The effect of disorder and nonlinearity on topological slow light

In photonic crystal waveguides, light can be significantly slowed at wavelengths near the Brillouin zone edge, where the group velocity approaches zero. This has the effect of making light interact more strongly with matter, potentially leading to significant enhancement of nonlinear processes such as frequency comb generation and entangled pair creation.

A significant shortcoming of these waveguides is that such slow light devices suffer from a narrow bandwidth and increased backscattering due to fabrication disorder, leaving them prone to Anderson localization. Photonic topological insulators exhibit chiral edge states that are protected from backscattering. These modes

typically cross the bulk band gap over a single Brillouin zone. Recently [1], it was proposed that engineering the edge termination of a photonic Chern insulator circumvents this problem by winding the topological edge state many times around the Brillouin zone. This makes these structures suitable to host robust slow light propagation - free of Anderson localization - over a broad range of frequencies. Here, we analytically and numerically study the stability of transport properties along such edges against disorder and nonlinearity.

These efforts culminate in an expression for the optimal number of windings in the Brillouin zone given a disorder strength.

[1] J. Guglielmon and M.C. Rechtsman, PRL 122, 153904