Probing band topology using modulational instability

TL;DR

This paper demonstrates that modulational instability in nonlinear topological photonic lattices can be used to probe topological invariants and generate non-trivial wave fields, linking nonlinear dynamics with topological properties.

Contribution

It introduces modulational instability as a novel method to analyze and create topologically non-trivial states in photonic systems, connecting nonlinear wave dynamics with topological band theory.

Findings

Long wavelength instabilities are sensitive to topological band inversions.

Energy spreads through the band due to nonlinear wave mixing.

Wave polarization singularities are created by the band Chern number.

Abstract

We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations of the nonlinear Bloch waves are sensitive to topological band inversions. At longer timescales, nonlinear wave mixing induces spreading of energy through the entire band and spontaneous creation of wave polarization singularities determined by the band Chern number. Our analytical and numerical results establish modulational instability as a tool to probe bulk topological invariants and create topologically non-trivial wave fields.