Windowed Green Function Method for Nonuniform Open-Waveguide Problems

TL;DR

The paper introduces a novel Windowed Green Function method that efficiently solves wave propagation problems in open dielectric waveguides, handling complex geometries and infinite structures without absorbing boundaries.

Contribution

A new WGF approach that improves waveguide simulations by eliminating the need for absorbing boundaries and seamlessly managing complex, infinite, and open-waveguide geometries.

Findings

Errors decrease faster than any negative power of window size

Handles infinite dielectric structures without absorbing boundaries

Demonstrated on various 2D waveguide problems

Abstract

This contribution presents a novel Windowed Green Function (WGF) method for the solution of problems of wave propagation, scattering and radiation for structures which include open (dielectric) waveguides, waveguide junctions, as well as launching and/or termination sites and other nonuniformities. Based on use of a "slow-rise" smooth-windowing technique in conjunction with free-space Green functions and associated integral representations, the proposed approach produces numerical solutions with errors that decrease faster than any negative power of the window size. The proposed methodology bypasses some of the most significant challenges associated with waveguide simulation. In particular the WGF approach handles spatially-infinite dielectric waveguide structures without recourse to absorbing boundary conditions, it facilitates proper treatment of complex geometries, and it seamlessly incorporates the open-waveguide character and associated radiation conditions inherent in the problem under consideration. The overall WGF approach is demonstrated in this paper by means of a variety of numerical results for two-dimensional open-waveguide termination, launching and junction problems.