A Novel Approach to Negative Refraction

An “extraordinarily strong” negative refractive index as large as -700 — more than 100 times larger than most previously reported — was achieved in metamaterials using a new technique developed by scientists at the Harvard School of Engineering and Applied Sciences (SEAS) in collaboration with Weizmann Institute of Science in Israel.

In a vacuum, light travels so fast that it can circle the Earth more than seven times within the blink of an eye. When light propagates through matter, however, it slows by a factor typically less than 5. This factor, called the refractive index, is positive in naturally occurring materials, and it causes light to bend in a particular direction when it shines on water or glass, for example.

Over the past 20 years, scientists have created artificial materials whose refractive indices are negative; these negative-index metamaterials defy normal experience by bending light in the “wrong” direction. They have been celebrated by both scientists and engineers for their unusual ability to manipulate electromagnetic waves and for their potential to be harnessed for technologies such as 3-D cloaking.

The chamber of the probe station where Donhee Ham’s research group tests the new metamaterials. (Image: Eliza Grinnell, Harvard SEAS Communications)

Now, the Harvard SEAS and Weizmann Institute scientists have demonstrated a drastically new way of achieving negative refraction in metamaterials by applying kinetic inductance, which is the manifestation of the acceleration of electrons subjected to electric fields, according to Newton’s second law of motion.

"This work may bring the science and technology of negative refraction into an astoundingly miniaturized scale, confining the negatively refracting light into an area that is 10,000 times smaller than many previous negative-index metamaterials," said principal investigator Donhee Ham, Gordon McKay Professor of Electrical Engineering and Applied Physics at SEAS.

The researchers' change in strategy from using magnetic inductance to kinetic inductance is based on a simple shift in ideas.

"Magnetic inductance represents the tendency of the electromagnetic world to resist change according to Faraday's law," Ham said. "Kinetic inductance, on the other hand, represents the reluctance to change in the mechanical world, according to Newton's law."

"When electrons are confined perfectly into two dimensions, kinetic inductance becomes much larger than magnetic inductance, and it is this very large two-dimensional kinetic inductance that is responsible for the very strong negative refraction we achieve," said lead author Hosang Yoon, a graduate student at SEAS. "The dimensionality profoundly affects the condensed-matter electron behaviors, and one of those is the kinetic inductance."

The experimental setup in Donhee Ham’s lab, shown here, tests the new metamaterials, which are fabricated on tiny chips. The metamaterials themselves are inside the probing chamber at the bottom right. Imaged through the black microscope, they appear on the screen at the top of this image. (Image: Eliza Grinnell, Harvard SEAS Communications)

Ham and Yoon employed a two-dimensional electron gas (2DEG) to obtain the large kinetic inductance. The very “clean” 2DEG sample, fabricated by Vladimir Umansky of Weizmann Institute, forms at the interface of two semiconductors: gallium arsenide and aluminum gallium arsenide.

Ham's team sliced a sheet of 2DEG into an array of strips and used gigahertz-frequency electromagnetic waves to accelerate electrons in the leftmost few strips. The resulting movements of electrons in these strips were "felt" by the neighboring strips to the right, where electrons are consequently accelerated.

In this way, the device propagates an effective wave to the right, in a direction perpendicular to the strips, each of which acts as a kinetic inductor because of the electrons' acceleration therein. This effective wave exhibited what the researchers call a "staggering" degree of negative refraction.

Not only can this new technology localize electromagnetic waves into ultra-subwavelength scales, but it is also very small in scale. Demonstrated with microwaves, this concept may prove important for operating terahertz and photonic circuits far below their usual diffraction limit, and at near field, if it is extended to other regions of the electromagnetic spectrum. It may also one day lead to extremely powerful microscopes and optical tweezers, which are used to trap and study minuscule particles like viruses and individual molecules.

(Left) Donhee Ham, Gordon McKay Professor of Electrical Engineering and Applied Physics at SEAS, is shown lecturing at the Harvard Thinks Big event. (right) Doctoral student Hosang Yoon, a member of Ham's lab and lead author of the paper. Yoon is a graduate of Seoul National University in Korea, where he ranked number one with a GPA of 4.28 out of 4.30 — a feat Ham, who attended the same college, calls "legendary." (Images: (left) Ben Sharbaugh, Harvard News Office; (right) Hosang Yoon)

For now, the device operates at temperatures below 20 K. However, similar results can be achieved at room temperature using terahertz waves, which Ham's team is already investigating by using graphene as an alternative two-dimensional conductor.

"While electrons in graphene behave like massless particles, they still possess kinetic energy and can exhibit very large kinetic inductance in a non-Newtonian way," Ham said.

The findings, supported by the Air Force Office of Scientific Research, were reported in today’s issue of Nature.

For more information, visit: www.seas.harvard.edu