Negative Refraction and Planar Focusing Based on Parity-Time Symmetric Metasurfaces

We introduce a new mechanism to realize negative refraction and planar focusing using a pair of parity-time symmetric metasurfaces. In contrast to existing solutions that achieve these effects with negative-index metamaterials or phase conjugating surfaces, the proposed parity-time symmetric lens enables loss-free, all-angle negative refraction and planar focusing in free space, without relying on bulk metamaterials or nonlinear effects. This concept may represent a pivotal step towards loss-free negative refraction and highly efficient planar focusing by exploiting the largely uncharted scattering properties of parity-time symmetric systems.

Figure 1

(a) Conventional negative refraction in a passive DNG medium, for light rays emitted by a source placed on the left side of the slab. The power flows away from the source, and the phase velocity in the slab is backward. (b) Negative refraction using $PT$-symmetric metasurfaces with real surface impedances $+R$ and $-R$. In this active scenario, both power flow and the phase velocity are directed from the active surface to the passive one, and negative refraction is obtained without the need for a bulk metamaterial.

Figure 2

(a) Equivalent circuit for the geometry of Fig. 1. We study the two-port $PT$-symmetric system composed of two parallel lumped resistors $+R=r{Z}_0$ and $-R=-r{Z}_0$ separated by a portion of transmission line of impedance $Z_0$, and electrical length $x$. (b)–(d) Magnitude of $S_{11}$ (b), $S_{22}$ (c), and $S_{21}=S_{12}$ (d) as a function of $x$ and $r$.

Figure 3

$PT$-based negative refraction for a TE polarized field for (a) a normally incident plane wave, (b) an obliquely incident plane wave, and (c) an obliquely incident Gaussian beam. The black arrows represent the average Poynting vector field, demonstrating the behavior described in Fig. 1. See also the corresponding time-harmonic animations in [33].

Figure 4

Planar focusing using a pair of $PT$-symmetric metasurfaces for a line current source placed on the left of the structure. We consider two different cases for the surface impedance $Z$, shown as a function of the transverse coordinate $y$ in the right panels. A constant surface impedance $Z=0.5{\eta }_0$ focuses a point source to a spot whose transverse size is close to the wavelength (a). An inhomogeneous surface impedance focuses all propagating spatial harmonics, resulting in a spot size with a transverse size equal to ${\lambda }_0/2$(b).