Higher-order Kerr effect and harmonic cascading in gases

A new publication investigates the possible contribution of cascaded harmonic generation to the higher-order Kerr nonlinearities recently observed in gases. This contribution adds to a particularly heated debate at the moment about whether the higher-order Kerr effect plays a role in filamentation dynamics in gas cells.

Abstract: The higher-order Kerr effect (HOKE) has been recently advocated to explain measurements of the saturation of the nonlinear refractive index in gases. Here we show that cascaded third-harmonic generation results in an effective fifth order nonlinearity that is negative and significant. Higher-order harmonic cascading will also occur from the HOKE, and the cascading contributions may significantly modify the observed nonlinear index change. At lower wavelengths cascading increases the HOKE saturation intensity, while for longer wavelengths cascading will decrease the HOKE saturation intensity.

In homogeneous, isotropic media the nonlinear variation of the refractive index can be expressed in terms of a power series of the light intensity. However, higher-order nonlinearities have usually been regarded as negligible, as compared to the leading third-order nonlinearity n2 (the Kerr effect). A recent experiment aimed at characterizing the higher-order Kerr effect (HOKE) has sparked a vivid debate on the actual role of these higher-order terms in nonlinear beam-propagation dynamics. Indeed, the effective saturation of the HOKE nonlinearity could lead to filamentation of femtosecond pulses in gases without the 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. Experiments have either confirmed or ruled out a preponderant role of HOKE in filamentation dynamics.


In a new paper we study cascading contributions to the nonlinear HOKE coefficients in gases. We show that in gases cascading can affect the nonlinear index change and in particular the saturation intensity. Specifically, to lowest order cascading comes from a phase-mismatched third-harmonic generation process, which we show generates an n4 term that is negative and of significant strength. Similarly, cascading of HOKE terms gives contributions to subsequent orders of nonlinearity (n6, n8, ...) with values comparable with recent experimental and theoretical HOKE coefficients. This implies that in the strong cascading limit, defined later, cascading may contribute significantly to the nonlinear dynamics.


M. Bache, F. Eilenberger and S. Minardi 
Higher-order Kerr effect and harmonic cascading in gases 
Optics Letters 37, 4612-4614 (2012)
online, arXiv:1209:1487, [pdf]