Gapless surface states in a lattice of coupled cavities: A photonic analog of topological crystalline insulators

We show that a tetragonal lattice of weakly interacting cavities with uniaxial electromagnetic response is the photonic counterpart of topological crystalline insulators, a new topological phase of atomic band insulators. Namely, the frequency band structure stemming from the interaction of resonant modes of the individual cavities exhibits an omnidirectional band gap within which gapless surface states emerge for finite slabs of the lattice. Due to the equivalence of a topological crystalline insulator with its photonic-crystal analog, the frequency band structure of the latter can be characterized by a $Z_2$ topological invariant. Such a topological photonic crystal can be realized in the microwave regime as a three-dimensional lattice of dielectric particles embedded within a continuous network of thin metallic wires.

Figure 1

(a) Tetragonal crystal with two cavities within the unit cell. (b) The bulk Brillouin zone and (c) the surface Brillouin zone corresponding to the (001) surface.

Figure 2

Frequency band structure for tetragonal lattice of resonant cavities within a plasmonic host (see Fig. 1) corresponding to the Green's tensor of Eq. (11) with $s_1^A=-s_2^B=1.2,s_2^A=-s_2^B=0.5,s_1^{\prime }=2.5,s_2^{\prime }=0.5,s_z=2$.

Figure 3

Frequency band structure for a finite slab $ABAB\cdots ABB$ of the crystal described in the legend of Fig. 2 made from 80 bilayers.

Figure 4

A possible realization of a photonic structure with gapless surface states: dielectric particles of square cross section, joined together with cylindrical coupling elements and embedded within a 3D network of metallic wires (artificial plasma).