AN ADAPTIVE APPROACH TO THE NUMERICAL-SOLUTION OF FRESNELS WAVE-EQUATION

An adaptive approach to the numerical solution of the wave propagation in integrated optics devices with ID cross sections is described. First, Fresnel's approximation of the exact wave equation resulting from Maxwell's equations is considered. A criterion to estimate the validity of this approximation is derived. First, discretization in longitudinal direction with stepsize control leads to a stationary subproblem for the transversal field distribution, which is then handled by an adaptive finite-element method. Thus, full adaptivity of the algorithm is realized. The numerical examples are concentrated on waveguide tapers.