Matrix-Based Analytical Model of Critical Coupling Length of Titanium In-Diffused Integrated-Optic Directional Coupler on Lithium Niobate Substrate

The critical coupling length Lc is the most important design parameter of an integrated-optic directional coupler, which is the basic building block of a variety of optical integrated circuits. The existing methods of estimating Lc of a Ti in-diffused waveguide directional coupler on LiNbO3 substrate are based on the beam propaga tion method (BPM), which requires huge computing time. A considerably simpler and computationally faster analytical method involving only multiplication of 2 x 2 matrices with no iterations is described in this article. A staircase type step-index profile is generated from the one-dimensional effective index profile in the lateral direction by partitioning the latter 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 individual transfer matrices (2 x 2) relating the field components in adjacent layers. Hence the wave amplitude in any layer may be computed as a function 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 region of the directional coupler and hence compute the coupling length. The values of Lc computed for a variety of devices agree closely with the published experimental results reported by several research groups. The computer program implementing the model runs reasonably fast in an ordinary PC and is versatile enough to consider arbitrary waveguide dimensions. Ti film thickness, and diffusion parameters for any wavelength of input light and for both transverse electric and transverse magnetic polarizations.