Light–matter interactions

Topological photonics Topology, a branch of mathematics that recently found wide applications in science, is concerned with the invariant properties of an object undergoing continuous transformation. Consequently, any physical quantity expressed by discrete topological invariants is unprecedentedly robust against large perturbations. The 2016 Nobel Prize in physics was awarded for research on topological physics. Likewise, photonics is also benefiting from band topologies—discrete global configurations of wave-functions in the Brillouin zone of periodic systems such as photonic crystals. Using topological photonics, photon transport without any localization and scattering loss is now feasible. Since the concept of photonic crystals was first proposed in 1987, Group L01 has been working on experiments with periodic dielectric materials. In 1994, our group reported laser-assisted crystallization of polystyrene spheres and strontium titanate (SrTiO3) particles (n = 2.5) with lattice constants of ~1.5 μm (1). Such photonic crystals are characterized by their band structures, while the hidden freedom of band topology was only unveiled in 2005. Topological photonics started with the proposal of a one-way waveguide as the edge state of a two-dimensional (2D) photonic crystal, which was experimentally demonstrated in 2009. In the following year, our group published the second set of experimental results (2) on this topic in the context of microwave frequencies. The idea is illustrated in Figure 1A. The edge mode of a magnetic photonic crystal has a gapless dispersion curve traversing the whole bandgap, connecting the bulk bands above and below. The group velocity of the edge mode has only one sign and propagates in one direction only, without scattering from arbitrary defects. Such a one-way edge state is analogous to the chiral edge state in the quantum Hall effect, providing a novel mechanism for planar integration of nonreciprocal photonic devices. In three dimensions, optical fibers are the best light guides and are ubiquitous in modern technologies. Using high-dimensional band topologies, we have shown that one-way fibers can be designed using 3D magnetic photonic crystals (3), as illustrated in Figure 1B. These