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

AuthorsGomila, Damià ; Oppo, Gian-Luca
KeywordsCoupled mode analysis
Photonic crystals
Pattern formation
Optical parametric oscillators
Nonlinear optics
Issue Date18-Jul-2005
PublisherAmerican Physical Society
CitationPhysical Review E 72, 016614 (2005)
AbstractWe 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.
Description8 pages, 8 figures.-- PACS nrs.: 42.65.Sf, 89.75.Kd, 05.65.+b, 42.70.Qs.-- ArXiv pre-print available: http://arxiv.org/abs/nlin/0503065v1
Publisher version (URL)http://dx.doi.org/10.1103/PhysRevE.72.016614
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