Topological Creation and Destruction of Edge States in Photonic Graphene

We experimentally demonstrate a topological transition of classical light in “photonic graphene”: an array of waveguides arranged in the honeycomb geometry. As the system is uniaxially strained (compressed), the two unique Dirac points (present in the spectrum of conventional graphene) merge and annihilate each other, and a band gap forms. As a result, edge states are created on the zigzag edge and destroyed on the bearded edge. These results are applicable for any 2D honeycomb-type structure, from carbon-based graphene to photonic lattices and crystals.

Figure 1

Microscope images of the input facets of the uncompressed, $s=1.0$ (a) and strongly compressed, $s=0.5$ (b) honeycomb waveguide array. Inset to (a) shows the vertical coupling constant $c_1$ and diagonal coupling constant $c_2$.

Figure 2

Spatial band structure of the (a) uncompressed and (b) compressed honeycomb photonic lattice. The black arrows in (a) indicate the direction that the Dirac points move when the system is compressed.

Figure 3

Schematic of Berry’s phase calculation demonstrating the values of $k_x$ for which a bearded edge state exists, via the bulk-edge correspondence theorem, for both (a) the uncompressed ($s=1$), and (b) strongly compressed ($s=0.5$) cases. The arrows point in the direction of the vector $\mathit{h}(\mathit{k})$. In (a), the black dots indicate the Dirac points, and the arrows indicate the direction they move upon compression. Bearded edge states are present in the shaded regions of (a), and are not present in (b).

Figure 4

Ratio of optical power on the bearded edge to that diffracted into the bulk, as a function of $k_x$: (a) shows experimental results, and (b) shows numerical results from beam-propagation simulations. Top left and right insets in (a) show the output beam at $k_x=0$ when $s=1$ and 0.5, respectively. The white ellipse indicates the position of the input beam on the bearded edge.

Figure 5

Similar to Fig. 4, but for the zigzag edge.