Achieving perfect imaging beyond passive and active obstacles by a transformed bilayer lens

A bilayer lens is proposed based on transformation optics. It is shown that Pendry’s perfect lens, perfect bilayer lens made of indefinite media, and the concept of compensated media are well unified under the scope of the proposed bilayer lens. Using this concept, we also demonstrate how one is able to achieve perfect imaging beyond passive objects or active sources which are present in front of the lens.

Figure 1

(Color online) Illustration of a bilayer slab structure obtained by coordinate transformations from a single slab layer.

Figure 2

(Color online) (a) Electric field distribution for a line current source $J_s=A\delta \left(z+0.01\lambda \right)\delta \left(x\right)$ interacting with a bilayer lens located in $z∊\left[0,4\lambda \right]$; (b) Field intensities at the exit boundary $z=4\lambda$ for the cases with the bilayer and without bilayer. The bilayer lens has ${ϵ}_1=4$, ${\mu }_1=1$, ${ϵ}_2=-4+0.008i$ and ${\mu }_2=-1+0.008i$ and $L_1=L_2=2\lambda$.

Figure 3

(Color online) (a) Electric field distribution for a line current source $J_s=A\delta \left(z+7/3\lambda \right)\delta \left(x\right)$ interacting with a Pendry’s lens ${ϵ}_L=-1+0.008i$ and ${\mu }_l=-1+0.008i$; (b) Electric field distribution when a dielectric cylinder is put in the front of the lens; (c) Electric field distribution when the dielectric cylinder together with its compensated cylinder are put outside and inside the lens, respectively. (d) Field intensity at the image plane $z=13/3\lambda$ for (a), (b), and (c). The dielectric cylinder has a radius of $2/3\lambda$ with the center at $z=-\lambda$ and $x=0$, and a refractive index of 2.

Figure 4

(Color online) Electric field distribution for (a) two current sources ${\overline{J}}_1=A\delta \left(x\right)\delta \left(z+1.9\lambda \right)\widehat{y}$ and ${\overline{J}}_2=-A\delta \left(x\right)\delta \left(z-1.9\lambda \right)\widehat{y}$ embedded in the bilayer; (b) only ${\overline{J}}_1$ is embedded in the bilayer. The bilayer lens has the same material parameters as in Fig. 2.

Figure 5

(Color online) Electric field distribution when (a) a current sheet $J_s=4A\delta \left(x+z/6\lambda \right),x∊\left[-2\lambda ,2\lambda \right]$ is put in the front of the lens of Fig. 3a; (b) the compensated current sheet is put inside the lens. (c) Field intensity at the image plane $z=13/3\lambda$ for (a), (b), and also Fig. 3a.