Perfect invisibility cloaking by isotropic media

In this paper the authors report that perfect invisibility cloaking could be achieved in a medium designed by a non-Euclidean conformal transformation. Wave behaviors could be controlled as well as the cloaking device configured by the general Euclidean approach dealing with the full Maxwell's equations. The cloaking medium proposed here is totally isotropic and can work in waves without the geometry and polarization limits; thus it is very promising for applications to build a device to hide large objects.

Figure 1

Schematic of the virtual space. It consists of two Riemann sheets with the upper one empty for air and the lower one placed with a usual Eaton lens in (a) and an inside-out Eaton lens in (b). On the upper sheet the incident light rays (short red arrows) heading toward the branch cut (yellow lines) will fall off onto the lower sheet and one loop later travel back onto the upper again. The long green arrows represent light rays not entering the lower sheet. Their interference with the light back from the lower sheet affects the performance of the whole device. Note the cloaking medium in (a) is pure dielectric but has equal magnetic and dielectric values in (b) for the bottom lens consisting of one negative ($-$) and one positive ($+$) half.

Figure 2

Cloaking effect with an Eaton lens incorporated. An Eaton lens is placed in the lower sheet to guide back the incident light rendering the region outside cloaked as represented by the black holes. The wave patterns in (a) and (b) are the snapshots corresponding to the harmonic eigenmodes of the Eaton lens at the order $l$ $=$ 2 and 40, respectively. The wave is denoted by the magnetic component normalized by the incident field.

Figure 3

Cloaking effect with an inside-out positive-negative Eaton lens incorporated. The wave patterns in (a) and (b) are simulated at wavelengths corresponding to the Eaton lens's harmonic order $l$ $=$ 2 and 4, respectively. In each group, the right (left) figure represents the wave incident from the left (bottom) side. The inside-out Eaton lens with half negative and half positive is employed here to cancel out the phase delay in the inner cloak core.

Figure 4

Cloaking effect of the device at different nonharmonic wavelengths. The cloak parameters are the same as discussed in Fig. 3. The wavelength λ equals 5.5$a$ (a), $a$ (b), 0.25$a$ (c), and 0.1$a$ (d), respectively. In each group the right is the wave picture and the left is the normalized corresponding biscattering figure. For the biscattering curve the polar angle starts from the $x$ axis parallel to the incident wave vector.

Figure 5

Cloaking effect with loss media. Usage of negative index materials will inevitably involve material loss issues. The inner cloaking cores (the lower Riemann sheet part) in (a)–(d) have imaginary permittivity and permeability of 0, 0.01, 0.03, and 0.1, respectively. One sees that the cloaking performance is very sensitive to signal attenuation.