Parity-time-symmetric teleportation

We show that electromagnetic plane waves can be fully “teleported” through thin, nearly fully reflective sheets, assisted by a pair of parity-time-symmetric lossy and active sheets in front and behind the screen. The proposed structure is able to almost perfectly absorb incident waves over a wide range of frequency and incidence angles, while waves having a specific frequency and incidence angle are replicated behind the structure in synchronization with the input signal. It is shown that the proposed structure can be designed to teleport waves at any desired frequency and incidence angle. Furthermore, we generalize the proposed concept to the case of teleportation of electromagnetic waves over electrically long distances, enabling full absorption at one surface and the synthesis of the same signal at another point located electrically far away from the first surface. The physical principle behind this selective teleportation is discussed, and similarities and differences with tunneling and cloaking concepts based on $\mathcal{PT}$ symmetry are investigated. From the application point of view, the proposed structure works as an extremely selective filter, both in frequency and spatial domains.

Figure 1

Proposed geometries of interest.

Figure 2

Reflection and transmission coefficients for the design in Fig. 1.

Figure 3

(a) Reflection and (b) transmission coefficients for $0^{\circ }, {30}^{\circ }$, and ${60}^{\circ }$ teleportation structures (a ${\theta }_{\mathrm{i}}$ teleportation structure is a structure which is designed to teleport an incident wave with incidence angle ${\theta }_{\mathrm{i}}$). Electric field distribution for (c) $0^{\circ }$, (d) ${30}^{\circ }$, and (e) ${60}^{\circ }$ teleportation structures at frequency $f=10$ GHz. Angular dependencies for (f) $0^{\circ }$, (g) ${30}^{\circ }$, and (h) ${60}^{\circ }$ teleportation structures at frequency $f=10$ GHz (here, we assume that the sheet resistances are angular independent). (i) Transmission-line model for $0^{\circ }$ teleportation structure.

Figure 4

Transmission coefficients for structures with (a) highly reflective inductive sheet and (b) highly reflective capacitive sheet. In both these examples $X=0.01\mathrm{\Omega }$ at $f=10$ GHz.

Figure 5

Circuit model for the $0^{\circ }$ teleportation structure (here $Z_0$ is the intrinsic impedance of the transmission line and $L$ shows the inductance of a sample inductive sheet). (b) Time-domain simulation of the circuit model ($0^{\circ }$ teleportation structure).

Figure 6

(a) Geometry of the proposed long-distance teleportation structure. Electric field distribution: (b) $0^{\circ }$ long-distance teleportation structure with the design parameters $R_{\mathrm{l}}=-R_{\mathrm{a}}={\eta }_0, d_{\mathrm{l}}=d_{\mathrm{a}}={\lambda }_0/4, d_{\mathrm{t}}=3{\lambda }_0$, and $f=10$ GHz; (c) ${30}^{\circ }$ long-distance teleportation structure with the design parameters $R_{\mathrm{l}}=-R_{\mathrm{a}}=\sqrt{3}{\eta }_0/2, d_{\mathrm{l}}=d_{\mathrm{a}}={\lambda }_0/2\sqrt{3}, d_{\mathrm{t}}=2\sqrt{3}{\lambda }_0$, and $f=10$ GHz. (d) Transmission-line model for $0^{\circ }$ long-distance teleportation structure.