Illusions and Cloaks for Surface Waves

Abstract

Ever since the inception of Transformation Optics (TO), new and exciting ideas have been proposed in the field of electromagnetics and the theory has been modified to work in such fields as acoustics and thermodynamics. The most well-known application of this theory is to cloaking, but another equally intriguing application of TO is the idea of an illusion device. Here, we propose a general method to transform electromagnetic waves between two arbitrary surfaces. This allows a flat surface to reproduce the scattering behaviour of a curved surface and vice versa, thereby giving rise to perfect optical illusion and cloaking devices, respectively. The performance of the proposed devices is simulated using thin effective media with engineered material properties. The scattering of the curved surface is shown to be reproduced by its flat analogue (for illusions) and vice versa for cloaks.

To date, almost all examples of TO^1,2,3,4,5,6 devices such as cloaking^{7,8,9,10,11,12} and optical illusion^{13,14,15,Fig. 5h can be accounted for by the rate of change of the material parameters on the cloak exceeding the allowable limits set by GO. Kee** in line with the quantitative method used to validate the proposed illusion device's performance we do the same for the cloaking device (Fig. 6). Here the two probe lines, each 10λ₀ in length, whose centers are 15λ₀ away from the origin of the deformation, are oriented as is shown in Fig. 6. In the first instance, θ is set to zero and the amplitude of E_z along the red probe line is plotted (Fig. 7a). Here we note that, as expected, due to the interference pattern created in the wake of the uncloaked surface deformation, the amplitude of E_z varies as it traverses down the probe-line (black curve in Fig. 7a). The cloaked surface deformation however, perfectly reproduces the characteristics of a plane wave (red curve in Fig. 7a), as one would expect. Next, the angle of incidence of the surface wave is set to and the amplitude of E_z along the blue probe line is plotted (Fig. 6). Once again, we see the expected interference pattern created in the wake of the uncloaked deformation (black curve in Fig. 7b), while the cloaked deformation perfectly recreates the behavior of a plane-wave (red curve in Fig. 7b). Taking these results and those in Fig. 5, into account one can conclude that the proposed cloaking device faithfully cloaks the surface deformation from surface waves.}

Figure 6

Probe line locations for cloaking device validation.

Figure 7

Quantitative validation of proposed cloaking device.

(a) θ_i = 0 (b) .

In this Letter we have proposed a general method to engineer arbitrary illusion and cloaking devices for surface waves. For the case of illusion devices, it is achieved by utilising a thin sub-wavelength coating of an anisotropic material to perfectly recreate the total scattering characteristics of an arbitrary surface for all angles of incidence as was demonstrated in a full-wave electromagnetic solver (COMSOL 4.3b). For the cloaking device, a similar derivation to that of the illusion device is employed and an asymmetric deformation coated with a anisotropic material, is shown to behave as if were a flat surface for all angles of incidence. The proposed illusion and cloaking devices, serve as proofs-of-concept for a highly generalized technique that can be adapted to other waves in fields such as thermodynamics and acoustics.