Optical analogs of Bloch-Zener oscillations in binary waveguide arrays: Wave-number-evolution perspective

We study optical analogs of Bloch oscillations and Zener tunneling in binary waveguide arrays (BWAs) with the help of the wave-number-based approach. We analytically derive two very simple laws describing the evolution of the central wave numbers of beams in BWAs that help us analytically obtain the propagation distances where the Zener tunneling takes place due to the interband transition and the distances where beams reach the turning points and change direction. These distances just depend on the strength of the linear potential and the initial wave number of input beams. We also show that nonlinearity of the Kerr type has a detrimental influence on the Bloch-Zener oscillations.