NUMERICAL-CALCULATIONS OF MODES OF OPTICAL WAVE-GUIDES WITH 2-DIMENSIONAL REFRACTIVE-INDEX PROFILES BY A FIELD CORRECTION METHOD

We describe a numerical method devised to calculate the lower-order modes of optical waveguides with two-dimensional transverse index profiles. This method is based on finite-difference approximation of the scalar wave equation and the minimization of the error in the field shape of a mode. The field correction method can be applied to waveguides with large index steps and generates the mode's scalar propagation constant and its field. To test the field correction method, it is applied to a three-layer optical fibre and the results are compared with exact solutions. The error in the calculations of the modal effective indices is found to be of the order of 10(-6). Example mode calculations are given for fused couplers and rib waveguides.