Nontrivial coupling of light into a defect: the interplay of nonlinearity and topology

Abstract

© 2020, The Author(s). The flourishing of topological photonics in the last decade was achieved mainly due to developments in linear topological photonic structures. However, when nonlinearity is introduced, many intriguing questions arise. For example, are there universal fingerprints of the underlying topology when modes are coupled by nonlinearity, and what can happen to topological invariants during nonlinear propagation? To explore these questions, we experimentally demonstrate nonlinearity-induced coupling of light into topologically protected edge states using a photonic platform and develop a general theoretical framework for interpreting the mode-coupling dynamics in nonlinear topological systems. Performed on laser-written photonic Su-Schrieffer-Heeger lattices, our experiments show the nonlinear coupling of light into a nontrivial edge or interface defect channel that is otherwise not permissible due to topological protection. Our theory explains all the observations well. Furthermore, we introduce the concepts of inherited and emergent nonlinear topological phenomena as well as a protocol capable of revealing the interplay of nonlinearity and topology. These concepts are applicable to other nonlinear topological systems, both in higher dimensions and beyond our photonic platform. Topological photonics: nonlinear couplingAn engineered photonic system has provided insights into the interplay between nonlinearity and topology. Shiqi Xia and coworkers used laser-writing technique to fabricate refractive-index patterns that form a Su-Schrieffer-Heeger lattice in a nonlinear optical crystal of strontium-barium-niobate (SBN:61), a well-known photorefractive material. Due to the presence of the nonlinearity, two optical beams of sufficient power propagating in different directions can, when they collide, couple into a non-trivial interface state in the system, which is otherwise not accessible due to topological protection. Theoretical analysis correctly explains the observed behavior and the nonlinear coupling phenomenon. The researchers say that their findings are of a general nature and can be applied to other nonlinear topological systems