This paper presents a fast and accurate quasi-analytic model for studying optical field propagation in weakly guiding dielectric structures. The proposed efficient and versatile computational scheme is obtained by merging the Hermite-Gauss (HG) total field expansion with the numerical collocation method and is particularly suited for longitudinally nonuniform structures. By means of a quasilinearization scheme, the same procedure has also been successfully applied to the analysis of field propagation in Kerr-nonlinear media. The latter achievement gives an indication of the great potentialities offered by this straightforward method. Several examples are discussed in the paper and in all cases the results computed by the proposed method favorably compare with those from alternative methods.
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