a HOPF bifurcation",

abstract = "The effects of additive white noise upon the dynamics of a system described by its Hopf normal form are investigated, with particular reference to the well-known model of a detuned single-mode laser. The power spectrum corresponding to the laser amplitude is determined by finite-difference solution of a partial differential equation, and analytical formulas are determined in the asymptotic limits of large parameters. The effect of the amplitude-phase coupling parameter in generating non-Lorentzian lineshapes is highlighted, and the regions of parameter space where accurate first-eigenvalue approximations of the Fokker-Planck equation exist are indicated.",

keywords = "Fokker-Planck equation, Hopf normal form, Oscillators, Semiconductor lasers, Stochastic differential equations, White noise",

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AU - Gleeson, J. P.

AU - O'Doherty, F.

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N2 - The effects of additive white noise upon the dynamics of a system described by its Hopf normal form are investigated, with particular reference to the well-known model of a detuned single-mode laser. The power spectrum corresponding to the laser amplitude is determined by finite-difference solution of a partial differential equation, and analytical formulas are determined in the asymptotic limits of large parameters. The effect of the amplitude-phase coupling parameter in generating non-Lorentzian lineshapes is highlighted, and the regions of parameter space where accurate first-eigenvalue approximations of the Fokker-Planck equation exist are indicated.

AB - The effects of additive white noise upon the dynamics of a system described by its Hopf normal form are investigated, with particular reference to the well-known model of a detuned single-mode laser. The power spectrum corresponding to the laser amplitude is determined by finite-difference solution of a partial differential equation, and analytical formulas are determined in the asymptotic limits of large parameters. The effect of the amplitude-phase coupling parameter in generating non-Lorentzian lineshapes is highlighted, and the regions of parameter space where accurate first-eigenvalue approximations of the Fokker-Planck equation exist are indicated.

KW - Fokker-Planck equation

KW - Hopf normal form

KW - Oscillators

KW - Semiconductor lasers

KW - Stochastic differential equations

KW - White noise

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EP - 1688

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 5

ER -

Non-lorentzian spectral lineshapes near a HOPF bifurcation

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Keywords

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