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Modeling of a Metasurface by a Thin Slab of Constant Voluminal Susceptibility

We present a critical perspective of the modeling of a metasurface by a thin slab of constant susceptibility. The key results are the following. 1) The modeling approximating the slab fields as uniform might be somewhat helpful, but has a restricted range of validity, 2) The modeling involving varying slab fields is essentially exact for a monoisotropic metasurface under normal incidence, 3) The modeling of monoisotropic metasurfaces under oblique incidence is much more complex, involving a pair of nonlinear integro-differential equations, 4) The modeling of more complex bianisotropic metasurfaces is certainly very involved to the point that it loses practicality.