Unconditionally stable procedure to propagate beams through optical waveguides using the collocation method.
The collocation method developed earlier for propagating beams through optical waveguides is unstable for moderately large values of the extrapolation interval. A new procedure is presented to solve the matrix propagation equation in a method that is unconditionally stable for arbitrarily large extrapolation intervals. The new method uses the Fresnel approximation. The numerical performance of the new formulation is compared with that of the original method and with the propagating-beam method.
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Taneja