Schmidt, F.F.Schmidt2022-03-032022-03-031993https://publica.fraunhofer.de/handle/publica/18390410.1109/50.241932An 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.enapproximation theoryfinite element analysisintegrated opticsoptical waveguide theoryadaptive approachnumerical solutionfresnel's wave equationwave propagationintegrated optics devicesfresnel's approximationexact wave equationmaxwell's equationsapproximationlongitudinal directionstep-size controlstationary subproblemtransversal field distributionadaptive finite-element methodwaveguide tapers621535journal article