Optical localization transition in a dual-periodical phase-modulated synthetic photonic lattice

We investigated optical localization and vibration in a synthetic photonic lattice (SPL) with two-phase modulators driven by different periodic voltages. By altering the periods of phase modulation, the induced phase circumfluences, band structure, and transmission behaviors of light in the SPL are studied. A transition from discrete diffraction to weak localization was observed in a small modulation period with equal modulation periodicities. For large modulation periods, the band structure exhibits a density distribution and the optical field delocalizes and vibrates. In contrast, strong localization occurs near the initial incident location with some moir\'e modulation periods of phases that correspond to a flat-band structure. This study reveals the effect of dual-periodic phase modulation on pulse propagation in discrete systems.