Abstract
| Language | English |
|---|---|
| Article number | 016614 |
| Number of pages | 8 |
| Journal | Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
| Volume | 72 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 18 Jul 2005 |
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Keywords
- optical systems
- optics
- physics
- photonic crystals
- band gap
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Coupled-mode theory for photonic band-gap inhibition of spatial instabilities. / Gomila, Damià; Oppo, Gian-Luca.
In: Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics , Vol. 72, No. 1, 016614, 18.07.2005.Research output: Contribution to journal › Article
TY - JOUR
T1 - Coupled-mode theory for photonic band-gap inhibition of spatial instabilities
AU - Gomila, Damià
AU - Oppo, Gian-Luca
PY - 2005/7/18
Y1 - 2005/7/18
N2 - 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.
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.
KW - optical systems
KW - optics
KW - physics
KW - photonic crystals
KW - band gap
UR - http://arxiv.org/PS_cache/nlin/pdf/0503/0503065v1.pdf
U2 - 10.1103/PhysRevE.72.016614
DO - 10.1103/PhysRevE.72.016614
M3 - Article
VL - 72
JO - Physical Review E
T2 - Physical Review E
JF - Physical Review E
SN - 1539-3755
IS - 1
M1 - 016614
ER -