Transformation Optics | The Metamateral Cloak Experiment

The Metamaterial Cloak Experiment: 2006

With the reduced cloak identified as a potential candidate for an experimental sample, the next step was to actually make a sample using metamaterial elements. The first metamaterial cloak design was developed by David Schurig in our group, who started with the modified split ring resonator element as shown in the figure below. The metamaterial approach consists of using simple elements like the resonator shown as a substitute for conventional materials. The dimensions of the element need only be smaller than the wavelength--a factor of five or so smaller is typical--and the wave is tricked into believing there is an actual medium present rather than just a collection of objects. By changing the geometry of the element and using effective medium retrieval techniques developed in our group, we are able to precisely achieve the requisite material parameters through the design process. The overall size of the SRR was dictated by the wavelength of the experiment, which was performed at microwave frequencies in a parallel plate waveguide at a frequency of 8.5 GHz. The targeted wavelength was about 3.5 cm, larger than the SRR dimension by a factor of ten.

During the design phase, it was found that the single split ring resonator (SRR), combined with the Teflon-based circuit board that was used (Duroid, from Rogers Corporation), could be tuned to achieve both the desired magnetic gradient as well as the constant dielectric value needed. The magnetic response could be tuned by changing the capacitive length "s," as shown in the figure. The electric response could be tuned by changing the radius of the edges, or the parameter "r." This meant that every metamaterial cell would contain only one element, and the sample would be relatively easy to fabricate.

Because the field mapping chamber had a height of one centimeter, each SRR was designed to occupy a 3.33 cm cell, with three SRRs used to span the height of the chamber. With only a gradient in the radial component of the permeability to be controlled, a single layer of the reduced parameter cloak requiring elements along one axis only could be constructed using strips of identical SRRs wrapped into a circle. A set of ten concentric circles could then be constructed, each with a slightly different SRR design, to achieve the final gradient. The diagrams below illustrate how the cloak was put together, resembling a flat disk. On each of the concentric layers, the SRR design was slightly modified, as depicted in the second figure below in which the layers are pushed up sequentially to reveal the SRRs on the hidden layers.

The Cloak Experiment - The field mapping chamber consisted of two metal plates (aluminum) with a 1 cm separation. The lower plate rested on two linear positioners, and could be stepped in any direction in the plane. Several microwave probes, inserted into the upper plate, could be used to measure the field at given points within the chamber, such that a map of the entire field pattern could be created. Although it takes a long time to complete a mapping, sometimes many hours, the final field map allows us to easily picture the interaction between a wave and the cloak or any other transformation optical metamaterial.

It is useful first to understand what wave looks like when there are no obstacles present. That field pattern is shown just below, mapped over the region in the center of the chamber. The field is incident from the left, where the slight outward curvature occurs because we are not quite able to produce a perfectly planar wave front. Still, the wave fronts are relatively planar, and the lack of any distortion means that there is little to no scattering within the chamber, and that the absorbing material that encircles the scattering region has eliminated reflection from the periphery.

If we now insert a metal disk into the cylinder, we expect that it will strongly scatter the microwaves. The experimental field mapping shown below, reveals what happens when the planar wave above strikes a copper cylinder. The wave fronts are entirely distorted, due to the scattering from the cylinder, with a very identifiable shadow in the forward direction. The metal cylinder, then, is highly visible, reflecting light in all directions, and reducing the amount of light downstream of the cylinder.

Hiding Inside the Metamaterial Cloak - Now for the big question: Can the reduced cloak make the copper cylinder less visible? The fully assembled cloak sample is shown in the photograph below. Three cross pieces were initially inserted to hold the concentric rings together. Notches were cut in the ten metamaterial strips, into which the cross pieces were inserted, making the assembly structurally stable. The centermost ring consisted of copper tape, which acted as the scattering cylinder to be cloaked. You can see from the figure that the assembly was relatively crude; the strips in some cases needed to overlap slightly at the edges. Because the innermost ring was copper, the cross pieces running through the center were not expected to interfere with the experiment, but were later removed when the experiments were repeated.

There were many reasons to be concerned about the performance of the metamaterial implementation of the transformation optical cloak. The cloak was attempting to replicate a transformation optical material, making it the most complicated metamaterial structure that had been assembled and tested up to that point. The simulations were clear that if we had really achieved the reduced parameter cloak material specifications, then we should be able to observe the cloaking mechanism; however, for such a complicated and exacting gradient structure, it wasnÂ’t clear that our design approach would be precise enough. Many factors had to come together just right in order for it to work. If any of the parameters were off, even modestly, the entire field pattern could be very different.

A field mapping of the metamaterial cloak and the cylinder was performed, and the results were remarkable! Shown below are the simulation (top) and measurement (bottom) of the reduced parameter cloak hiding the metal cylinder. Although we have approximated this complicated, transformation optical design using just ten layers of split ring resonators, the field patterns for the simulation versus the experiment nearly coincide. In the simulation, there was less curvature in the incident wave, but aside from that difference all other aspects are very similar. The overall reflection and shadowing are observably reduced when the cloak surrounds the metal cylinder, and the emerging wave fronts are very nearly restored. Also, the details of the field inside the cloak are in amazingly good agreement with the simulation. In fact, the only way that you can tell the experimental fields apart from the simulation is just by the traces of the concentric circles that appear in the experimental field map. Other than that, the various signatures of the cloak reproduce quite well in the experiment.

