Localization and delocalization of light in synthetic photonic lattices with hybrid Bloch-Anderson modulations

We investigate the localization and delocalization transition in a synthetic mesh lattice (SML) with the hybrid modulations comprising of a gradient phase and phase disorders that are utilized to induce Bloch oscillation and Anderson localization, respectively. On the basis of Bloch oscillation, phase and coupling disorders are introduced in the SML by randomly altering the longitudinal phase and transverse coupling. The results shows that the phase disorder generally washes out the Bloch oscillation with the enlarging randomness. Whereas, the coupling disorder results in increasing number of oscillations initially and causes strong localization with a large random value. When two kinds of disorders are simultaneously added, the optical transition between localization and delocalization are realized by modulating the two strengths of disorders. Our work reveals the interaction of Bloch oscillation and disorders in two discrete systems, which provide a method to achieve optical localization.