When two periodic 2D patterns are stacked onto each other with a slight twist, a third larger pattern called a moiré lattice emerges. The study of moiré patterns in layered crystals has captivated scientists ever since it was demonstrated that two sheets of graphene can run the gamut of electronic properties – including superconductivity, magnetism and Mott insulation – simply by varying the twist angle between the sheets. Recently, the optics community has joined the bandwagon and now a team of researchers, led by Fangwei Ye from Shanghai Jiao Tong University, has replicated the moiré effect in 2D lattices made of light.
The researchers “stacked” two 2D optical lattices by interfering two light beams. Before interfering, one beam was intercepted with two prepatterned masks that were rotated with respect to one another. The masks altered the beam’s intensity and phase, imprinting the patterns onto the beam like a stencil. The pattern is then projected onto a strontium barium niobite crystal. This moiré pattern can be tuned by the relative intensity of the interfering light beams and rotation angle between the mask patterns.
“Our work was inspired by the ‘magic’ angle in bilayer graphene,” Ye says. “We wondered, how will light waves respond if we stack two optical lattices? We’re the first to study the physics behind photonic moiré lattices.”
Wave localization
The researchers investigated how a third light beam, the probe, evolved when it was passed through the moiré pattern. At sufficiently high intensity contrasts between the first two moiré beams, the probe maintained its initial shape with little angular spread, a process known as wave localization.
Light waves undergo diffraction and diffusion, resulting in their tendency to spread out like the rays from a flashlight. The ability to counter this spreading is important for preventing information loss in optical communications.
Moiré lattices offer a new way to localize light in 2D, Ye and his team have found. This mirrors why electrons superconduct or freeze in their tracks in twisted bilayer graphene: flat energy bands. Photons in flat energy bands are packed into a narrow spectrum of energies, which supports only the modes that resist diffraction.
Moiré studies to come
Given that moiré lattices in light and 2D crystals share similar flat-band phenomena, the researchers recognize that their optical system can be used as a proxy to study moiré physics in 2D crystals. Moiré photons approximately follow the Schrodinger Equation, the governing rule of electrons. Optical systems are also easier to work with compared to 2D crystals, which tend to restructure into more energetically favourable configurations.
“That’s exactly why optics guys [referring to his team] can ‘simulate’ some physics for the condensed matter guys in the optical lab,” Ye said.
‘Magic-angle’ graphene is an unconventional superconductor
This flat-band phenomenon is not infallible. For instance, light localization is lost at certain twist angles. To make their localization strategy more robust, Ye and his team aim to generate solitons – solitary waves that do not change shape as they move – in their moiré lattices. In fact, Ye suspects that soliton formation might be uniquely easier in moiré lattices.
“Since there’s almost no diffraction in a moiré lattice, we don’t need strong nonlinearity (such as high laser powers) to form solitons. That makes life easier.”
The research is reported in Nature.
