First of all, you are correct that nonlinear optics usually requires high field strengths. But...
>Photons are bosons and therefore are very reluctant to interact, essentially requiring nonlinearities.
Please don't throw out random sciency terms. First of all, interaction is pretty much by definition nonlinear. Second, photons are not reluctant to interact. Photon-photon scattering is negligible (which has nothing to do with them being bosons, as gluons and mesons readily demonstrate), but nonlinear optics doesn't rely on photon-photon scattering.
>Photons are bosons and therefore are very reluctant to interact, essentially requiring nonlinearities.
Please don't throw out random sciency terms. First of all, interaction is pretty much by definition nonlinear. Second, photons are not reluctant to interact. Photon-photon scattering is negligible (which has nothing to do with them being bosons, as gluons and mesons readily demonstrate), but nonlinear optics doesn't rely on photon-photon scattering.