Metamaterials and Cloaking

METAMATERIALS

David R. Smith was this year's Walter Selove lecturer at Penn. He gave two talks on his work in developing metamaterials and using them in a cloaking device. I did some background reading to understand the principles behind the cloaking device. There were two papers, published back to back in Science that I read through:

Optical Conformal Mapping
Ulf Leonhardt
Science 312, 1777--1780 (2006)

Controlling Electromagnetic Fields
J.B. Pendry, D. Schurig, and D.R. Smith
Science 312, 1780--1782

They make a lot more sense after hearing Dr. Smith's lectures and talking with him over lunch.

Question 1: What is a material?

Dr. Smith made a convincing argument that, from the perspective of electrodynamics, a material is something with a permittivity and a permeability. These are the only parameters that enter Maxwell's equations for describing electromagnetic fields in matter. This is already an effective theory --- fundamentally, QED would describe any electromagnetic phenomena. The permittivity and permeability represent a type of coarse-graining in which the atomic properties are averaged of distances that are large compared to the atomic scale (say the Bohr radius), but small compared with the wavelength of light in question.

Question 2: What is a metamaterial?

If the wavelength of light is large enough, we can imagine averaging the fields over scales large enough to be manipulated by intelligent beings. For visible light, one might consider nanoscale patterns etched on a wafer. For microwaves, objects as large as wires and loops could form the effective medium.

A metamaterial is a medium in which you control the atoms. Dr. Smith cited the work of John Pendry as demonstrating how one could build up a material with a negative index of refraction (negative permeability and permittivity). A negative value of the permittivity is not uncommon. It occurs in metals near a plasmon resonance. Dr. Smith was part of a team at UCSD that built an array of wire loops and posts with both a negative permittivity and a negative permeability.

Question 3: What does a metamaterial do?

Control over the permeability and permittivity allows for some interesting phenomena. Dr. Smith's group demonstrated a negative index of refraction by performing a simple Snell's law experiment. Light is bent in the opposite direction. Many other possibilities were discussed by a Soviet physicist named Veselago in 1968, such as a phase velocity opposite the direction of propagation, and lensing from a flat slab. More recently, Pendry proposed a "perfect lens" which would allow focusing of non-propagating modes --- the near fields that are always ignored in textbook problems.

Another phenomena is called cloaking. It's gotten a lot of media attention and Dr. Smith's work has made the covers of several scientific publications.


CLOAKING

Both the papers from Science address the possibility of cloaking. An interesting mathematical property of Maxwell's equations is that a coordinate transformation can be completely described by a transformation of the fields, the permittivity, and the permeability. This has practical consequences, as both papers illustrate.

Suppose you want to cloak a region of space --- i.e., you don't want any electromagnetic fields to penetrate the region, and you don't want any waves reflected or absorbed. Light rays follow geodesics (e.g., Fermat's principle). If the geodescis of spacetime were to travel around the region to be cloaked, this would be a neat solution of the problem. A coordinate transformation can implement this solution. That coordinate transfomration leads to field lines the curve around the cloaked region and their corresponding permittivity and permeability. This is where metamaterials come in. They allow one to engineer the permittivity and permeability as needed.

Dr. Smith's group at Duke perfomred numerical simulations to determine the properties their metamaterial would need to cloak a disc from microwave radiation. They built the required structure (rather, an approximation to the ideal structure), then demonstrated that waves pass right around the central disc for the most part, even when a strong scatterer is placed inside.

So has Dr. Smith ushered in the age of Klingon cloaking devices? Not yet. He is the first to point out the limitations of his devices. They have a very small bandwidth, meaning they only work for a very small range of wavelengths. In addition, it's hard to manipulate matter on very small scales, so cloaking in the optical range is still a technical challenge, even for a single frequency. To effective cloak a device, one would need to cover a large range of frequencies.

Cloaking was more a proof of principle than The Next Big Thing. More practical applications include antennas and lenses that can do things they don't tell you about in freshman physics.

The mechanism behind cloaking --- an effective warping of spacetime --- got me thinking about general relativity. Are there gravitational object that could actually warp spacetime in the same way, so that light would pass right around them? Black holes pull everything in. I suppose a very dense region of antigravity would be required to deflect light around an object. Still, if this were possible, the cloak would work at all frequencies, because the actual geodesics of spacetime would curve around the object. It would not be the result of an effective dielectric constant that depends on frequency. Light, particles, rocks, and anything else would travel along the same geodesics. It would be cloaked from everything, not just light!