Thursday, May 12, 2016

Fractal "Superlens" Defeats Diffraction Limit

New advances in the design of metamaterials—specially engineered substances which have properties not found in nature—may have just overcome one of the major challenges in designing compact optical devices. The breakthrough, reported in Physical Review B, could allow scientists to study nanoscale structures using visible light: a task that was, until now, thought impossible.

Electromagnetic radiation of any kind, whether we're talking about visible light, radio waves, or x-rays, has a specific wavelength based on its energy. The more energy a photon has, the shorter its wavelength is. This presents something of a problem, however, when trying to study things on an extremely small scale. When an object is smaller than the wavelength of the light it's illuminated with, it's very difficult to get a good picture of that object—photons can pass right through it, or bounce off at odd angles. It's a bit like trying to get a good photo of a person using a camera that picks up radio waves; you might be able to tell there's something there, but the picture would inevitably come out "fuzzy"—the photons can't be focused down onto a small enough area. This is why ultra-detailed photos of microscopic structures, like the pollen grains pictured below, often have to be taken with a special tool called a scanning electron microscope, which doesn't use light at all but rather—as the name suggests—electrons.

Pollen grains, imaged using a Scanning Electron Microscope.
This resolution limit—called the diffraction limit—depends on three things: the wavelength of the light being used, the size of the lens, and the index of refraction of the medium that light is passing through. One way to get around this limit is to use a larger lens, or bring the lens closer to the object. However, this only works up to a point, and gets unwieldy pretty quickly as a lens scales up.

Another way to improve an optical system's resolution is to use light of a higher energy, which has a correspondingly shorter wavelength. However, this presents problems of its own. For instance, when trying to study a biological molecule like DNA, photons of higher energy than visible light have the potential to ionize the molecule—tearing electrons loose from their atoms and influencing the molecular structure.

Split-ring resonators can have a negative
index of refraction, a property not found
in any natural material.
However, the other manipulable variable in the diffraction limit equation, the refractive index, has shown great promise in recent years. More than a decade ago, the invention of metamaterials like the split-ring resonator (left), which has a negative index of refraction for certain wavelengths, promised to turn modern optics on its head and make problems like this a thing of the past. There have been stumbling blocks, however—split-ring resonators are only good at certain wavelengths, and tend to be very "lossy"—a signal needs to be very bright in order to make it through and still be intelligible. But all that could be due to change soon, with the new technique reported in this new paper.

The authors of the paper used a new design for their resonating "superlens". Instead of the split-ring design, theirs is based on a geometric fractal shape known as the Hilbert curve.
This graphic shows the construction of a fractal Hilbert curve, built from an infinite number of self-similar, repeating shapes.
The new design—featuring a single, long wire bent into the incredibly complex shape shown above, functions at a broad range of energies within the microwave spectrum, giving researchers the ability to focus these photons down onto an area one fifteenth the size of the microwaves' wavelength. This unique ability stems from the "self-similar" fractal shape, where identical structures arise at different scales.
A graphic illustrating the new design, where a Hilbert curve-shaped
resonator focuses microwaves down onto a detector.
Image Credit: M. Dupré, et al. Phys. Rev. B. (2016)
It might be odd to think of a wire acting as a lens, but fundamentally the process is pretty similar to how cell phones use antennae to catch and transmit the microwaves that make up a cellular signal. The researchers hope their discovery will lay the groundwork for the development of a similar system that functions at visible wavelengths. If the technology could be applied to visible light, it could enable scientists to study fragile molecules, or even allow us see deep into space with greater resolution than ever before.

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