Optics, metamaterials and the first bastion of utility

Studying optics has always been fun because most of its assertions are not far removed from its first principles. Even if this doesn’t mean it’s fully understood (which won’t happen for as long as quantum mechanics has any mysteries), the simplicity of optics helps understand how an interferometer works just as easily as it is to understand how a magnifying glass does. At its heart, devoid of the deception of gravity and remaining an adherent of geometry, optics has for long been the domain of pure logic (at least if you don’t dig deep enough).

This perception is exemplified by the prism, which demonstrates how higher frequencies of light – or electromagnetic radiation in general – are refracted by greater amounts as the radiation passes from a lighter through a denser medium.

At the same time, what this quick intelligibility of the optical properties of materials begets is an invitation to mess with it. Consider: That violet light bends more than red has nothing to do with the dimensions of a prism; the tetrahedral shape only amplifies the extent of deviation. This means that the change in refractive index by frequency is a property of the material itself, not how it is shaped: a prism the size of the pyramids of Giza will behave the same way a prism the size of a frog does. This is possible because the response to light of different frequencies is dictated at the atomic level. Each atom’s electromagnetic interaction with the radiation changes according to the atomic structure and the radiation’s frequency.

And it’s only when each atom has the liberty to effect this response irrespective of the response of the material around it will Giza-pyramid prism and frog prism be able to have the same response. Take this non-locality away and you have – on the downside – none of the wonder of witnessing the first principles at play and – on the upside – the ability to deeply manipulate the predictable character of optical structures. That’s what a team of Portuguese scientists have achieved with a metamaterial prism that they built, which bends the red frequency of light more than the violet one, resulting in a reverse rainbow.

While the refractive index, n', increases with frequency in a conventional prism, the opposite happens in a metamaterial prism. Credit: Appl. Phys. Lett. 105, 264101 (2014)
While the refractive index, n’, increases with frequency in a conventional prism, the opposite happens in a metamaterial prism. Credit: Appl. Phys. Lett. 105, 264101 (2014)

Metamaterials are, at least, materials that are not naturally found and are products of human engineering. More deservingly, however, metamaterials are capable of feats so far removed from the first principles that their effects seem magical. In the example of the Portuguese reverse-rainbow prism, the metamaterial is actually an insulator material that has been embedded with a crisscrossing of metallic wires, like those made of copper, through which an electric current is passed. Such an arrangement violates the condition of non-locality: it makes the atoms’ response contingent upon changes in the electric field due to the wire, and because the wires traverse the cross-section of the metamaterial, atoms in one part are effectively influenced by atoms in another part through the intervening changes in the current.

Image: Geometry of the metamaterial (from another paper). Credit: Phys. Rev. B 79, 153109 (2009)*
Geometry of the metamaterial (from another paper). Credit: Phys. Rev. B 79, 153109 (2009)*
As the paper, published in Applied Physical Letters in December 2014, notes:

[The reverse rainbow] may be attributed to the fact that long metallic wires tend to obstruct the wave propagation more effectively for low frequencies, because the wires length is infinitely large in the unbounded metamaterial. Thus, the refractive index of the effective medium is increasingly large for lower frequencies, and in the limit of no loss, it diverges to +∞ in the static limit.

This unique response is characterized as an anomalous dispersion and attributed to non-local topology. And anybody who is familiar with the history of quantum mechanics knows the unsettling history of the study of non-locality. Most famously, Bell’s theorem requires that for quantum mechanics to be a complete theory, one of locality or realism must be untrue. When dealing with metamaterials, it is again the loss of locality that eliminates intuitive, logical behavior. Even if – thermodynamically speaking – the control volume has changed, the cognitive dissonance implied by the prism’s response as a whole to light is what makes it a metamaterial prism: a resource with which to leverage the non-classical properties of classical entities.

An equally counter-intuitive application is in negative refraction metamaterials. When a beam of light passes through a denser material, such as a slab of glass, it bends upon entering the material at a certain angle: the denser the material, the more the bending. At one point, the beam of light is bounced right back when the material becomes fully opaque. A slab of a negative refraction metamaterial, on the other hand, will refract the beam of light inward into itself, as shown below.

Image: An illustration of negative refraction. Credit: Wikimedia Commons
An illustration of negative refraction. Credit: Wikimedia Commons

This deceptively simple behavior has been shown to enable almost-lossless transmission in certain frequencies with a device called the split-ring resonator. Specifically, when you shine visible light on an opaque block of the kind of composite metamaterials that an SRR uses, it will be focused on the other side. This is not possible with conventional materials. The SRR itself consists of an interlocking sheet of fiberglass (as shown in the array above) wherein the right/front-aligned faces are embossed with two concentric copper split-rings and the left-back-aligned faces with single vertical wires.

A depiction of a split-ring resonator. Credit: Wikimedia Commons
A depiction of a split-ring resonator. Credit: Wikimedia Commons

The configuration is responsible for mimicking atoms’ interaction with the magnetic component of an electromagnetic wave, only at a much larger scale for the metamaterial to leverage. In such cases, engineers have been able to manipulate the metamaterial’s electric permittivity and magnetic permeability, which dictate its interaction with electromagnetic radiation. At this point, you realize, we are so far from the first principles that we might not have started have started from the first principles at all, only from a geometrically convenient macroscopic approximation.

Instead, it seems the comprehensibility of optics has rendered its first principles especially susceptible to manipulation, so much so that even its newly minted macroscopic consequences are no longer recognizable. A glance at the Wikipedia page for metamaterials is peppered with applications in optics more than anything else, possibly because the interaction of electromagnetic radiation with the surface of materials is the first – and thus most accessible – bastion of utility.

Potential applications of metamaterials are diverse and include remote aerospace applications, sensor detection and infrastructure monitoring, smart solar power management, public safety, radomes, high-frequency battlefield communication and lenses for high-gain antennas, improving ultrasonic sensors, and even shielding structures from earthquakes. The research in metamaterials is interdisciplinary and involves such fields as electrical engineering, electromagnetics, classical optics, solid state physics, microwave and antennae engineering, optoelectronics, material sciences, nanoscience, semiconductor engineering, and others.

*The image is licensed from the American Physical Society. It may not be reproduced without permission from APS.