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Metamaterials |
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| The new shape of electromagnetism
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Metamaterials have re-ignited the interest in electromagnetism in the past few years. When everyone thought the field was dead, these artificial structures have provided the opportunity to manipulate light in extraordinary ways previously thought impossible. I have been interested in transformation electromagnetics, cloaking, FDTD simulations, time-domain and transient effects, as well as techniques to make practical metamaterial applications. Below is a sample of the research involved.
Frequency Response of Metamaterial Devices Metamaterials have the capability of acquiring exotic electromagnetic parameters that are not readily found in nature, such as permittivity and permeability smaller than one or even negative. This advantage comes at a cost: due to causality constraints, they cannot maintain their properties for all frequencies, but rather exhibit them over a very narrow band (ideally, they work optimally at a single frequency only). This work here examines what happens when a metamaterial device such as the cylindrical cloak, which is constructed using dispersive elements, is excited from a narrowband signal.
The Drude dispersion model is used, which describes among other things the dependence of the permittivity of a metamaterial element as s function of frequency, shown above. The source pulse's spectrum is seen to overlap with a large section of the parameter's value, thus different frequencies will sample different effective permittivity values. Other dispersive material parameters vary accordingly.
The top graph above shows the bandwidth if various types of cloaks. Only the ideal cloak has a perfect operation at the nominal frequency, as well as the largest bandwidth. The bottom graph shows the effect of losses: when a material has a loss tangent of 0.05 or higher, the cloaking effect basically ceases to exist.
The above graph shows what happens when multiple pulses at varying frequencies are launched against the ideal cloak. In (c), pulses with high frequencies are reinforced while pulses with low frequencies are dissipated - this is due to the dispersion in the material parameters.
Interesting things happen when frequencies smaller that the cloak's operating frequency are launched against the device. The incident wave perceives the device as a cylinder with 3 layers: One positive material, one epsilon-negative material, and one doubly-negative material. These are the locations where the permittivity and permeability of the cloak material become zero, effectively creating PEC and PMC walls.
The graph above shows the total field distribution when plane waves at different frequencies are launched against the ideal and matched reduced cloaks. For low frequencies, the devices behave like meta scatterers (due to the presence of the PEC/PMC walls), but for high frequencies they behave as dielectric scatterers, thus more field is reaching the receiving (right) side of the domain, causing blueshift effects and spectral shifts.
The videos below show the propagation of short pulses through the ideal cloak (left) and the ideal concentrator (right). The reflections and distortions are due to the dispersion are clearly visible.
Relevant references: Dispersive Cylindrical Cloaks under Non-Monochromatic Illumination (paper)
Normally, these perfect cloaks require anisotropic materials which are terribly difficult to manufactured in practice. That's way instead of an ideal 3D cloak, a more simple and limited ground-plane cloak has been introduced, which is much easier to realize experimentally. The main principle is shown below.
In the same way that temperature gradient cause an effective refractive index and the light rays bend above a hot surface, in a similar way the ground-plane cloak bends the rays around an object placed on a ground plane (a mirror) by introducing the corresponding refractive index gradients.
However, transformation electromagnetics does not indicate the engineering detail with which the cloaks such be build. Here, an example is shown where a ground-plane cloak is constructed out of simple dielectric blocks. The initial design of 64x15 blocks is simplified, first by ignoring any dispersive sections, and second by reducing the detail of the structure. The idea is that, as long as the wavelength of light cannot resolve the details of the structure, the cloaking device should work almost perfectly.
Indeed, the results here indicate that for a cloak designed to operate around 600 THz (that's the center of the visible spectrum), it can be made from blocks that are made as big as two wavelengths, and the spectrum is restored up to 1600 THz. So, an incident pulse will be reflected almost perfectly from the ground plane that includes the cloak, as if only a perfect ground plane was placed there. At 600 THz, the spectrum of the original pulse is restored, with only slight deterioration between the full high-resolution cloak and the simplified ones. The dispersive sections are very small compared to the wavelength and do not affect the performance. The differences are more pronounced near 1600 THz. This is an aid not only for this specific case but for any device designed through transformation electromagnetics: it does not need to be very detailed, as long as the building metamaterial blocks are around one wavelength large, or smaller. See more details on this matter in [1]. The videos below illustrate the function of the ground-plane cloak when a pulse is incident on an object. The first figure shows the pulse impinging on a flat plane. The second figure shows the same pulse but when an object is placed on the plane, and the reflected wave is distorted. The third figure shows the effect of the cloak placed around the object, where the proper scattering pattern of an almost perfectly reflected wave is restored. This is an non-orthogonal FDTD simulation using a 64x15 cloak.
The idea can be extented to make a directional cloak, by removing the ground plane and mirroring the object and the cloak around the axis. Then the shadow previously observed is filled with energy, increasing the power transmition along the axis of propagation by one order of magnitude. This design is broadband, lossless, simple to build and of tremendous interest to antenna engineers, as it can help them bypass objects effectively.
Above is shown the hype-curve for the field of transformation-based cloaking. While the original ideal designs will be very hard to be achieved, the more practical approaches have better chance of dominating the future of cloaking.
Relevant references: Ground-Plane Quasi-Cloaking for Free Space
Another application of cloaking is to use the bending of the waves to create an efficient absorber. The idea is to take advantage of the longer path the rays follow inside a cloak. If loss is added in the cloaking material (which is fairly easy and naturally occuring), the energy dissipated inside the cloak and little wave energy reaches behind, as shown below.
Compared to conventional absorbers of the same size (i.e. a simple dielectric that has the same loss tangent), the above-mentioned absorber creates a superior absorption pattern will little back-scattering. It is better than the conventional absorber, or the matched conventional absorber (a matched-to-vaccum section of space with high loss). A more practical "discrete" absorber consisting of 10 layers also retains most of the absorbing performance. For details, see [2]. Relevant references: Manipulating Loss in Electromagnetic Cloaks for Perfect Wave Absorption (paper, arxiv)
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Cloaking is the most imaginative application of metamaterials. The goal is to design a device that, when surrounding a specific object, it makes it invisible over some portion of the electromagnetic spectrum. The so-called ideal cloak, proposed by Pendry, completely and perfectly bends light rays around it. An example of such a cloak covering a cylindrical object is shown here, in an FDTD simulation of a plane wave impinging on a metallic core surrounded by a perfect cloak.
