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

Gomila, Damià and Oppo, Gian-Luca (2005) Coupled-mode theory for photonic band-gap inhibition of spatial instabilities. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 72 (1). 016614-1. ISSN 1063-651X

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    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.

    Item type: Article
    ID code: 6172
    Keywords: optical systems, optics, physics, photonic crystals, band gap, Optics. Light
    Subjects: Science > Physics > Optics. Light
    Department: Faculty of Science > Physics
    Related URLs:
    Depositing user: Miss Darcy Spiller
    Date Deposited: 22 May 2008
    Last modified: 19 Jul 2013 03:48
    URI: http://strathprints.strath.ac.uk/id/eprint/6172

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