Analysis of multiple-rib waveguide structures by the discrete-spectral-index method

The discrete-spectral-index (DSI) method is extended to analyse multiple-rib waveguide structures which contain 𝒬 (⩾2) ribs. By constructing general Fourier series for the E-field variation parallel to the semiconductor layers within the waveguide, a simple transcendental equation is derived for the propagation constants of the structure. The modal indices calculated via DSI for symmetric 4-rib and 5-rib waveguide arrays are within 0.001% of those computed by the semivectorial finite difference method; thus the validity of the formulation is established. Together with the ability of the DSI method to calculate overlap integrals directly, the accurate analysis and design of multiple-rib waveguide couplers have thereby been simplified and made more efficient