Higher-order Kerr effect and harmonic cascading in gases

In centrosymmetric media the nonlinear variation of the refractive index can be expressed in terms of a power series of the light intensity I: Δn = n
₂
I + n
₄
I
²
+...+n
_2m
I
^m
. Usually higher-order nonlinearities are considered negligible compared to the leading third-order nonlinearity n
₂
(Kerr effect). A recent experiment measured the higher-order Kerr effect (HOKE) in gases, and this started a debate on how HOKE affects nonlinear beam-propagation dynamics. The observed saturation of the HOKE nonlinearity could lead to filamentation of femtosecond pulses in gases without plasma playing an active role. The mechanism advocated in this case to arrest collapse of the wave packet was the saturation of the nonlinearity rather than the formation of plasma, as commonly accepted. This paper studies cascading contributions to the nonlinear HOKE coefficients in gases.