Lattice topological edge and corner modes of photonic crystal slabs

Surface lattice modes, generated by the evanescent coupling between localized modes of optical resonators arranged in a two-dimensional (2D) array, generally exhibit remarkable optical response beyond the single photonic particle. Here, by employing the lattice mode concept, we demonstrate that lattice topological edge and corner modes can be achieved in properly designed photonic crystal (PhC) slabs. Such slabs consist of an array of finite-sized second-order topological insulators mimicking the 2D Su-Schrieffer-Heeger model. The proposed lattice edge and corner modes emerge within the topological band gap of the PhC slab, which dictates their topological nature. In particular, the band diagram of the lattice corner modes shows that they possess non-degenerate eigenfrequencies and dispersive bands. In addition, we show that the eigenfrequency of the lattice topological modes can be shifted by tuning the intercell and/or intracell optical coupling. Finally, by finely tuning the geometric parameters of the slab, we realize a lattice corner mode possessing flatband dispersion characteristics. Our study can find applications to topological lasing, nonlinearity enhancement, and slow-light effects in topological photonic systems