Abstract
A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin’s method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In addition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach.
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Xiao, J., Sun, X. & Zhang, M. Three-dimensional beam propagation method based on the variable transformed Galerkin’s method. Sci China Ser F 47, 34–43 (2004). https://doi.org/10.1360/02yf0169
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DOI: https://doi.org/10.1360/02yf0169