Observation of Photonic Topological Valley Hall Edge States

We experimentally demonstrate topological edge states arising from the valley-Hall effect in two-dimensional honeycomb photonic lattices with broken inversion symmetry. We break the inversion symmetry by detuning the refractive indices of the two honeycomb sublattices, giving rise to a boron nitridelike band structure. The edge states therefore exist along the domain walls between regions of opposite valley Chern numbers. We probe both the armchair and zigzag domain walls and show that the former become gapped for any detuning, whereas the latter remain ungapped until a cutoff is reached. The valley-Hall effect provides a new mechanism for the realization of time-reversal-invariant photonic topological insulators.

Figure 1

(a) Schematic diagram of inversion-symmetry-broken honeycomb lattices with armchair and (b) and zigzag edge domain walls. Red and green waveguides indicate a different refractive index, and blue indicates straw waveguides. Red shaded regions indicate domain walls. (c) Band structure of the inversion-symmetry-broken graphene defined by $u_1{\mathbf{b}}_1+u_2{\mathbf{b}}_2$, where ${\mathbf{b}}_1=(2\pi /3a)(1,\sqrt{3})$ and ${\mathbf{b}}_2=(2\pi /3a)(1,-\sqrt{3})$ are reciprocal lattice vectors and $a$ is the lattice constant. (d) Continuum edge band structures with periodic boundary conditions on both the $x$ and $y$ directions at $\lambda =1650\mathrm{nm}$ and $k_y=0$ when the armchair or (e) zigzag edges are placed at the domain wall. (f),(g) Corresponding band structures at $\lambda =1450\mathrm{nm}$. Red and blue dashed lines indicate energies of eigenmodes that are excited by coupling with the straw waveguide when we excited modes at midgap and significantly below midgap, respectively. Green and red bands in (e) and (g) indicate edge states located at the domain wall close to and far away from straw waveguides, respectively. Therefore, only the green bands are accessible in the experiment.

Figure 2

(a) Measured edge intensity ratio and (b) penetration ratio when we excite modes at midgap. Blue and red dots are measured at zigzag and armchair edge domain walls, respectively. (Inset) Diffracted light measured at the output facet. Waveguides where light is injected are marked with a yellow dashed circle.

Figure 3

(a) Measured edge intensity ratio and (b) penetration ratio when we excited modes significantly below midgap. Blue and red dots are measured at zigzag and armchair edge domain walls, respectively. (Inset) Diffracted light measured at the output facet. Waveguides where light is injected are marked with a yellow dashed circle.

Figure 4

(a) Diffracted light measured at the output facet when we inject directly at the center of the zigzag and (b) the armchair domain walls. (c) Diffracted light measured at the output facet when $\mathrm{\Delta }{n}_A=\mathrm{\Delta }{n}_B=\mathrm{\Delta }{n}_s$ and the straw waveguide mode is initially excited for the zigzag orientation and (d) the armchair domain walls. All measurements are carried out at $\lambda =1450\mathrm{nm}$. Waveguides where light is injected are marked with a yellow dashed circle.