By 2003, researchers had verified that not only were these engineered materials possible, but they also could enable "perfect" lenses that were nevertheless flat. Now metamaterials are being demonstrated not just for electromagnetic waves, but for anything that can be described by wave functions, thereby reversing the laws of nature for acoustic engineering, ultrasound, microwaves, light and magnetism.

"What we have is a larger version, structurally, of a photonic crystal, adjusted for the wavelength of ultrasound," said John Page, a professor at the University of Manitoba in Winnipeg. "Our metamaterials use artificial atoms arranged in a lattice that filters acoustic wavelengths the way that photonic crystals filter optical wavelengths."

Metamaterials substitute macroscopic objects for atoms in a giant crystalline lattice-here made from tungsten carbide beads surrounded by water and packed flat into planes, with a spacing between beads set to a subwavelength of the wavelength you want to affect. For instance, microwave metamaterial makers set their spacing to 1/20 of the wavelength they want to filter.

"Today we use about 7,000 beads per layer for our flat acoustic lens," said Page. "We use 1-mm balls when we want to affect frequencies of around 1 MHz, but in principle you could scale this approach to audible frequencies, just by using much larger structures."

In Page's phononic-crystal metamaterial (where a phonon is a quantum of sound, just as a photon is a quantum of light), the spacing of the artificial atoms creates band-gaps by perfectly reflecting those wavelengths back on themselves, but at an opposite phase, thereby canceling them out. The gap in the band of frequencies is thus created in the metamaterial.

In photonic crystals, reversing Snell's Law to a left-hand rule is equivalent to a negative index of refraction (all natural materials have a positive index of refraction). Page's recent demonstration showed that a negative index of refraction is possible for acoustic lenses too.

Page demonstrated the world's first flat ultrasonic lens in July. Before Page, engineers had to construct a fluid-filled convex acoustic lens to focus ultrasound, but flat lenses will provide sharper focusing, better depth of field and be cheaper to manufacture. "Now engineers can take a point source of ultrasound and focus it on the other side with a flat acoustic lens," said Page.

Since demonstrating its flat acoustic lens, Page's research group has built a prism-shaped acoustic lens that the group hopes will dispel any lingering doubts that a negative index of refraction can be efficiently harnessed to build real acoustic lenses.

"Lately we have built some very beautiful experiments that demonstrate this negative index of refraction with a new prism-shaped acoustic lens that clearly shows that you can bend ultrasound negatively," said Page.

According to Page, even though acoustic waves are based on movement within a medium-instead of on the "wavelike" functions of particles-the same principles rule: that is, positive permeability and permittivity.

"The quantum of a sound wave is a phonon-which does not have mass like a photon, but they are nevertheless a quantum of energy, and thus also have an analog to negative permeability and permittivity," said Page.

Page said photonic and phononic crystals both work because the wave front follows the direction of group or pulse velocity of the wave, rather than its phase velocity. The pulse velocity is the speed of the top of a pulse, whereas the phase velocity is the speed of the entire wave taken as a whole. Because of the metamaterial's band structure, the direction of the group velocity can diverge from the direction of the phase velocity. In fact, Page's metamaterial bends the group velocity at the negative angle of ordinary direction of the phase velocity, resulting in a negative index of refraction.

"In essence, you get the waves bending back on themselves in a negative direction inside the crystal, then when they leave it they bend back in the direction they started out in, and that is how you form a focus on the far side of the crystal, because they crossed over inside it," Page said.

Today, acoustic lenses for ultrasound resemble a traditional lens for light, except that they are usually filled with water (making a concave lens diverge, whereas a convex lens focuses). But with phononic metamaterials, the acoustic lens becomes flat like a fresnel lens.

Page's artificial crystal metamaterial was constructed by first patterning a substrate to define precisely where the artificial atoms of the first layer reside. With walls on the sides, the other layers are allowed to self-assemble above the first patterned layer, by merely pouring ball bearings in atop the patterned layer and allowing them to settle into planes.

For his flat-lens demonstration, Page used .8-mm tungsten carbide beads surrounded by water, with the beads closely packed in a face-centered cubic crystal structure along the body diagonal ("111" crystal direction). The large acoustic mismatch for this combination of materials enabled a complete bandgap for frequencies between 0.98 and 1.2 MHz.

"We build these crystals in water-so water is our continuous-phase [material]-and then we have this array of touching balls, which scatter the ultrasonic waves by virtue of the interplanar distance between crystallographic planes," said Page. "They also Bragg scatter, giving rise to a diffraction peak at its bandgap frequency and negative-index-of-refraction properties not available in normal materials."

The lens' interesting flat-focusing function was found by Page's group to be above the band gap-that is, at frequencies between 1.57 and 1.63 MHz. At 1.57 MHz, the waves were focused into a tight spot (about 5 mm). At 1.6 MHz, however, the incident beam became spread out by the crystal in a field pattern. Thus, the transmitted field pattern changed completely with only a 2 percent change in frequency.

The smallest achieved diameter of the focal spot was 2.4 mm, which is very close to the diffraction limit, and its depth of field was 44 mm. Also, the focal length could be smoothly varied by slightly changing the frequency.

Sound-bending effects

Page predicted that with his approach, a variety of acoustic superlenses can now be created-from lenses with ideal focusing characteristics to beam-shaping lenses with long focal zones. In addition, according to Page, all the properties of phononic crystal are scalable too, so his work with ultrasound will eventually be used to shape new sound-bending effects that provide new tools for creating sound beams.

For now, the researchers have achieved a metamaterial acoustic lens that is as good as a traditional acoustic lens. For its next milestone, however, the group wants to demonstrate a flat fresnel-like lens that actually outperforms a traditional acoustic lens.

"In our first experiment we have gotten results as good as what you get with a traditional lens," said Page. "Next we want to use the unusual properties of our lens to demonstrate that we can beat the wavelength limit on traditional lenses, to create a so-called super or perfect lens in acoustics. Such a perfect lens has already been demonstrated at microwave frequencies."

Separately, Xiangdong Zhang of Beijing Normal University and Zhengyou Liu of Wuhan University have created a computer simulation of how to design two-dimensional phononic crystals that they claim enable "left-handed" materials. The simulation's phononic crystals contained acoustic gaps between columns of water and mercury, which only allowed certain wavelengths of sound to pass through the material.