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Finite-difference methods used to model photonic wave localization in 3D quasicrystals

By Aditi Risbud April 12, 2017
Schematic representation of photonic wave localization in a three-dimensional icosahedral quasicrystal. Incident photonic waves are trapped in the quasicrystal due to localization. Image courtesy of Kahyun Hur, Korea Institute of Science and Technology.

Scientists at the Korea Institute of Science and Technology (KIST), led by Kayhun Hur, have made the first theoretical demonstration of the localization of photonic waves in a three-dimensional (3D) quasicrystal. This promising finding suggests that quasicrystals could one day be precisely engineered to control localization of electrons, phonons, and photons.

Quasicrystals are a unique type of crystalline material with local order but no long-range periodicity. The discovery of these materials in aluminum-manganese alloys garnered materials scientist Dan Shechtman the 2011 Nobel Prize in Chemistry. Quasicrystals exhibit unusual properties due to their mixed structural characteristics. Because translational symmetry strongly governs the transport properties of every form of wave, wave transport in quasicrystals—including localization—has been a long-standing area of research interest. In particular, icosahedral quasicrystals possess a 3D photonic bandgap, which could allow for control of light at the nanoscale.

In crystalline materials, waves with wavelengths commensurate with the crystal’s periodicity can transmit without scattering loss, leading to ballistic transmission. In contrast, because of frequent scattering, wave transport in disordered materials is usually described by random walks, resulting in diffusive transmission. Quasicrystals exhibit both diffusive transport due to their aperiodicity, along with a well-defined coherent path due to their crystalline nature. These materials therefore provide a compelling test system to investigate wave localization in three dimensions.

As reported in a recent issue of Nature Physics, the KIST team used finite-difference methods to model photonic wave localization in a 3D icosahedral quasicrystal. Wave localization phenomena were investigated by analyzing the spatial and temporal evolution of photonic waves. Using photonic band structures of quasicrystals called rhombic triacontahedrons (see Figure), the research team generated transmission spectra and compared these to a diamond structure for reference. Their findings demonstrate that wave localization occurs in quasicrystalline materials. This fundamental insight will help researchers to determine how to control or steer waves in quasicrystals.

“This proof-of-principle study breaks new ground by showing that it is possible to localize photonic waves even in a disorder-free medium solely relying on the absence of translational invariance in quasicrystals,” says Bohm-Jung Yang of Seoul National University in South Korea, who was not involved in the research.

Hur and colleagues suggest that wave localization in quasicrystals can be utilized for a variety of applications related to wave transport: replacing reflecting mirrors in lasers, incorporating quasicrystalline nanostructures into thermoelectrics as phononic insulators to improve the thermoelectric figure of merit, or as acoustic insulators. In addition, the superior wave trapping properties of quasicrystals make them excellent candidates as light-trapping layers in photovoltaics.

“Due to the universal features of wave transport in 3D quasicrystals, we believe there will be other, huge potential applications of these materials based on control of wave localization,” Hur says.

This article was originally published in MRS Bulletin.