Spectral photonic lattices with complex long-range coupling

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.