MATRIX-BASED ANALYTICAL MODEL OF CRITICAL COUPLING LENGTH OF TITANIUMIN-DIFFUSED INTEGRATED-OPTIC DIRECTIONAL COUPLER ON LITHIUM-NIOBATE SUBSTRATE

The critical coupling length L-c is the most important design paramete r of an integrated-optic directional coupler, which is the basic build ing block of a variety of optical integrated circuits. The existing me thods of estimating L-c of a Ti in-diffused waveguide directional coup ler on LiNbO3 substrate are based on the beam propagation method (BPM) which requires huge computing time. A considerably simpler and comput ationally faster analytical method involving only multiplication of 2 x 2 matrices with no iterations is described in this article. A stairc ase type step-index profile is generated from the one-dimensional effe ctive index profile in the lateral direction by partitioning the latte r into a large number of thin sections of different refractive indices . The overall transfer matrix of the step-index; layered structure so obtained may be computed by the progressive multiplication of individu al transfer matrices (2 x 2) relating the field components in adjacent layers. Hence the wave amplitude in any layer may be computed as a fu nction of the input wave amplitude for different angles of incidence. This method has been successfully employed to compute the propagation constants for symmetric and asymmetric guided modes in the coupled reg ion of the directional coupler and hence compute the coupling length. The values of L-c computed for a variety of devices agree closely with the published experimental results reported by several research group s. The computer program implementing tile model runs reasonably fast i n an ordinary PC and is versatile enough to consider arbitrary wavegui de dimensions. Ti film thickness, and diffusion parameters for any wav elength of input light and for both transverse electric and transverse magnetic polarizations.