Topological protection of photonic mid-gap cavity modes
  Defect modes in two-dimensional periodic photonic structures have found use in a highly diverse set of optical devices. For example, photonic crystal cavities confine optical modes to subwavelength volumes and can be used for Purcell enhancement of nonlinearity, lasing, and cavity quantum electrodynamics. Photonic crystal fiber defect cores allow for supercontinuum generation and endlessly-single-mode fibers with large cores. However, these modes are notoriously fragile: small changes in the structure can lead to significant detuning of resonance frequency and mode volume. Here, we show that a photonic topological crystalline insulator structure can be used to topologically protect the resonance frequency to be in the middle of the band gap, and therefore minimize the mode volume of a two-dimensional photonic defect mode. We experimentally demonstrate this in a femtosecond-laser-written waveguide array, a geometry akin to a photonic crystal fiber. The topological defect modes are determined by a topological invariant that protects zero-dimensional states (defect modes) embedded in a two-dimensional environment; a novel form of topological protection that has not been previously demonstrated. 
Jiho Noh, Wladimir A. Benalcazar, Sheng Huang, Matthew J. Collins,   Kevin Chen, Taylor L. Hughes, Mikael C. Rechtsman
cond-mat.mes-hall physics.optics