Photonic Bloch oscillations and Wannier-Stark ladders in exponentially chirped Bragg gratings

The formation of photonic Bloch oscillations and Wannier-Stark ladders is demonstrated in an exponentially chirped one-dimensional Bragg grating. The photonic Bloch oscillations are investigated using Hamiltonian optics, and direct analogies are made with electron dynamics in periodic potentials. The results of transfer matrix calculations are presented, which show the existence of a photonic Wannier-Stark ladder that should be detectable in experiments.