True versus effective Kerr nonlinear response in optical filamentation

The optical Kerr effect, and the nonlinear polarization in general, represents an important light-matter interaction governing many regimes encountered in the nonlinear optics. We reason that in the context of optical filamentation one should distinguish the third-order Kerr effect occurring at relatively low light intensities from the effective Kerr nonlinearity relevant to higher intensity. While many properties of filaments can be captured well with a third-order nonlinear polarization model with a nonlinear index chosen somewhat higher than the true nonlinear index operative at low intensities, our comparative simulations indicate that some filamentation aspects carry significant signatures from the higher-order nonlinearity.