Multiple backscattering in trivial and non-trivial topological photonic crystal edge states with controlled disorder

We present an experimental investigation of multiple scattering in photonic-crystal-based topological edge states with and without engineered random disorder. We map the spatial distribution of light as it propagates along a so-called bearded interface between two valley photonic crystals which supports both trivial and non-trivial edge states. As the light slows down and/or the disorder increases, we observe the photonic manifestation of Anderson localization, illustrated by the appearance of localized high-intensity field distributions. We extract the backscattering mean free path (BMFP) as a function of frequency, and thereby group velocity, for a range of geometrically engineered random disorders of different types. For relatively high group velocities (with $n_g < 15$), we observe that the BMFP is an order of magnitude higher for the non-trivial edge state than for the trivial. However, the BMFP for the non-trivial mode decreases rapidly with increasing disorder. As the light slows down the BMFP for the trivial state decreases as expected, but the BMFP for the topological state exhibits a non-conventional dependence on the group velocity. Due to the particular dispersion of the topologically non-trivial mode, a range of frequencies exist where two distinct states can have the same group index but exhibit a different BMFP. While the topological mode is not immune to backscattering at disorder that breaks the protecting crystalline symmetry, it displays a larger robustness than the trivial mode for a specific range of parameters in the same structure. Intriguingly, the topologically non-trivial edge state appears to break the conventional relationship between slowdown and the amount of backscattering.