This article presents a method to determine the scattered electromagnetic (EM) fields in the interconnected regions with common metasurface boundaries. This method uses a boundary element method (BEM) formulation of the frequency domain version of Maxwell's equations, which expresses the fields present in a region due to surface currents on the boundaries. Metasurface boundaries are represented in terms of surface susceptibilities which when integrated with the generalized sheet transition conditions (GSTCs) gave rise to an equivalent configuration in terms of electric and magnetic currents. These representations are then naturally incorporated into the BEM methodology. Four examples are presented for EM scattering of a Gaussian beam to illustrate the proposed method. In the first example, a metasurface is excited with a diverging Gaussian beam, and the scattered fields are validated using a semianalytical method. The second example is concerned with a nonuniform metasurface modeling a diffraction grating, whose results were confirmed with a conventional finite-difference frequency-domain (FDFD) method. To illustrate the flexibility of the method, the third example uses a metasurface that implements a polarization rotator. Finally, a fully absorbing metasurface is simulated and compared to the FDFD simulations to emphasize the advantages of BEM method.

Boundary element method (BEM), electromagnetic metasurfaces, field scattering, generalized sheet transition conditions (GSTCs), method of moments (MOMs)
IEEE Transactions on Antennas and Propagation
Department of Electronics

Stewart, S.A. (Scott A.), Moslemi-Tabrizi, S. (Sanam), Smy, T, & Gupta, S. (2019). Scattering Field Solutions of Metasurfaces Based on the Boundary Element Method for Interconnected Regions in 2-D. IEEE Transactions on Antennas and Propagation, 67(12), 7487–7495. doi:10.1109/TAP.2019.2935131