Topologically protected refraction of robust kink states in valley photonic crystals

Abstract

Recently discovered1,2 valley photonic crystals (VPCs) mimic many of the unusual properties of two-dimensional (2D) gapped valleytronic materials [3][4][5][6][7][8][9] . Of the utmost interest to optical communications is their ability to support topologically protected chiral edge (kink) states [3][4][5][6][7][8][9] at the internal domain wall between two VPCs with opposite valley-Chern indices. Here we experimentally demonstrate valley-polarized kink states with polarization multiplexing in VPCs, designed from a spin-compatible four-band model. When the valley pseudospin is conserved, we show that the kink states exhibit nearly perfect out-coupling e ciency into directional beams, through the intersection between the internal domain wall and the external edge separating the VPCs from ambient space. The out-coupling behaviour remains topologically protected even when we break the spin-like polarization degree of freedom (DOF), by introducing an e ective spin-orbit coupling in one of the VPC domains. This also constitutes the first realization of spin-valley locking for topological valley transport.

Valley‐Hall Photonic Topological Insulators with Dual‐Band Kink States

“…Next, we construct a “kink”‐type domain wall between two valley‐Hall PTIs with opposite mass terms (or opposite Δ r ). Across the domain wall, the valley‐Chern numbers are opposite, resulting in the existence of a pair of topological kink states at the domain wall around K/K′ valley . Note that the above analysis is applicable for both pairs of Dirac points at different frequencies, therefore, topological kink states exist at both bandgaps.…”

“…Note that the Berry curvatures near K′ valley, which are not shown here, are opposite to those near K valley. Integrating the Berry curvature around K/K′ valley, we obtain the valley‐dependent number at K/K′ valley analytically, . The mass term m is characterized by the difference between the frequency of RCP and that of LCP, and is adjusted by altering Δ r in our case.…”

“…According to k·p method, the effective Hamiltonian around K/K′ valley can be expressed as H K/K′ ( δ k ) = ±( v D δk x σ x + v D δk y σ y ) ± mv D 2 σ z , where δ k = k − k K/K′ is the displacement of wave vector k to K/K′ valley in the reciprocal space, v D is the group velocity, m is the effective mass term, and σ i = ( i = x, y, z ) are elements in the Pauli matrices . Solving the effective Hamiltonian, we can obtain the Berry curvature at K/K′ valley, .…”

Topological Photonic Integrated Circuits Based on Valley Kink States

“…As a new binary degree of freedom labeled by different corners of the hexagonal Brillouin zone of 2D Dirac materials, valley pseudospin provides an additional strategy to implement topologically robust transport in electronics, acoustics, and photonics . Instead of breaking TRS, reduction of spatial‐inversion symmetry (SIS) can generate a nonvanishing valley‐dependent Berry curvature and lead to quantum valley‐Hall effect, which predicts the existence of a valley kink state at the domain wall between regions of different topological valley phases .…”

Selective Excitation of Band Extrema in Valley Photonic Crystals

“…[10][11][12][13] With inversion symmetry breaking, the degenerate Dirac points at K/K will split into two band extrema and form a pair of valley pseudospin with orbital-angular-momentum-like (OAMlike) phase vortex. [15][16][17][18][19] On the other hand, there is another kind of band extremum emerging at zone center (i.e., point), which could be effectively described as double/single near-zero index metamaterials based on Mie resonance. [15][16][17][18][19] On the other hand, there is another kind of band extremum emerging at zone center (i.e., point), which could be effectively described as double/single near-zero index metamaterials based on Mie resonance.…”