Abstract
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.
Highlights
We present the normalized field profile of Hz at the X symmetry point in the insets of Figs. 2(e) and 2(f), determined in the x-y plane crossing through the middle of the photonic crystal (PhC) slab and perpendicular onto the z-axis
The frequencies of the four corner modes are shifted and, interestingly enough, their order changes, too. These findings indicate that the frequency dispersion of the topological edge and corner modes can be controlled by properly engineering their intercell optical interaction
When the Zak phase is extended to 2D, namely, in the 2D FBZ, the x-component of the 2D Zak phase, for example, can be written as follows:
Summary
It consists of a periodic arrangement of PhC supercells, each of which being composed of a finite number of square unit cells. When the four air holes are shifted inwardly or outwardly along the Γ − M crystal symmetry axis, the band degeneracy is lifted and the photonic system emulates the 2D SSH model [32] In this model, there are four atoms in each unit cell, and by tuning the intracell (atoms in the same unit cell) and intercell (atoms in different unit cells) hopping amplitudes ta and tb , by varying the distance between the atoms, one can induce topological phase transitions. Varying the parameters n and m provides a convenient way to tune the intra- and inter-cell optical coupling of edge and corner optical modes and the optical properties of lattice topological modes
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