Another illustration of the fields relative to the cloak is shown below. Essentially, this experiment demonstrated the viability of designing and fabricating a transformation optical medium. As far as invisibility was concerned, though, the transformation optical/metamaterial approach left quite a bit to be desired. First off, the experiment was done at microwave frequencies, which we are not able to 'see' in the first place. That's ok for an experiment like this, since it is only the principle that is being investigated. A more significant issue, however, is bandwidth: the metamaterial cloak worked at 8.5 GHz and only at 8.5 GHz. At the time we weren't sure just how far away from that frequency the cloak would operate, but we knew it wasn't much farther. The limited bandwidth of the cloak is an inherent limitation for all cloaks that reroute light in this manner; while you can create a coating that will nearly eliminate reflection over a fairly large bandwidth, you cannot eliminate all scattering (and shadows) over anything but a relatively tiny bandwidth. Translated to visible, it would mean you could conceal an object from perhaps one color, but not from all colors.

But Does the Cloak Actually Cloak? - The field mapping experiment showed that very complex media--anisotropic with both electric and magnetic response that vary as a function of position throughout space--could become reality with metamaterials. The detailed field patterns within the cloak as predicted by full-wave numerical simulations for the nonexistent virtual medium, actually corresponded to those mapped in the experimental apparatus. In spite of all of the approximations involved and uncertainties within the design process, it did seem that the transformation optical cloak behaved as anticipated.

But, as comforting and satisfying as the field maps are to view, they primarily confirm that the transformation optical design can be implemented in metamaterials. They don't confirm whether the metamaterial cloak... well... if it actually cloaks! Any conclusion about the actual performance of the device with respect to cloaking can only be obtained indirectly.

How do we tell how well the metamaterial cloak actually cloaks?

When a wave strikes an object, it scatters from the object, sending power out in potentially all directions. If we total up all of the power scattered from the object, we obtain a measure of just how much the object scatters. However, the total power will depend on how much power we illuminated the target with, so it's a good idea to normalize or divide the total scattered power by the incident power. Usually, it is actually the incident intensity, or power per unit area, that is used for the comparison, so that the quantity of interest is the scattering cross-section, or SCS. Measuring the SCS is the means by which we can obtain a quantitative assessment of the cloaking performance.

In 2010, Nathan Kundtz in our group decided to take a closer look at the cloak, repeating the original experiment with the goal of actually measuring the SCS. A summary of the field mapping experiment is shown below, where we see comparisons of the empty chamber (no scattering cylinder); just the cylinder; and the cylinder with the cloak. Comparing the second two figures, it becomes very clear that the presence of the cloak is actually having a very significant impact in terms of reducing the shadow, as well as reducing the distortion in the phase fronts throughout the entire region. This distortion is caused by interference between the incident wave and the scattered wave, so reduction in distortion suggests that the scattering has, in fact, been reduced.

From the measured field maps, we can extract the fields over a ring that surrounds the cloak, as shown in the diagram below. After subtracting the incident field, which can be measured with the chamber first empty, the fields over the ring correspond specifically to the fields scattered from the object or objects within. While that scattering may vary as a function of angle, initially here we are only concerned if the metamaterial cloak reduces the overall scattering.

As in the experiments that were performed in 2006, the cloak was designed to operate at microwave frequencies, this time at around 10 GHz. A similar sequence of measurements was performed, including the empty chamber, a copper cylinder (the object to be cloaked), and the copper cylinder surrounded by the cloak. The figure below shows the results. A metal cylinder has a generally flat SCS as a function of frequency (8-12 GHz, dashed blue line). The SCS of the metamaterial cloak, however, varies widely with frequency, but does indeed fall rapidly to a minimum right at the design frequency. In fact, its SCS is lower than that of the cylinder, even though the cloak design was never optimized. So, the metamaterial cloak actually does provide a modest reduction in the SCS, and therefore it does provide some degree of cloaking.

The measurement results also show another trend; at frequencies away from the design frequency of 10 GHz, the SCS for the cloak is much larger than for the copper disk! That is, the "cloak" scatters much more energy than the object it is supposed to be hiding. This result was not unexpected, however; the fundamental constraints on the cloak imply, as discussed above, that the effect can only be realized in a passive material for a relatively small bandwidth. This measurement provided the first practical indication of what that bandwidth actually was, and how much larger the scattering becomes away from the design frequency.

Useful References

Controlling electromagnetic fields
J. B. Pendry, D. Schurig, D. R. Smith
Science 312, 1780 (2006)

Metamaterial electromagnetic cloak at microwave frequencies
D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith
Science 314, 977 (2006)

Scattering cross-section of a transformation optics-based metamaterial cloak
N. Kundtz, D. Gaultney, D. R. Smith
New Journal of Physics 12, 043039 (2010)