A Comparison of Commonly-used Trial Functions in the Variational Analysis of Ti:LiNbO3 Channel Waveguides

Abstract

Two common trial functions used in the variational method to solve the waveguiding modes of Ti:LiNbO 3 channel waveguides are compared in this paper. The first one has four parameters and the other has just two. The respective modal-field profiles described by them, as well as the respective fiber-to-waveguide coupling efficiencies estimated by these models, are rather different. We propose a self-consistent concept to examine the qualities of the trial fields and then show that the two-parameter model is better.

A Novel Method of Assessing Trial Modes of Dielectric Rectangular Waveguides

“…And the mode parameters are sought by the SOS algorithm [10][11][12]. The authors had shown that it is an efficient tool of optimizing the multivariable functions and solving the variational equations.…”

“…We had proposed a comprehensible self-consistent concept to do with it [12]. The concept and its usage are briefly described as follows.…”

“…Conventionally, the accuracy and validity of the variational analysis, depend on the trial functions, are checked by comparing the stationary solutions with the experimental data or other numerical results. In this work, we employ a simple self-consistent concept [12] instead of the conventional methods to examine the fitness of two trial modes of the dielectric rectangular waveguides. The concept and its usage are quite comprehensible.…”