Continuously tunable topological defects and topological edge states in dielectric photonic crystals

Topological defects in solid-state materials are crystallographic imperfections that local perturbations cannot remove. Owing to their nontrivial real-space topology, topological defects such as dislocations and disclinations could trap anomalous states associated with nontrivial momentum-space topology. The real-space topology of dislocations and disclinations can be characterized by the Burgers vector B, which is usually a fixed fraction and integer of the lattice constant in solid-state materials. Here we show that in a dielectric photonic crystal - an artificial crystalline structure - it is possible to tune B continuously as a function of the dielectric constant of dislocations. Through this unprecedented tunability of B, we achieve proper controls of topological interfacial states, i.e., reversal of their helicities. Based on this fact, we propose a topological optical switch controlled by the dielectric constant of the tunable dislocation. Our results shed light on the interplay of real and reciprocal space topologies and offer a scheme to implement scalable and tunable robust topological waveguides in dielectric photonic crystals.