A wavenumber-based analytical treatment of Bloch-Zener oscillations of light in binary waveguide arrays. Two simple laws describe how a beam's central wavenumber evolves along the propagation direction under a linear index gradient. From them one obtains closed-form propagation distances where the beam sits at the Dirac points (so interband Zener tunneling occurs) and where it reaches the turning points of its Bloch oscillation; these distances depend only on the linear-potential strength and the input beam's initial wavenumber. The analysis also shows Kerr nonlinearity degrades the oscillations, giving a compact predictive picture of when tunneling and turning happen in such photonic lattices.
Tran and Tran study optical analogues of Bloch oscillations and Zener tunneling in binary waveguide arrays (BWAs) using a wavenumber-based description of light propagation. In a BWA with a superimpos…