ANALYSIS OF VECTORIAL MODE FIELDS IN OPTICAL WAVE-GUIDES BY A NEW FINITE-DIFFERENCE METHOD

An important class of dielectric optical waveguides has stepped refrac tive index profiles. For these waveguides we present a new finite-diff erence approach free of spurious modes. The coupled difference equatio ns are formulated in terms of the transverse magnetic field components H(x) and H(y). We show how the boundary conditions can be formulated and included in the finite difference scheme to obtain a unique set of equations. For a step-index fiber a comparison of the numerical resul ts with the analytical solution shows that the relative error in the p ropagation constant is as low as 4.4 x 10(-7) for an index difference of 7.3%. For a rib waveguide, we compare our results with previously p ublished data based on other methods. Field plots of the dominant and the weak transverse field components of the magnetic field for the fun damental mode of a buried rib waveguide are also given.