Abstract
Edge states protected by bulk topology of photonic crystals show robustness against short-range disorder, making robust information transfer possible. Here, topological photonic crystals under long-range deformations are investigated. Vertices of each regular hexagon in a honeycomb crystalline structure are shifted randomly to establish a deformed system. By increasing the degree of random deformations, a transition from an ordered system to an amorphous system are investigated, where the close of topological bandgap is clearly shown. We further present comprehensive investigations into excitation methods of the proposed deformed system. Due to the lack of strict periodicity, excitation of topological edge modes becomes difficult. Chiral and linearly polarized sources as two different methods are investigated respectively. It is found that chiral sources are sensitive and rely on the ordered lattice. Even a weak long-range deformation can bring fluctuations to transmission. We further designed and fabricated metal-dielectric-metal sandwich-like samples working in the microwave band. Using linearly polarized source, we detected the existence of topological transport in the deformed system. This work investigates excitation and robustness of bulk topology against long-range deformations and may open the way for exploiting topological properties of materials with a deformed lattice.
Highlights
Systems with spatial order are the predominate topic in physical science where every individual unit cell behaves the same
Much of this is motivated by the simplicity of the analysis, as the behavior of waves interacting in a system can be deduced elegantly from rigorous formulas once properties of the unit cell are known
Inspired by the nature of foam that every node is shared by three bubbles, we propose the deformed systems as shown in Fig. 1(b), where vertices are shifted randomly
Summary
Systems with spatial order are the predominate topic in physical science where every individual unit cell behaves the same. Using chiral waveguides or perturbations in the cylindrical structures breaks z symmetry and opens a nontrivial band gap [26,27] Within most of these structures, a long-range ordered lattice is required to be preserved with translational symmetry where the unit cell is repeated periodically over the entire space. Topological surface states at interfaces between the free space and bulk of quasicrystals or amorphous systems have been studied [32,33,34] Another emerging topic is that of topological edge modes existing at the interface of two different amorphous materials. Amorphous systems with broken time-reversal symmetry have been reported with unidirectional edge modes along the interface between two different amorphous bulks [35,36] It is natural, to further investigate topological transport between different deformed structures without breaking time-reversal symmetry. We further designed and fabricated two samples with straight and triangular interfaces, respectively, based on the three-dimensional (3D) printing technique and measured topological transport within the band gap
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