Zero refractive index

By Jeff Hecht
The latest example of the amazing versatility of metamaterials is the demonstration of one that has a refractive index of zero, just reported in Physical Review Letters . Theorists had predicted the possibility of zero-refractive-index materials, and some similar effects have been reported, but the metal-clad glass waveguide developed by Albert Polman's group at the Center for Nanophotonics of the FOM Institute AMOLF (Amsterdam, Netherlands) with Nader Engheta of the University of Pennsylvania (Philadelphia, PA) is the first to have a near-zero index throughout.

Zero-index materials, like negative-index materials , do not occur in nature, but can be built by assembling subwavelength elements into a structure designed to have the desired characteristics. The left part of the figure shows an electron microscope image of the metamaterial, a small slab of glass encased in silver forming a waveguide 200 nm wide and 2 µm long. The strong interaction between the metal and the glass on that scale gives an entire waveguide an effective refractive index of 0 at 770 nm.

Electron microscope image of a zero-index waveguide, showing a silver-coated nanoscale glass slab 200 nm wide and 2 µm long. The images at right compare the standing-wave pattern visible in a 400-nm-wide tube which disappeared in a 190-nm-wide tube, showing the material has a refractive index of zero at 770 nm. (Courtesy of Albert Polman)

The phase velocity of light is the speed of light divided by the refractive index of the medium, so phase velocity should be infinite for a zero-index material. Similarly, wavelength in a zero-index material should be infinite because it equals the wavelength in vacuum divided by refractive index. To study how the light behaved, Polman and colleagues used a technique they had developed earlier called "cathodoluminescence spectroscopy" to examine light waves in waveguides at various widths. When the index was above zero in a 400 nm waveguide, the light formed standing waves showing normal light propagation, as shown in the figure. But for a 190 nm waveguide the index was near zero, and the standing waves disappeared, as shown at right in the figure, indicating nearly constant phase and nearly infinite phase velocity and wavelength through the waveguide.

Infinite phase velocity does not violate Einstein's cosmic speed limit because phase velocity cannot carry information. Group velocity, the speed of a modulated optical signal, decreases with the refractive index below one, eventually reaching zero for a zero-index material.

That's not all that happens. "As the index approaches n=0 the losses increase, damping out the waves. The index then becomes a complex number of which the real part is 0," Polman told me in an email. That means no light is left to travel at infinite speed after a short distance. Wenshan Cai of Georgia Tech, who wrote a Viewpoint for the online publication Physics , told me the light should travel about 50 to 100 µm--far enough to be useful in integrated optics, but not over macroscopic distances.

A 2011 report of zero refractive index was based on different physics, combining two photonic-crystal materials, one with positive index and the other with negative index, so the net phase advance through the entire structure is zero. A key difference is that the building blocks of photonic-crystal materials are large enough to be seen by the wave, typically half a wavelength, but those of metamaterials are much smaller, so the incident wave responds to it as if it was a bulk material.
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