Cylindrical Invisibility Cloak with Simplified Material Parameters is Inherently Visible

It was proposed that perfect invisibility cloaks can be constructed for hiding objects from electromagnetic illumination [J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006)]. The cylindrical cloaks experimentally demonstrated [D. Schurig et al., Science 314, 977 (2006)] and theoretically proposed [W. Cai et al., Nat. Photon. 1, 224 (2007)] have however simplified material parameters in order to facilitate easier realization as well as to avoid infinities in optical constants. Here we show that the cylindrical cloaks with simplified material parameters inherently allow the zeroth-order cylindrical wave to pass through the cloak as if the cloak is made of a homogeneous isotropic medium, and thus visible. To all high-order cylindrical waves, our numerical simulation suggests that the simplified cloak inherits some properties of the ideal cloak, but finite scatterings exist.

Figure 1

Variation of the scattering coefficients, examined in each cylindrical wave order, as a function of $b$. For $m=1$, 2, the curves are fitted using Savitzky-Golay smoothing filter according to numerically derived data points (dots).

Figure 2

The zeroth-order transmission coefficient.

Figure 3

(a1)–(a3) $E_z$ snapshot, $E_z$ norm, and scattered $E_z$ field, respectively, for a simplified cloak with $a=0.1\mathrm{m}$ and $b=0.2\mathrm{m}$. (b1)–(b3) Same fields but for a simplified cloak with $a=0.1\mathrm{m}$ and $b=0.5\mathrm{m}$. (c1)–(c3) Same fields but for a near-to-ideal cloak with $a=0.101\mathrm{m}$ and $b=0.5\mathrm{m}$.