Ultrafast and broadband optical nonlinearities from strongly phase-mismatched second harmonic generation

The third order optical nonlinearities are often used to broaden the spectral bandwidth of ultrafast pulses for supercontinuum generation or pulse compression [1]. The self-focusing nature of cubic Kerr nonlinearity usually limits the applicable pulse energy. An alternative way is using the second order optical nonlinearity, for instance the nonlinearity generated with cascaded second harmonic generation process. In this case, the nonlinearity is controllable in both magnitude and sign through Δk. It could become a desirable self-defocusing nonlinearity if a positive Δk is chosen. However, there are only a handful of reports about the harness of cascaded nonlinearity. The Kerr-like cascading nonlinearity scales as n_{2, casc} ∝ -d²_eff/Δk. For a successful implementation, focus has been on having the birefringent phase matching first and then tune to small Δk to overcome the material Kerr nonlinearity and have overall negative nonlinearity. The dillema is in most such cases, the d_eff is small and quite low Δk values are needed. Such low Δk gives cascading response that is resonant due to the group-velocity mismatch (GVM), and therefore cannot support ultrafast interaction. Practically by this solution only very limited wavelength regimes support this kind of interaction, as done in e.g. [2].