Discrete Nonlocal Nonlinearity in Quadratic Waveguide Arrays

Discrete models are routinely used in mathematical physics to predict the behavior of complex physical systems. They describe the interactions between and within several similar entities, which in general can be either linear or nonlinear. Optical waveguide arrays (WGAs) are a common experimental system described with discrete equations [1]. However, direct nonlinear interaction between neighboring waveguides, an important ingredient of many discrete models [2], has not yet been experimentally realized in WGAs. Here we analyze nearest-neighbor nonlinear interactions in WGAs with second-order or quadratic nonlinearity. By using symmetries in the interacting waveguides we enable experimental access to these nonlinearities and demonstrate their distinct effects on second-harmonic generation (SHG).