An assessment of finite differences techniques for planar slab dielectric optical waveguide.

摘要

In developing a procedure of fabricating a planar optical waveguide, three characteristic elements must be considered: (1) effective refractive index values, (2) the thickness of the guided region, (3) the precisely correct active profile shape.; The most important purpose of this thesis is to describe methods for determining parameters for planar step-index optical waveguides and graded-index optical waveguides having Gaussian and inverse hyperbolic cosine squared profiles. Therefore, this thesis describes a computer program modified for this project and originally developed as a thesis project by Timothy G. Merse at the University of Louisville in 1991. This thesis describes the development of a Finite Difference Method (FDM) algorithm to find a solution for planar slab waveguide parameters.; The program entitled “program optics” uses the inverse WKB method (Wentzel-Kramers-Brillouim method) to calculate graded-index waveguide parameters. Program Optics also applies the TRC (Transverse Resonance Condition) to exactly calculate the optical parameters for step-index waveguides.; Combining two numerical techniques, the finite-difference method and the beam propagation method (FD-BPM) algorithm, allows us to evaluate eigenvalues, effective index of refraction for the mth modes, directly from the Helmholtz equation for both graded-index and step-index waveguides. Electric field distribution can also be obtained using the eigenvalues obtained from solving the eigenvalue problem.