Dust mix could negatively refract light

Fabricating a negative-refractive-index lens that works well at visible wavelengths and is of reasonable size would be a coup for any photonics researcher.

Nov 1st, 2005
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Dust mix could negatively refract light

Fabricating a negative-refractive-index lens that works well at visible wavelengths and is of reasonable size would be a coup for any photonics researcher. Such a lens, made of a flat slab of metamaterial-a properly designed array of subwavelength resonant structures-would focus light without aberrations. But metamaterials are complex structures, containing arrangements of wires, conducting arcs, and so on; they benefit if they have array spacing much smaller (ten times or so) than the wavelength of the light they are to focus. Creating a practical metamaterial for visible light is a tall order indeed.

But what if periodic arrays were not required? Then one could fabricate millions of subwavelength structures and dispense them into a mold like sand to make a lens. And what if the nanostructures themselves were almost as simple as grains of sand?


When the negative-phase-velocity parameter ρ for a material is negative, the material can negatively refract light. A hypothetical substance consisting of well-mixed nanoparticles of two properly chosen (also hypothetical) dielectrics has a ρ that dips below zero for volume fractions (fa) ranging between 0.28 and 0.92. The two dashed lines represent ρ for each of the two constituent materials.
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That’s what Akhlesh Lahktakia of Pennsylvania State University (University Park, PA) and Tom Mackay of the University of Edinburgh (Edinburgh, Scotland) asked themselves. They modeled homogeneous mixtures of two hypothetical isotropic dielectric-magnetic materials, each pulverized to 1/10-wavelength-size (or smaller) grains, then the two intermingled homogeneously.1

For the composite, however, the researchers found that a certain parameter ρ (the sum of the inverse dielectric loss factor and the inverse magnetic loss factor) can dip below zero for certain volume fractions of the two components. A negative ρ signifies that a substance supports negative phase velocity and can negatively refract.

The refractive indices of the hypothetical substances allowed for an “imaginary” component, which in practical terms means that the substances could attenuate light as well as refract it. For this reason, a lens made of a homogeneous composite may have to be very thin-a fraction of the wavelength if the attenuation is not sufficiently small, says Lahktakia.

The challenge is to translate this hypothetical material into something real. The researchers, who are theorists, not materials scientists, have no specific materials in mind for the components. “The knowledge base of materials (either in part or completely) extends to a few million materials,” notes Lahktakia. “Now that we have mathematically shown the possibility, experimentalists can be inspired to realize this architecture for negatively refracting materials.” He notes that geometry could also play a part-for example, instead of spherical grains, a composite could contain spheroidal and ellipsoidal grains, or even grains with a distribution of shapes.

“The first exemplar, indicated in our paper, is not going to be the only one,” he says. “Other regions of the materials-property-parameter space need to be looked into, now that it is known that such a route is possible.”

John Wallace

REFERENCE

1. arXiv:physics/0505005 v1 (April 30, 2005).

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