Bandstructure measurement in nonlinear optical waveguide arrays

We demonstrate a technique for measuring the linear bandstructure of periodic systems with quadratic nonlinearity. The phase-matching constraints of parametric optical frequency mixing are employed to probe the longitudinal wavevectors of the eigenmodes. The method is verified experimentally by measuring the diffraction relation of eigenmodes in periodically poled titanium-indiffused lithium niobate waveguide arrays with second-harmonic generation.