Bifurcations and stability of gap solitons in periodic potentials
- Department of Mathematics, McMaster University, Hamilton, Ontario, L8S 4K1 (Canada)
- Nonlinear Physics Group and Centre for Ultra-high Bandwidth Devices for Optical Systems (CUDOS), Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200 (Australia)
We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear Schroedinger equation with a sinusoidal potential, such as photonic crystals, waveguide arrays, optically-induced photonic lattices, and Bose-Einstein condensates loaded onto an optical lattice. We study bifurcations of gap solitons from the band edges of the Floquet-Bloch spectrum, and show that gap solitons can appear near all lower or upper band edges of the spectrum, for focusing or defocusing nonlinearity, respectively. We show that, in general, two types of gap solitons can bifurcate from each band edge, and one of those two is always unstable. A gap soliton corresponding to a given band edge is shown to possess a number of internal modes that bifurcate from all band edges of the same polarity. We demonstrate that stability of gap solitons is determined by location of the internal modes with respect to the spectral bands of the inverted spectrum and, when they overlap, complex eigenvalues give rise to oscillatory instabilities of gap solitons.
- OSTI ID:
- 20636610
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 70, Issue 3; Other Information: DOI: 10.1103/PhysRevE.70.036618; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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