Transformation Optics Combined With Line-Integrals for Fast and Efficient Mode Matching Analysis of Waveguide Devices

Mode matching method is here applied to waveguide fields calculated in a transformation optics framework. The proposed approach allows to obtain modes in terms of an expansion onto analytical basis functions for a waveguide of general cross-section provided that the contour can be expressed as a single-valued function in polar coordinates. Mode matching surface integrals are then easily reconducted to line-integrals on the contour thanks to the analytic expansion. The effectiveness of the proposed technique is validated against full-wave results from a commercial simulator and measurements available in literature. The proposed method shows a substantial speed-up, especially if the contour contains arcs of circumference, with a comparable accuracy. An in-depth study on the numerical convergence of mode matching and on the accuracy of the line integral formulation is also provided.