Planar nonuniform and spatially dispersive metasurface as a substitute for optical system

We propose a method to obtain the tangential surface susceptibility of a single nonuniform and spatially dispersive metasurface achieving the same optical work as a complex optical system based on the generalized sheet transition conditions (GSTCs). To do so, a windowed Fourier transform is applied to ensure the realization of a design ray mapping condition and introduces the necessity of a locally periodic approximation. Then, we emulated and compared the optical performances of an analytically designed aplanatic singlet to the computed single metasurface. The ray mapping condition of the reference design composed of two local metasurfaces is conserved and the on-axis optical performances of the single aplanatic metasurface are the same as the reference singlet. The off-axis performances are slightly different from the reference but expected from different optical systems.