Bloch dynamics of light waves in helical optical waveguide arrays

Abstract

Propagation of light waves in one-dimensional and two-dimensional photonic lattices made of uniformly twisted (helical) arrays of evanescently coupled optical waveguides is theoretically investigated and shown to provide a classic wave optics analog of the quantum dynamics of a Bloch particle in an electromagnetic field. For a one-dimensional waveguide array, it is demonstrated that the behavior of discretized light in the array exactly mimics the wave packet dynamics of a quantum harmonic oscillator on a lattice, with the existence of quasiharmonic and quasi-Bloch oscillations. For a two-dimensional twisted waveguide array, it is shown that propagation of discretized light exactly mimics the quantum motion of an electron in a two-dimensional crystalline potential subjected to a uniform magnetic field, orthogonal to the crystal plane, combined with a repulsive harmonic electrostatic force.