The Semivectorial Beam Propagation Method

We present details of an efficient semivectorial beam propagation method. In this method, the propagation is performed by solving the finite-difference equation in alternating directions. Different from traditional split-operator beam propagation method, the index term is not separated from spatial differentiations. Since boundary conditions at dielectric interfaces can be satisfied by two orthogonal polarizations individually, the method is semivectorial. The performance can be enhanced by using a nonuniform grid. By modifying the routine, it can also be applied to periodic structures. Numerical results of rib waveguides are presented.