Modes computation in arbitrarily shaped waveguides by a transformation optics approach

This article applies a new method to analyze modes in empty waveguides having perfectly conducting walls and a rather generic cross-section. The method is based on a coordinate transformation that maps the generic profile of the waveguide cross-section to a circular waveguide (CW) filled with an anisotropic material. Modes in this latter waveguide can be represented as a series over the corresponding free-space CW modes. This representation is particularly useful if used as a modal expansion over the port of a 2.5D or 3D device treated with a transformation optics approach. The method is particularly efficient when the waveguide is “similar” to a CW. Applications are shown to the analysis of some waveguides of arbitrary cross-section with a view on practical applications.