Working Paper Article Version 1 This version is not peer-reviewed

# Nonlinear Control of Photonic Higher-Order Topological Bound States in the Continuum

Version 1 : Received: 26 July 2021 / Approved: 28 July 2021 / Online: 28 July 2021 (09:35:54 CEST)

How to cite: Hu, Z.H.; Bongiovanni, D.; Jukić, D.; Jajtić, E.; Xia, S.; Song, D.; Xu, J.; Morandotti, R.; Buljan, H.; Chen, Z. Nonlinear Control of Photonic Higher-Order Topological Bound States in the Continuum. Preprints 2021, 2021070616 Hu, Z.H.; Bongiovanni, D.; Jukić, D.; Jajtić, E.; Xia, S.; Song, D.; Xu, J.; Morandotti, R.; Buljan, H.; Chen, Z. Nonlinear Control of Photonic Higher-Order Topological Bound States in the Continuum. Preprints 2021, 2021070616

## 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 unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states which are also BICs in a laser-written second-order topological lattice, and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such an HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.

## Keywords

Higher-order topological insulators; topological bound states in the continuum; nonlinear optics; SSH lattice

## Subject

PHYSICAL SCIENCES, Acoustics

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