What are Electromagnetic Metamaterials?
Materials interact with light and other electromagnetic fields. Because of this, materials can be used to control light in various ways, forming the basis for optical devices. A lens, for example, is a device that takes rays of light and causes them either to converge or diverge. The properties of a lens are related to the material of which it is made, as well as its shape. Optical fibers and waveguides represent another example optical devices: optical fibers are formed by 'pulling' carefully designed combinations of glasses, and can be used to guide light over surprisingly large distances.
The quality and diversity of optical devices is, at least in part, determined by the available range of electromagnetic properties of the materials used to make the devices. But, existing materials display only a subset of the electromagnetic properties that are theoretically available. One way to expand the available range of material properties is by adjusting the composition of materials at the molecular level using chemistry. Another approach is to broaden our definition of a material to include artificially structured media--that is, media in which the electromagnetic response results from a macroscopic patterning or arrangement of two or more distinct materials.
The DARPA Metamaterials logo |
Over the last several years there has been a surge of interest in artificiall materials because of their potential to expand the range of electromagnetic properties in materials. In a paper published in 2001, Rodger Walser from the University of Texas, Austin, coined the term 'metamaterial' to refer to artificial composites that '...achieve material performance beyond the limitations of conventional composites.' The definition was subsequently expanded by Valerie Browning and Stu Wolf of DARPA (Defense Advanced Research Projects Agency) in the context of the DARPA Metamaterials program that started also in 2001. Their basic definition:
Metamaterials are a new class of ordered composites that exhibit exceptional properties not readily observed in nature. These properties arise from qualitatively new response functions that are: (1) not observed in the constituent materials and (2) result from the inclusion of artificially fabricated, extrinsic, low dimensional inhomogeneities.
While the original metamaterials definition encompassed many more material properties, most of the subsequent scientific activity has centered on the electromagnetic properties of metamaterials
Electromagnetic Parameter Space
Electromagnetic waves are governed by Maxwell's equations, which show that these waves contain both electric and magnetic fields (see the figure below). When an electromagnetic wave enters in a material, the fields of the wave interact with the electrons and other charges of the atoms and molecules that compose the material, causing them to move about. This interaction alters the motion of the wave--changing its speed or wavelength, for example. The details of wave-matter interaction can get very complicated; however, as complicated as it is, the electromagnetic response for most materials can be distilled in a relatively simply manner in Maxwell's equations.
Anatomy of an Electromagnetic Wave: Electromagnetic waves consist of in-phase, oscillating electric and magnetic fields. Plane waves, as shown here, have electric and magnetic fields that are polarized at right angles to each other. The field directions in a plane wave also form right angles with respect to their direction of travel (the propagation direction). |
Two of Maxwell's equations, appropriate to describe wave propagation within a material, are summarized in the figure to the right. Without going into the detail of what these equations mean, or how they are solved, we can observe the following: There are two fields that are coupled in these equations--one electric (E) and the other magnetic (H). In addition, there are two other parameters, called the electric permittivity (Greek symbol epsilon) and the magnetic permeability (Greek symbol mu).
Maxwell's equations in a material. |
Most of us have a certain concept as to what constitutes a material. We understand that materials have intrinsic properties--cut a piece of plastic in half, each half is still a piece of plastic. We also know that, ultimately, plastic is composed of discrete molecules that may have properties very different from those of the composite. But, since molecules are on the microscopic or nanoscale, visible light doesn't 'see' the individual molecules, and thus a piece of plastic resembles a perfectly smooth object. We call such a material homogeneous if its properties do not vary between any two points within the material.
Glass, plastic, metal--all familiar materials have intuitive features that make them relatively easy for us to identify. But whatever the physical aspects of a substance are that provide the cues for us to identify it as a material, what constitutes a material for electromagnetic waves is very different. From the point-of-view of Maxwell's equations, a material is defined, at least to a first approximation, as some collection of objects (whether atoms, molecules, composites or anything else) that can be described by a permittivity and a permeability. That's the end of the story.
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Knowing that the permittivity and permeability are the only relevant material parameters for electromagnetic waves, we can imagine a 'material parameter space' into which all materials can be placed. On one axis we plot values of the permittivity, and on the other we plot values corresponding to the permeability. In the plot to the left, the material parameter axes intersect at the origin (where both permeability and permittivity are equal to zero). In this crude but reasonably descriptive approximation, we can imagine that all materials--as far as electromagnetic waves are concerned--are represented by points on this map. The region in the upper right quadrant is where the permittivity and permeability are both positive. Since most known materials have this property, this region of material parameter space has been the most explored. However, the larger part of the map--three quarters, in fact--has been much less explored. This is because materials are just not so easily available in these regions. In fact, materials that lie in the third quadrant, where the permittivity and permeaiblity are both less than zero, do not appear in nature at all!
While nature appears to have limitations in terms of the material properties that are found, artificially structured metamaterials are not limited in the same way. The hope, then, is that more of the material parameter space can be made accessible with metamaterials. An important step towards this goal was made in 2000, when a metamaterial was demonstrated to have a permittivity and permeability both less than zero.
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