RIGOROUS FINITE-DIFFERENCE ANALYSIS OF COUPLED CHANNEL WAVE-GUIDES WITH ARBITRARILY VARYING INDEX PROFILE

A rigorous finite-difference formulation is presented for the hybrid-mode analysis of coupled diffused dielectric channel waveguides. The method includes the two-dimensional continuous index profile variations directly in the finite-difference form of coupled equations and, hence, avoids the shortcomings inherent in usual staircase approximations. The formulation in terms of the wave equation for the transverse components of the magnetic field leads to an eigenvalue problem where the nonphysical, spurious modes do not appear. Moreover, the analysis includes the complete set of hybrid-modes, takes mode-conversion effects and complex waves, if they exist, into account, and allows the calculation of dielectric channel waveguides with large index difference levels. Dispersion characteristic examples are calculated for coupled structures suitable for optical integrated circuits, such as channel waveguides with refractive-index variations of stepped, linear, Gaussian, exponential and complementary error function profile. The theory is verified by comparison with accurate results available from other methods.