Fundamental limits of ultrathin metasurfaces

Abstract

We present a set of universal relations which relate the local transmission, reflection, and polarization conversion coefficients of a general class of non-magnetic passive ultrathin metasurfaces. We show that these relations are a result of equal forward and backward scattering by single layer ultrathin metasurfaces, and they lead to confinement of the transmission, reflection, and polarization conversion coefficients to limited regions of the complex plane. Using these relations, we investigate the effect of the presence of a substrate, and show that the maximum polarization conversion efficiency for a transmissive metasurface decreases as the refractive index contrast between the substrate and cladding layer increases. Furthermore, we demonstrate that a single layer reflective metasurface can achieve full 2π phase shift coverage without altering the polarization if it is illuminated from the higher refractive index material. We also discuss two approaches for achieving asymmetric scattering from metasurfaces, and realizing metasurfaces which overcome the performance limitations of single layer ultrathin metasurfaces.

Figure 1

Schematic illustrations of (a) a metasurface with gradually varying scatterers, and (b) a periodic metasurface. (c) Cross section view of the periodic metasurface shown in (b). A normally incident plane wave is impinging on the metasurface. The transmitted and reflected plane waves, and the polarization converted plane waves are also shown. (d) Illustration of the equivalent volume current density that has replaced the periodic metasurface. E_i, E_r0, and E_t0 are the electric fields of the incident, reflected and transmitted plane waves for a bare interface, respectively. The electric field of the light scattered by the metasurface is labeled by E_s|| for the part with the same polarization as E_r0 and E_t0, and by E_s⊥ for the part with polarization orthogonal to the polarizations of E_r0 and E_t0.

Figure 2. Accessible regions of the complex plane for the transmission and reflection coefficients of a metasurface for n₂ > n1.

Figure 3

(a) Regions of the complex plane admissible for the polarization conversion coefficients t_⊥ and r_⊥. (b) Maximum polarization conversion efficiency for a transmissive and reflective ultrathin metasurface as a function of the ratio of the refractive index of the substrate to that of the cladding.