  An Integral Equation (IE) based electromagnetic field solver using
metasurface susceptibility tensors is proposed and validated using variety of
numerical examples in 2D. The proposed method solves for fields generated by
the metasurface which are represented as spatial discontinuities satisfying the
Generalized Sheet Transition Conditions (GSTCs), and described using tensorial
surface susceptibility densities, $\bar{\bar{\chi}}$. For the first time, the
complete tensorial representation of susceptibilities is incorporated in this
integrated IE-GSTC framework, where the normal surface polarizabilities and
their spatial derivatives along the metasurface are rigorously taken into
account. The proposed field equation formulation further utilizes a local
co-ordinate system which enables modeling metasurfaces with arbitrary
orientations and geometries. The proposed 2D BEM-GSTC framework is successfully
tested using variety of examples including infinite and finite sized
metasurfaces, periodic metasurfaces and complex shaped structures, showing
comparisons with both analytical results and a commercial full-wave solver. It
is shown that the zero-thickness sheet model with complete tensorial
susceptibilities can very accurately reproduce the macroscopic fields,
accounting for their angular field scattering response and the edge diffraction
effects in finite-sized surfaces.
