Complex coupled mode theory electromagnetic mode solver

We present a method for computing waveguide eigenmodes based on complex coupled mode theory (CCMT). This approach generalizes Fourier transform methods by allowing an arbitrary but convenient basis set to be used for the expansion. In the presented approach, one is free to choose an arbitrary basis representation; for example, we show the use of electromagnetic modes of a cylindrical metal waveguide. CCMT-computed modes are compared with modes computed using analytic expressions and results obtained using a finite difference solver. In cases where the basis set is small, the method can efficiently re-compute modes after structural refinements are made, and can efficiently compute dispersion. The parallel nature of the algorithm makes it well suited to a graphics processing unit implementation, as demonstrated here.