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A methodology for determining the scattered Electromagnetic (EM) fieldspresent for interconnected regions with common metasurface boundaries ispresented. The method uses a Boundary Element Method (BEM) formulation of thefrequency domain version of Maxwell's equations - which expresses the fieldspresent in a region due to surface currents on the boundaries. Metasurfaceboundaries are represented in terms of surface susceptibilities which whenintegrated with the Generalized Sheet Transition Conditions (GSTCs), gave riseto an equivalent configuration in terms of electric and magnetic currents. Sucha representation is then naturally incorporated into the BEM methodology. Twoexamples are presented for EM scattering of a Gaussian beam to illustrate theproposed method. In the first example, metasurface is excited with a divergingGaussian beam, and the scattered fields are validated using a semi-analyticalmethod. Second example concerned with a non-uniform metasurface modeling adiffraction grating, whose results were confirmed with conventional FiniteDifference Frequency Domain (FDFD) method.

Scattering Field Solutions of Metasurfaces based on the Boundary Element Method (BEM) for Interconnected Regions