Nonlinear dissipative systems, particularly optical dissipative solitons are well described by complex Ginzburg-Landau equation. Solutions of two- and three-dimensional complex cubic-quintic Ginzburg-Landau equation assuming exponential dependence on propagation parameter are studied. Approximate analytical stationary solutions of cubic-quintic Ginzburg-Landau equation are found by solving systems of ordinary differential equations. We are solving two-point boundary problems using adapted shooting method. Stable and unstable branches of the bifurcation diagram are identified using linear stability analysis. In this way we established conditions for generation and propagation of stable dissipative solitons in two and three dimensions. These results are in agreement with numerical simulation of cubic-quintic Ginzburg-Landau equation and the recently established approach based on variational method generalized to dissipative systems and therein established stability criterion.
We study all-evanescent eigenmodes of a one-dimensional infinite periodic structure with alternating left-handed and right-handed materials that propagate perpendicularly to the surface or guided eigenmodes. Investigation of dispersion properties of such Bloch modes is shown to be crucial for understanding of an efficient radiation energy transport across the periodic multilayer structure. Frequency pass bands and gaps are found as a function of the two orthogonal wave vectors: the Bloch wave vector k_B and the surface wave vector k_S. We demonstrate that pass bands of both TE- and TM-polarizations can exist and, under certain conditions, may overlap.
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