A finite difference BPM analysis of bent dielectric waveguides

A new version of the scalar TE wave equation is introduced, one that is particularly useful in bent waveguide analysis. The slowly varying envelope equation in cylindrical coordinates for the field amplitude E is finite-differenced, with no other approximations made to it. It will be shown that this version of the equation has several advantages over other forms and gives good results for the power loss rates even at radii ⩽100 μm, as well as being useful for the study of curved structures with varying radii of curvature. Evidence is provided to show that the loss rates calculated from this equation using the two dimensional finite difference beam propagation method compare favorably with other numerical and analytical results found in the literature. Special care must be taken when applying transparent boundary conditions as the curvature increases