Abstract

Periodical optical waveguides have been the subject of many theoretical and experimental studies, both in the linear regime (since they can be used to realize optical wavelength filters [1, 2]) and in the nonlinear regime ( in which the counter-balancing of group velocity dispersion, due to the periodic variation of the linear refractive index, and the effect of nonlinearity, leads to the so called “gap-solitons” [3, 4]). In the study of periodic optical waveguides it is generally assumed that the functions describing the two counterpropagating modes can be separated into the product of two independent components. One (say F(x,y)) for the dimensions where the guiding effect provided by linear variation of the refactive index is supposed to be unaffected by nonlinearity and determined as a solution of a linear problem; the other (say q_1,2(z, t)) describes the time evolution of the envelope in the direction where the guiding effect is given only by the nonlinearity. In doing so all the influence of the nonlinearity on the mode shape F(x,y) is lost and the approach may thus hide some important features of the governing equation. We study here counterpropagating waves in a periodic slab waveguide, without applying the separation of variables described above: this leads to discover important features of two dimensional gap solitons, which could be exploited for all optical storage of information. In pursuing this goal we make use of a variational method [5] and we then confirm the validity of our analytical results through numerical integration of the governing equations.

© 1995 Optical Society of America