Computationally determined existence and stability of transverse structures. I. Periodic optical patterns

G.K. Harkness, W.J. Firth, G.L. Oppo, J.M. McSloy

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

We present a Fourier-transform based, computer-assisted, technique to find the stationary solutions of a model describing a saturable absorber in a driven optical cavity. We illustrate the method by finding essentially exact hexagonal and roll solutions as a function of wave number and of the input pump. The method, which is widely applicable, also allows the determination of the domain of stability (Busse balloon) of the pattern, and sheds light on the mechanisms responsible for any instability. To show the usefulness of our numerical technique, we describe cracking and shrinking patches of patterns in a particular region of parameter space.
LanguageEnglish
Pages046605-1
Number of pages46604
JournalPhysical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume66
Issue number4
DOIs
Publication statusPublished - Oct 2002

Fingerprint

Transverse
Saturable Absorber
Balloon
Cracking
Shrinking
balloons
Numerical Techniques
Stationary Solutions
Hexagon
Pump
Patch
Parameter Space
Fourier transform
absorbers
Cavity
pumps
cavities
Model

Keywords

  • transverse structures
  • optics
  • optical cavity
  • waves
  • photonics

Cite this

@article{3ab054fc3ada47169f6843e43e5499e4,
title = "Computationally determined existence and stability of transverse structures. I. Periodic optical patterns",
abstract = "We present a Fourier-transform based, computer-assisted, technique to find the stationary solutions of a model describing a saturable absorber in a driven optical cavity. We illustrate the method by finding essentially exact hexagonal and roll solutions as a function of wave number and of the input pump. The method, which is widely applicable, also allows the determination of the domain of stability (Busse balloon) of the pattern, and sheds light on the mechanisms responsible for any instability. To show the usefulness of our numerical technique, we describe cracking and shrinking patches of patterns in a particular region of parameter space.",
keywords = "transverse structures, optics, optical cavity, waves, photonics",
author = "G.K. Harkness and W.J. Firth and G.L. Oppo and J.M. McSloy",
year = "2002",
month = "10",
doi = "10.1103/PhysRevE.66.046605",
language = "English",
volume = "66",
pages = "046605--1",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "4",

}

TY - JOUR

T1 - Computationally determined existence and stability of transverse structures. I. Periodic optical patterns

AU - Harkness, G.K.

AU - Firth, W.J.

AU - Oppo, G.L.

AU - McSloy, J.M.

PY - 2002/10

Y1 - 2002/10

N2 - We present a Fourier-transform based, computer-assisted, technique to find the stationary solutions of a model describing a saturable absorber in a driven optical cavity. We illustrate the method by finding essentially exact hexagonal and roll solutions as a function of wave number and of the input pump. The method, which is widely applicable, also allows the determination of the domain of stability (Busse balloon) of the pattern, and sheds light on the mechanisms responsible for any instability. To show the usefulness of our numerical technique, we describe cracking and shrinking patches of patterns in a particular region of parameter space.

AB - We present a Fourier-transform based, computer-assisted, technique to find the stationary solutions of a model describing a saturable absorber in a driven optical cavity. We illustrate the method by finding essentially exact hexagonal and roll solutions as a function of wave number and of the input pump. The method, which is widely applicable, also allows the determination of the domain of stability (Busse balloon) of the pattern, and sheds light on the mechanisms responsible for any instability. To show the usefulness of our numerical technique, we describe cracking and shrinking patches of patterns in a particular region of parameter space.

KW - transverse structures

KW - optics

KW - optical cavity

KW - waves

KW - photonics

UR - http://dx.doi.org/10.1103/PhysRevE.66.046605

U2 - 10.1103/PhysRevE.66.046605

DO - 10.1103/PhysRevE.66.046605

M3 - Article

VL - 66

SP - 46605

EP - 46601

JO - Physical Review E

T2 - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 4

ER -