Observation of nonlinear disclination states

TL;DR

This paper reports the first experimental observation of nonlinear topological disclination states in photonic waveguide arrays, demonstrating how nonlinearity and topology interplay to control localized states at disclinations.

Contribution

It introduces the experimental realization of nonlinear disclination states in photonic structures and explores their control via power and structural parameters.

Findings

Nonlinear disclination states bifurcate from linear states.

Their propagation constants and localization are power-dependent.

Efficient excitation requires focusing on disclination core waveguides.

Abstract

Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations. Appearance of these topological states is consistent with the bulk-disclination correspondence principle, and is due to the filling anomaly that results in fractional charges to the boundary unit cells. So far, topological disclination states were observed only in the linear regime, while the interplay between nonlinearity and topology in the systems with disclinations has been never studied experimentally. We report here bon the experimental observation of the nonlinear photonic disclination states in waveguide arrays with pentagonal or heptagonal disclination cores inscribed in transparent optical medium using the fs-laser writing technique. The transition between nontopological and topological phases in such structures is controlled by the Kekul\'e distortion coefficient $r$ with topological phase hosting simultaneously disclination states at the inner disclination core and spatially separated from them corner, zero-energy, and extended edge states at the outer edge of the structure. We show that the robust nonlinear disclination states bifurcate from their linear counterparts and that location of their propagation constants in the gap and, hence, their spatial localization can be controlled by their power. Nonlinear disclination states can be efficiently excited by Gaussian input beams, but only if they are focused into the waveguides belonging to the disclination core, where such topological states reside.