Coupled-mode theory for photonic band-gap inhibition of spatial instabilities

Damià Gomila, Gian-Luca Oppo

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24 Citations (Scopus)

Abstract

We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean-field models for singly and doubly degenerate optical parametric oscillators. Analytical expressions for the new (higher) modulational thresholds and the size of the "band gap" as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory. Then, by means of a nonlinear analysis, we derive amplitude equations for the unstable modes and find the stationary solutions above threshold. The form of the unstable mode is different in the lower and upper parts of the band gap. In each part there is bistability between two spatially shifted patterns. In large systems stable wall defects between the two solutions are formed and we provide analytical expressions for their shape. The analytical results are favorably compared with results obtained from the full system equations. Inhibition of pattern formation can be used to spatially control signal generation in the transverse plane.
LanguageEnglish
Article number016614
Number of pages8
JournalPhysical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume72
Issue number1
DOIs
Publication statusPublished - 18 Jul 2005

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Coupled-mode Theory
Photonic Band Gap
coupled modes
photonics
Band Gap
Pattern Formation
Photonic Crystal
Unstable
Optical Parametric Oscillator
Amplitude Equations
thresholds
Mean-field Model
Bistability
Signal Control
parametric amplifiers
Stationary Solutions
Nonlinear Analysis
Optical System
crystals
Transverse

Keywords

  • optical systems
  • optics
  • physics
  • photonic crystals
  • band gap

Cite this

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title = "Coupled-mode theory for photonic band-gap inhibition of spatial instabilities",
abstract = "We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean-field models for singly and doubly degenerate optical parametric oscillators. Analytical expressions for the new (higher) modulational thresholds and the size of the {"}band gap{"} as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory. Then, by means of a nonlinear analysis, we derive amplitude equations for the unstable modes and find the stationary solutions above threshold. The form of the unstable mode is different in the lower and upper parts of the band gap. In each part there is bistability between two spatially shifted patterns. In large systems stable wall defects between the two solutions are formed and we provide analytical expressions for their shape. The analytical results are favorably compared with results obtained from the full system equations. Inhibition of pattern formation can be used to spatially control signal generation in the transverse plane.",
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AB - We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean-field models for singly and doubly degenerate optical parametric oscillators. Analytical expressions for the new (higher) modulational thresholds and the size of the "band gap" as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory. Then, by means of a nonlinear analysis, we derive amplitude equations for the unstable modes and find the stationary solutions above threshold. The form of the unstable mode is different in the lower and upper parts of the band gap. In each part there is bistability between two spatially shifted patterns. In large systems stable wall defects between the two solutions are formed and we provide analytical expressions for their shape. The analytical results are favorably compared with results obtained from the full system equations. Inhibition of pattern formation can be used to spatially control signal generation in the transverse plane.

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