Object-dependent cloaking in the first-order Born approximation

We consider the cloaking of a slab object in scalar wave theory within the first-order Born approximation. We show that in the forward direction cloaking is achieved for any transversally invariant, positively refracting, and absorbing object by using a lossy, negative-index metamaterial cloak. Cloaking is perfect and occurs for incident fields having any spatial structure and bandwidth. In the backward direction cloaking is found to be possible for self-imaging fields. In both cases the refractive-index distribution and dispersive properties of the cloak slab resemble those of the object slab. The method of object-dependent cloaking with weak scatterers may find useful applications.

Figure 1

Illustration of slab geometry for cloaking. The field $U^{(i)}(\mathbf{r},\omega )$ is incident along the $z$ axis in vacuum on the object (at $0⩽z⩽a$) and cloak (at $a_1⩽z⩽a_2$) slabs having the refractive-index distributions of $n_o(z,\omega )$ and $n_c(z,\omega )$, respectively. The field scattered by the object is $U_o(\mathbf{r},\omega )$ and that by the cloak is $U_c(\mathbf{r},\omega )$.

Figure 2

Illustration of the refractive indices of the object, $n_o(z,\omega )$, and the cloak, $n_c^{\pm }(z+a_1,\omega )$, in the complex plane: (a) forward scattering and (b) backward scattering. The parameters $\epsilon (z,\omega )\ll 1$ and $\psi (z,\omega )$ specify the refractive index of the object slab, whereas $\varphi (\omega )$ is related to the incident field in the case of backscattering.