Cascading second-order versus direct third-order nonlinear optical processes in a uniaxial crystal

We present an experimental and theoretical study of sum-frequency generation of two infrared photons and one visible photon in a lithium iodate crystal. The sum-frequency light can be generated directly in a third-order process as well as in two subsequent second-order processes. By comparing experimental results to numerical and analytical calculations, we demonstrate that the three possible cascading processes, i.e. two second-order cascading processes with phase matching in either the first or the second step and a cascading process with overall phase matching with both steps equally mismatched, are comparable in intensity to the direct third-order process. Polarization and angular-dependent measurements are used to assign the different processes. By using a spectrally broad infrared pulse and a spectrally narrow visible pulse we investigate the possibility of using the spectrally resolved nonlinear signals as a tool to unravel their origin. For the cascading processes, phase matching of the first step results in a spectrally broad sum-frequency signal while overall and second step phase matching give rise to a narrow signal.