Three-dimensional finite difference beam propagation algorithms for photonic devices

Finite difference beam propagation techniques are developed for photonic devices with step-index distributions and arbitrarily large index differences. One technique, the eigenvector expansion method allows large propagation steps along uniform waveguide sections. The second technique, a propagation matrix series expansion method, is particularly suitable for three-dimensional wave propagation simulations. It can easily handle 10⁵ discretization points on personal computers or workstations. The first method employs absorbing boundary conditions while the second utilizes transparent boundary conditions at the edges of the computational windows. The accuracy and applicability of these techniques is demonstrated for several 2-D and 3-D test structures