Topologically Protected Edge Modes in Longitudinally Driven Waveguides
A tight-binding approximation is developed for deep longitudinally driven photonic lattices. The physical system considered is that of a laser-etched waveguide array which is helically-varying in the direction of propagation. Focus is placed on the so-called Lieb and Kagome lattices. The lattice is decomposed into sublattices each of which are allowed move independently of one another. The linear Floquet bands are constructed for various rotation patterns such as: different radii, different frequency, phase offset and quasi one-dimensional motion. Bulk spectral bands with nonzero Chern number are calculated and found to support topologically protected edge waves that propagate scatter-free around defects. New dynamics such as bulk-edge leakage are explored. Finally, nonlinear modes are found to propagate unidirectionally at lattice defects.