Eigenmode analysis of optical waveguides by an improved finite-difference imaginary-distance beam propagation method

Abstract

The imaginary-distance method is applied to an improved finite-difference beam propagation method (IFD-BPM) based on the generalized Douglas method in order to carry out eigenvalue analysis of an optical waveguide. First, we formulate the IFD-BPM to include the polarization dependence. The imaginary-distance method is explained, in which only the eigenmode is generated from an arbitrary incident field including the eigenmode. Next, in order to verify the effectiveness of the method, eigenmode analysis is carried out for a step index type slab waveguide. We found that by using the IFD-BPM, a much more accurate eigenmode analysis than obtained by the conventional method is possible. Further, in regard to the method for choosing the reference index of refraction, important in the evaluation of the effective index of refraction, a simple method was conceived in which the reference index is successively updated. To provide an application example, the present method and the effective index method were combined for the eigenmode analysis of a three-dimensional multiple quantum well waveguide. The agreement with the results obtained by other methods was excellent. Finally, by using the alternate directional implicit solution method based on the GD method, a graded index fiber is analyzed. From the evaluation of the effective index of refraction, the effectiveness of the method in direct three-dimensional analysis is demonstrated. © 1998 Scripta Technica, Electron Comm Jpn Pt 2, 81(4): 1–9, 1998