Computer simulations suggest that unconventional refraction should be produced by certain kinds of collective excitation in 3D optical lattices. [Image: Lancaster University]
Scientists in the United Kingdom and Japan have carried out computer simulations showing how visible light passing through a 3D lattice of atoms can undergo negative refraction (Nat. Commun., doi: 10.1038/s41467-025-56250-w). The approach overcomes some of the limitations associated with artificial metamaterials, and the researchers say it should be achievable with existing laboratory setups.
An exotic optical phenomenon
Negative refraction is an exotic optical phenomenon in which light propagating from one medium to another bends not toward the normal, as in conventional refraction, but beyond the normal. First described theoretically in the 1960s, the effect has been observed in metamaterials—artificial materials usually consisting of arrays of subwavelength-sized elements that confer both negative permittivity and permeability.
Physicists at the University of California, San Diego, USA, first demonstrated negative refraction in 2000 at microwave frequencies. Invisibility cloaks operating in the same region of the electromagnetic spectrum were demonstrated a few years later. Since then, others have achieved similar results with sound waves.
Negative refraction has been observed at optical frequencies, but losses have so far hindered the realization of a number of eye-catching proposed applications, including optical invisibility cloaks and lenses with a resolution well beyond the diffraction limit. Part of the problem lies in precisely fabricating resonators on nanometer scales.
Researchers have already proposed demonstrating optical negative refraction in atomic arrays, but the schemes in question are based on quantum interference effects involving weak magnetic dipole transitions. According to Janne Ruostekoski, Lancaster University, UK, exploiting these transitions relies on experimental parameters—such as very high refractive indices at high densities—that are currently unachievable.
Carrying out detailed atomic simulations, they found that the much-sought-after effect should arise as an emergent phenomenon as atoms undergo collective scattering when held in an optical lattice.
Negative refraction with atoms
In the latest work, Ruostekoski and his colleague at Lancaster University Kyle Ballantine, working with Lewis Ruks, NTT Basic Research Laboratories, Japan, show that such conditions are not necessary for optical negative refraction. Carrying out detailed atomic simulations, they found that the much-sought-after effect should arise as an emergent phenomenon as atoms undergo collective scattering when held in an optical lattice.
The researchers simulated an infinite series of 2D planes of atoms, in which atoms are separated by distances smaller than the wavelength of light. Rather than considering specific types of atom, they instead modeled two kinds of electronic transition that are characteristic of certain metals—a two-level transition and a four-level process.
Working out the effect of the closely spaced atoms on an incoming optical laser beam, they found that the multiple scatterings experienced by the light induce a collective behavior, which they term transverse Bloch band resonances—an analogy of electron conduction bands in crystal solids. These collective excitations travel in the direction determined by light-mediated interactions between the atoms, which can be inverted compared with the normal propagation path, resulting in the trademark signature of negative refraction.
Simulation tests
Ruks and colleagues confirmed their results in simulations of less idealized, few-layer arrays and also showed that the negative refraction ought to exist across a range of conditions—including various laser frequencies, transmission directions and atomic spacings—and should be robust to experimental imperfections such as missing or fluctuating atoms.
The researchers are confident that their simulations are accurate, since they used a methodology that correctly predicted the outcome of previous experiments involving atoms that were held in optical lattices and exposed to weak resonant light. The team also says that putting its predictions to the test should be possible, given the high bar already set in similar experiments—including observations of anti-ferromagnetism in a 3D lattice featuring some 800,000 atoms.
Ruostekoski is cautious about the prospects for headline applications such as perfect lenses. But more generally, he says that the research “opens avenues for pursuing applications in highly controllable, clean systems and also possibilities for studying genuinely quantum effects in light transmission.” Some of the technical hurdles that need to be overcome first, he adds, include ensuring that few atoms go missing from the optical lattices and confining atoms tightly in sufficiently deep optical wells.