Abstract

Among the various computional methods, the finite-difference method (FDM) has been frequently applied to several kinds of structures due to its easy application and simple manupulation. Recently, semi-vectorial FDM was introduced for the rib waveguide, characterized by piecewise constant refractive index distribution with uniform grid size.[1] In this paper, we present a versatile FDM for quasi-TM modes, which can handle the boundary conditions across abrupt index-changes. This method is flexible in that it uses the nonuniform discretization (Fig.1), which allows us to slice the grid finely in the region of the waveguide and sparcely in the region outside. It also allows us to extend the boundary of the metal box to arbitrary points yet using a limited number of grid lines. We can place grid lines at the positions of index discontinuity flexibly. By setting up grid lines and corresponding cell structure in a judicious way, we can reduce the redundant computer calculations and obtain the desirable accuracy with less memory size as little as 1/4 of that needed otherwise and, therefore, calculation amount is by far reduced. Increasing the number of grid lines ,of course, leads to more accurate solutions. Using this nonuniform FDM, we model the low-loss, minimum-mode-size Ti:LiNbO₃ diffused channel waveguides fabricated in our laboratory. [2] The waveguides were fabricated on the z_ surface of optical grade LiNbO₃ wafers and characterized at 1.3 μm. The smallest quasi-TM mode size (1/e intensity full width of 3.9 μm and full depth of 2.8 μm) was obtained for waveguides fabricated at 1025°C for 6 hours with Ti thickness of 800° A and Ti strip width of 4 μm.

© 1989 Optical Society of America