Localization-delocalization transition in an electromagnetically induced photonic lattice

We investigate the localization-delocalization transition (LDT) in an electromagnetically induced photonic lattice. A four-level tripod-type scheme in atomic ensembles is proposed to generate an effective photonic moire lattice through the electromagnetically induced transparency (EIT) mechanism. By taking advantage of the tunable atomic coherence, we show that both periodic (commensurable) and aperiodic (incommensurable) structure can be created in such a photonic moire lattice via adjusting the twist angle between two superimposed periodic patterns with square primitive. Furthermore, we also find that by tuning the amplitudes of these two superimposed periodic patterns, the localization-delocalization transition occurs for the light propagating in the aperiodic moire lattice. Such localization is shown to link the fact that the flat bands of moire lattice support quasi-nondiffracting localized modes and thus induce the localization of the initially localized beam. It would provide a promising approach to control the light propagation via the electromagnetically induced photonic lattice.