Improvement of metasurface continuity conditions

We analyse the limitations of an ideal zero-thickness sheet model, based on electromagnetic susceptibility tensors, to synthesize a sub-wavelength thick metasurface. First, the ideal zero-thickness model is used to synthesize an absorbing metasurface in terms of its susceptibilities. Then, we show the discrepancies between the response of the zero-thickness metasurface and the response of a sub-wavelength thin slab possessing the same electromagnetic susceptibilities. Finally, we derive higher order continuity conditions to provide a more rigorous treatment of the problem of sub-wavelength thick metasurfaces.