The effective index of optical waveguide based on finite difference beam propagation method

In this paper a new method based on Finite Difference Beam Propagation Method (FD-BPM) is presented to find the effective index of different kinds of optical waveguides. In the first step, we use FD-BPM for the general optical waveguide (Fig.]) which is excited with a Gaussian pulse. In the second step, we trace the propagation of the wave along the waveguide. After some steps, the wave could be decomposed into a set of modes. For each of these modes we compute its energy in all 9 regions of space in order to distinguish the modes that could be propagated. Finally we sweep the frequency and for each frequency we compute the effective index for each mode by using the stored energy in each region. In this way the relation between the stored energy and the effective index is formulated. To verify the developed method and its applicability, the derived equations and computed numerical results are compared with published results available for rib-waveguide and ridged waveguide. A good agreement in each case is found.