Localized Dispersive States in Nonlinear Coupled Mode Equations for Light Propagation in Fiber Bragg Gratings.

Dispersion effects induce new instabilities and dynamics in the weakly nonlinear description of light propagation in fiber Bragg gratings. A new family of dispersive localized pulses that propagate with the group velocity is numerically found, and its stability is also analyzed. The unavoidable different asymptotic order of transport and dispersion effects plays a crucial role in the determination of these localized states. These results are also interesting from the point of view of general pattern formation since this asymptotic imbalance is a generic situation in any transport-dominated (i.e., nonzero group velocity) spatially extended system

Coupled mode theory for on-channel nonlinear microcavities

We consider a nonlinear microcavity separating a waveguide channel into two parts so as the coupling between them is possible only due to the resonant properties of the microcavity. We provide a rigorous derivation of the equations used in the phenomenological coupled mode theory for such systems. This allows us to find the explicit formulas for all fitting parameters such as decay rates, coupling coefficients and characteristic intensities in terms of the mode profiles. The advantages of using the semi-analytical approach are discussed, and the accuracy of the results is compared with the strictly numerical methods. A particular attention is paid to multilayered structures since they represent the simplest realization of on-channel microcavities.Comment: 21 pages, 4 figure