Nonlinear control of photonic higher-order topological bound states in the continuum

TL;DR

This paper explores the interaction of nonlinearity, higher-order topology, and bound states in the continuum (BICs) in photonic HOTIs, revealing tunable topological BICs and nonlinear state transitions with potential device applications.

Contribution

It demonstrates the first experimental observation of nonlinear coupling of HOTI BICs with other states and introduces a theoretical framework for tuning topological BICs via nonlinearities.

Findings

Observation of topological corner states as BICs in a photonic lattice

Nonlinear coupling leads to transition from corner states to solitons

Topological BICs can be actively tuned by focusing and defocusing nonlinearities

Abstract

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to a HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here, we demonstrate the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states which, serendipitously, are also BICs in a laser-written second-order topological lattice. We further demonstrate nonlinear coupling with edge states at a low nonlinearity, transitioning to solitons at a high nonlinearity. Theoretically, we calculate the analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by both focusing and defocusing nonlinearities. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.