Invisibility and supervisibility: Radiation dynamics in a discrete electromagnetic cloak

We study the radiation dynamics of an electric dipole source placed near or inside a discrete invisibility cloak. We show that the main features of radiation dynamics can be understood in terms of the interaction of the source with a nonideal cloak in which local-field effects associated with the discrete geometry play a crucial role. As a result, radiation dynamics in a discrete cloak can differ drastically from what a source would experience in an ideal, continuous cloak. This can lead, for instance, to an enhancement of the emission by the cloak, thus making the source more visible to an outside observer than it would be without the cloak. The two main physical mechanisms for enhanced, or inhibited, radiation dynamics are the coupling of the source to leaky modes inside the cloak, and the coupling of the source with the lattice of the discrete cloak, via the local field. We also explore the robustness of the effect to material dispersion and losses.

Figure 1

Schematic diagram of discretization in DDA picture. (a) The nominal physical system: a continuum magnetodielectric material implemented by subwavelength resonators. (b) Conventional fine-grained discretization with position dependent responses. (c) High-level discretization with a single pair of polarizability tensors for each resonator.

Figure 2

Map of the $y$ (top) and $z$ (bottom) components of the electric field in the $z=0$ plane (arb. units) for a cloak with $b=2a$. The wavelength is $\lambda =b$. The source is an electric dipole oriented along $y$ (b) or $z$ (c) and located (outside the domain of the plot) at $(-3.5b,0,0)$. The inset shows a cross section of the cloak through the $z=0$ plane. (The strength of the electric field is arbitrary, being proportional to the strength of the dipole source.)

Figure 3

(a) Normalized emission rate as a function of distance from the center of a spherical cloak for an electric dipole, for two orientations, radial (solid line) and tangential (dashed line), of the dipole moment. Parameters: $\lambda =b=2a$, $d=b/50$. (b) same as (a) for $d=b/25$. The horizontal dashed line marks the free-space emission rate.

Figure 4

Normalized emission rate as a function of the wavelength for a source at the center of the cloak ($b=2a$, $d=b/50$). The inset shows the energy density inside the cloak at the peak wavelength $\lambda \approx 0.8b$.

Figure 5

Normalized decay rate as a function of frequency for a source located at a distance $r$ from the center of a cylindrical cloak. For each resonance, the corresponding map of the energy density is shown.

Figure 6

Total, radiative, and nonradiative decay rates for an electric dipole source at the center of a dispersive, lossy, composite cloak with $d=a/25$ and ${\omega }_{\epsilon }={\omega }_{\mu }={\omega }_g=2\pi c/\left(1.5a\right)$; ${\Gamma }_{\epsilon }={\Gamma }_{\mu }={\omega }_g/10$. The inset shows the real and imaginary parts of the dispersion profile.

Figure 7

Same as Fig. 6 with ${\omega }_{\epsilon }={\omega }_{\mu }={\omega }_g=2\pi c/a$.