Modeling software is generally used to show the fields and flows that are impossible to see with the eye or instruments. A group of researchers has done just the opposite: They ran computer simulations that showed it should be possible to fabricate the metamaterials necessary to build an "invisibility cloak" that makes an object invisible to certain frequencies.

The required electromagnetic properties of the cloaking shell are not of the sort found in natural materials. Knowledge of how to engineer materials with specific and complex electromagnetic properties has increased dramatically, and there is now an understanding of how to create "metamaterials" that behave as if they were continuous materials with permittivity, ε, and permeability, μ, that can vary with direction and position, and can even be negative. Early efforts at creating these materials were unsuccessful, but numerical simulations made it easy to study real-world material imperfections.

Figure 1: Computational domain and boundary conditions for the Full-Wave Cloaking Simulation.The PEC (perfect electrical conductor)shell has a diameter of 0.2 m, which is 1.33 wavelengths of the incident 2-GHz transverse electric(TE) polarized time-harmonic uniform plane wave.

The geometry of the COMSOL Multiphysics simulation is simple (Figure 1). It solves the 2D cylindrical problem in which a perfect electrical conductor (PEC) infinite circular cylinder is wrapped by a cloaking shell. The PEC shell is a strong reflector of electromagnetic energy, and the goal is to mask this scattering in all directions. On the left and right sides are regions of PMLs (perfectly matched layers), which simulate the infinite domain in which the system resides. A uniform plane wave is launched by a sheet of uniform current density near the left edge of the domain. The top and bottom boundaries are perfect magnetic conductors (PMC) so that a uniform plane wave with its electric field pointed out of the page can terminate without reflection on these edges.

Note that this model does not simulate the fine structure actually fabricated. Instead it simulates continuous materials that for this application are anisotropic and smoothly inhomogeneous. The next step is determining how to design the physical structures that approximate the desired continuous material properties.

A first simulation (Figure 2a) showed the fields for the ideal cloaking shell that has continuously variable permittivity and permeability prescribed by the original theory. As it travels from left to right, the plane wave is smoothly deformed by the cloaking shell, much like river water flowing around a rock. An observer on the right side would thus see only the undisturbed wave, rendering the scattering object transparent and effectively invisible. The next step was to see the effects of adding energy absorption as is expected in real-world materials. The model added substantial energy absorption to the shell's permittivity and permeability, and Figure 2b shows that the cloaking effect does not fall apart in the face of losses. The object would now cast a shadow because the incident electromagnetic power is partially absorbed before it can exit the shell, but the wave is otherwise undisturbed and thus the object does not reflect in any other direction.

Figure 2: The Electric Field Distribution near the cloaked object (the white center). Electromagnetic power flows from left to right. The x-axis extends across±0.6m, and the y-axis extends across ± 0.4m. Shown are: (a) ideal parameters, (b) ideal parameters with loss, (c) 8-layer stepwise approximation, and (d)reduced material parameters.

The next challenge addresses the present inability to build continuously variable metamaterials. Instead, it must be approximated with discrete layers. A simulation of the case with eight discrete homogeneous cylindrical layers (Figure 2c) showed that the cloaking effect, while not perfect, is still evident. Finally, it is difficult to control all three of the key electromagnetic parameters in a fabricated metamaterial at one time. Would it be possible to hold one or two of them constant and vary only one of them and still get reasonable results? Figure 2d shows the field distribution when the cloaking shell is composed of a simplified material in which only the radial component of permeability is spatially varying. Although there is considerable scattering, the smooth deformation of the wave fronts still shows the cloaking principal at work.

To find out how it would work in practice, the team designed and fabricated an eight-layer metamaterial structure with the simplified cloaking shell parameters described above. The experimentally measured fields were in almost exact agreement with the simulated fields, which confirmed that the fabricated metamaterial structure achieved the target electromagnetic parameters.

This article is based on work done by Steven A. Cummer, David Schurig, and David Smith of Duke University using multiphysics software from COMSOL, Inc. For more information, click here.