An improved semivectorial beam propagation method using a finite-element scheme

A three-dimensional semivectorial finite-element beam propagation method, which treats only a linearly polarized transversal electric field and uses the Pade approximation, is described. The electric field should satisfy the conditions that either E/sub t/ or n/sup 2/E/sub t/ is continuous whether E/sub t/ is parallel to or perpendicular to the refractive-index discontinuous interface in an optical waveguide. The matrix-equation treated in this analysis is asymmetric, unlike the symmetric matrix-equation treated in the scalar analysis. Thus, this analysis needs twice the computer memory, but the number of calculation steps for the matrix elements is the same and the computing time is similar to that of the scalar analysis. This allows an accurate and efficient analysis of the polarization dependence of lightwave propagation in arbitrary step-index optical waveguides.