Diffraction management and soliton dynamics in frequency-chirped ℙT symmetric lattices

We address two closely related problems: diffraction management and soliton dynamics in parity-time ( ℙT) symmetric lattices with a quadratic frequency modulation. The normal, anomalous, or zero diffraction is possible for narrow beams with a broad band of spatial frequencies. The frequency band of nondiffraction beams can be enlarged by increasing the chirp rate of lattices. Counter-intuitively, the gain-loss component plays the same role as the real part of lattice on the suppression of diffraction, which leads to an effective reduction of critical lattice depth for nondiffraction beams. Additionally, we reveal the existence of a novel type of "bright" solitons in defocusing Kerr media modulated by chirped ℙT lattices. We also demonstrate that lattice chirp can be utilized to suppress the instability of solitons. Our results expand the concept of ℙT symmetry in both linear and nonlinear regimes, and may find interesting optical applications.