Rapid 3-D electromagnetic simulation of quasi-periodic structures

We describe a new 3-D electromagnetic simulation technique capable of fast, accurate modeling of complex cav- ity/waveguide structures. The method subdivides the structure into sections that can be analyzed independently, using 3-D finite element modeling, then reassembled to compute a reduced-order matrix representation of Maxwell's equations. Eigensolutions of the reduced order matrix equations correspond to eigenmodes of the complete 3-D structure, but total solution time can be orders of magnitude less than direct simulation for large complex structures. We demonstrate the method using examples in both 2-D and 3-D, having up to 50 cavities with non-uniform properties. The technique is shown to be numerically robust, even when strong losses exist in the system. Index Terms— Coupled mode analysis, Electromagnetic propa- gation, Mode matching methods, Reduced order systems, Waveg- uides. Ik hk(x), (4) where Vk and Ik are the coefficients of the expansions, and each 3-D basis field ek(x) or hk(x) is non-zero only within a single section and may be discontinuous at the boundary of that section. We write the electric displacement and magnetic induction fields locally using the linear constitutive relations, D(x )= � (x)E(x) (5) B(x )= µ(x)H(x). (6) Using these definitions, we can substitute the field terms and project Maxwell's equations onto the same basis fields to obtain a set of matrix equations in the expansion coefficients,