An adaptive approach to the numerical solution of Fresnel's wave equation

An adaptive approach to the numerical solution of the wave propagation in integrated optics devices with 1-D cross sections is described. 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. Discretization in longitudinal direction with step-size 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 focus on waveguide tapers.