Perfect control of reflection and refraction using spatially dispersive metasurfaces

Nonuniform metasurfaces (electrically thin composite layers) can be used for shaping refracted and reflected electromagnetic waves. However, known design approaches based on the generalized refraction and reflection laws do not allow realization of perfectly performing devices: there are always some parasitic reflections into undesired directions. In this paper we introduce and discuss a general approach to the synthesis of metasurfaces for full control of transmitted and reflected plane waves and show that perfect performance can be realized. The method is based on the use of an equivalent impedance matrix model which connects the tangential field components at the two sides on the metasurface. With this approach we are able to understand what physical properties of the metasurface are needed in order to perfectly realize the desired response. Furthermore, we determine the required polarizabilities of the metasurface unit cells and discuss suitable cell structures. It appears that only spatially dispersive metasurfaces allow realization of perfect refraction and reflection of incident plane waves into arbitrary directions. In particular, ideal refraction is possible only if the metasurface is bianisotropic (weak spatial dispersion), and ideal reflection without polarization transformation requires spatial dispersion with a specific, strongly nonlocal response to the fields.

Figure 1

Illustration of the desired performance of an ideally refracting metasurface.

Figure 2

Equivalent $T$ circuit of a reciprocal metasurface for the considered case of one linear polarization (TE).

Figure 3

Equivalent $T$ circuit of a nonreciprocal transmitarray realization of refractive metasurfaces.

Figure 4

Illustration of the desired performance of an ideally reflecting metasurface. TE incidence is assumed and the metasurface is located in the $yz$ plane.

Figure 5

Comparison between the power efficiencies of the passive metamirror which reflects a single plane wave [surface impedance (41), dashed curve] and the optimized metamirror which minimizes reflections into nondesired directions [surface impedance (43), solid curve] at normal incidence.

Figure 6

The required normalized input impedance $Z_{11}/{\eta }_1$ of the ideal metamirror for ${\theta }_{\mathrm{i}}=0^{\circ },{\theta }_{\mathrm{r}}={70}^{\circ },{\varphi }_{\mathrm{r}}=0^{\circ }$.

Figure 7

The required normalized input impedance $Z_{11}/{\eta }_1$ for passive metamirrors in the case when ${\theta }_{\mathrm{i}}=0^{\circ },{\theta }_{\mathrm{r}}={70}^{\circ },{\varphi }_{\mathrm{r}}=0^{\circ }$. One period of the metamirror along the $z$ coordinate is shown. The solid, dashed, and dotted lines correspond, respectively, to the lossy metamirrors [Eq. (41)], the lossless metamirrors creating two reflected plane waves [Eq. (43)], and the conventional nonuniform reflectors [Eq. (47)].

Figure 8

Illustration of the desired performance of an ideal metamirror which perfectly transforms a TE incident wave into a TM reflected wave.