Propagation of Light Beams in a Focnsing Optical Medinm with a System of Parallel Wavegnides

摘要

Studies of propagation of nonlinear optical beams in waveguides of various configurations (parallel optical waveguides and layered optical media) have recently become an object of increased interest. Theoretical description of real waveguides is a sufficiently complicated problem. We study a system of weakly coupled plane-parallel waveguides of small thickness in a nonlinear optical medium by modeling the variation of the linear refractive index in waveguides with respect to the surrounding medium by 8-functions. Then analytical calculations are simplified, and the original problem is reduced to a study of a finite-dimensional dynamical system with known parameters that are functions of the parameters of the original optical system. The amplitude (weakly varying in space) of a monochromatic electromagnetic wave of the form E = E(z , x) exp(iΩt - iKx), which propagates in the x-direction in a nonlinear optical medium with a system of plane-parallel lightguides normal to the z-axis is approximately described (in dimensionless variables) by the nonlinear evolution equation