Analogs of quantum-Hall-effect edge states in photonic crystals

Abstract

"Photonic crystals" built with time-reversal-symmetry-breaking Faraday-effect media can exhibit "chiral" edge modes that propagate unidirectionally along boundaries across which the Faraday axis reverses. These modes are precise analogs of the electronic edge states of quantum Hall effect (QHE) systems, and are also immune to backscattering and localization by disorder. The "Berry curvature" of the photonic bands plays a role analogous to that of the magnetic field in the QHE. Explicit calculations demonstrating the existence of such unidirectionally-propagating photonic edge states are presented.

Fiber guiding at the Dirac frequency beyond photonic bandgaps

“…Close to the Dirac frequency, photon transport in the transverse plane of the lattice is describable by the massless Dirac equation 14,15 :…”

“…This relativistic quantum mechanics model can be adopted to optics by a slight modification to the interpretation of the modal function. In photonic crystals, the wave function y 1,2 / e 6ih /r represents the envelope amplitude of a basis function (Bloch state) 14 , and the basis wave function intrinsic to a cylindrical geometry is a cylindrical wave function 17 w / J 0 (Kr), where K54p/(3a). Therefore, at the Dirac frequency, the physical quantities E z and H z in the photonic crystal are characterized by J 0 (Kr)e 6ih /r.…”

“…Photonic crystals have been studied extensively for their bandgap 1 and special in-band dispersion effects such as negative refraction 13 . However, another really interesting feature of photonic crystals is the Dirac points that appear at corners of the Brillouin zone [14][15][16][17] . A Dirac point, as illustrated in Figure 1, is a conical singularity surrounded by a region of linear dispersion in the band structure of triangular, hexagonal, or kagome lattices.…”

Light Guiding by Effective Gauge Field for Photons

“…However, it is a nontrivial task to generate an effective gauge field for photons [5][6][7][8][9][10]18]. In this section, we propose a realization of optical wave guiding by an effective gauge field.…”

“…Photons are neutral particles, and hence there is no naturally existing gauge field that couples to photons. Nevertheless, in recent years, various mechanisms for creating effective gauge field for photons have been proposed [5][6][7][8][9][10][11][12][13][14] and demonstrated [15][16][17]. In particular, it has been pointed out by Fang et al [18] that a photonic gauge field can be created in a dynamically modulated photonic structure by controlling the modulation phase.…”