Abstract

In this paper the authors will present both numerical and analytical results on the coupled mode equations that describe the evolution of counterpropagating beams in periodic waveguides. These coupled mode equations are a generalization, by an addition of one transverse diffraction term, of the equations that describe wave trains in a fiber filter whose grating is of the order of the wavelength of light. We will first show how the well known gap soliton solutions of the fiber filter extend to the planar waveguide structure. These solutions represent beams that are cw in the transverse direction and have the soliton profile in the direction of propagation. We then numerically show whether transverse modulational instabilities arise. Finally, we numerically study the dynamics of pulses propagating along the waveguide. Here, we compare the dynamics of the coupled mode theory with that of the two dimensional nonlinear Schrodinger equation (2D NLS), which has been suggested as a good limit when the pulses are spatially broad. An interesting feature of this comparison is that for the 2D NLS in the anomalous regime, a collapse in finite time is predicted. We then want to determine if this also happens in the coupled mode analysis.

© 1992 Optical Society of America