Spectral photonic lattices with complex long-range coupling

Abstract

Photonic systems such as arrays of coupled waveguides are well suited to emulating quantum mechanics with periodic lattice potentials, allowing the investigation of many physical phenomena in a convenient experimental setting. Usually, photons will “hop” only between neighboring lattice sites at a rate given by a purely real coupling coefficient, thus limiting the rich physics enabled by long-range coupling with complex coupling coefficients. Here we suggest and experimentally realize a spectral photonic lattice that can be configured to realize a wide variety of complex-valued coupling parameters over arbitrary lattice separations. In this system, a weak signal propagates across discrete frequency channels, driven by nonlinear interaction from stronger pump lasers. Our approach allows the experimental investigation of new discrete lattice physics—as an example, we demonstrate two novel instances of the discrete Talbot effect.