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

: Schmidt, F.


Journal of Lightwave Technology 11 (1993), Nr.9, S.1425-34
ISSN: 0733-8724
Fraunhofer HHI ()
approximation theory; finite element analysis; integrated optics; optical waveguide theory; adaptive approach; numerical solution; fresnel's wave equation; wave propagation; integrated optics devices; fresnel's approximation; exact wave equation; maxwell's equations; approximation; longitudinal direction; step-size control; stationary subproblem; transversal field distribution; adaptive finite-element method; waveguide tapers

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.