Lossless tensor surface electromagnetic cloaking for large objects in free space

Electromagnetic cloaking for large objects in free space using a lossless impenetrable tensor impedance surface is proposed. The key enabling feature is enforcement of the pointwise lossless condition via introduction and optimization of surface waves that carry power along the curved bounding surface of the cloaked region. In a pointwise lossless and reciprocal manner, the cloaking surface converts the incident plane wave into surface waves on the lit side, carries the power along the surface into the shadow side, and continuously releases a propagating wave to reconstruct the incident field behind the object. Overcoming the difficulties associated with currently available active and passive metasurface cloaks, the proposed cloaks may be realized entirely using passive constituents and they are effective for electrically large free-standing objects that cast shadows. The surface cloaks may be realized as subwavelength-thin passive tensor gradient metasurfaces.

Figure 1

Local lossless conditions for a medium or surface. (a) A medium with tensor parameters of a permittivity $\mathbf{\epsilon }$, a permeability $\mathbf{\mu }$, a magnetoelectric coupling $\mathbf{\xi }$, and an electromagnetic coupling $\mathbf{\zeta }$. (b) An impenetrable surface with a tensor surface impedance ${\mathbf{Z}}_s$. (c) A penetrable surface with a magnetic impedance ${\mathbf{Z}}_{\mathrm{sm}}$, an electric admittance ${\mathbf{Y}}_{\mathrm{se}}$, a magnetoelectric coupling ${\mathbf{K}}_{\mathrm{em}}$, and an electromagnetic coupling ${\mathbf{K}}_{\mathrm{me}}$.

Figure 2

A surface cloak configuration for a 2D circular cylinder of radius $a$ subject to a TE-polarized plane-wave illumination.

Figure 3

TM-polarized SW design for a $a=4\lambda$ cylinder using $k_c=2k$. (a) The optimized $H_{tz}\left(\varphi \right)$. (b) The radial components of the Poynting vector at $\rho =a$ for the total as well as for individual TE- and TM-polarized fields. A $+x$-propagating plane wave of unit amplitude illuminates the cylinder.

Figure 4

The lossless and anisotropic reactance elements for the $a=4\lambda$ cylinder obtained using the least squares process. They are in terms of the arc length variable $\ell =a\varphi$ and the upper semicircular range $0<\ell <\pi a$ is displayed. The parameters in $-\pi a<\ell <0$ are mirror images of these with respect to $y=0$.

Figure 5

Simulation results for a cylinder of $a=4\lambda$. (a) A snapshot of $E_z$ for a PEC cylinder. A snapshot of (b) $E_z$ and (c) $H_z$ for a cloaked cylinder. Parts (a) and (b) share the same color axis. The cylinders are subject to unit amplitude $(E_0^{\mathrm{i}}=1\mathrm{V}/\mathrm{m})$ plane-wave illumination.

Figure 6

Performance characterization of the $a=4\lambda$ surface cloak. (a) Comparison of $E_{tz}\left(\varphi \right)$ between design [Fig. 5] and the ideal case corresponding to the incident field (thin solid curves). (b) Comparison of ${\sigma }_{2\mathrm{D}}$ between the PEC cylinder [Fig. 5] and the cloaked cylinder [Fig. 5].

Figure 7

Cloaking performance for a cylinder of $a=8\lambda$. (a) A snapshot of $E_z$ for a cloaked cylinder. (b) Comparison of ${\sigma }_{2\mathrm{D}}$ between a PEC cylinder and a cloaked cylinder.