The signal observed in [1] results from cross-coupling between two laser beams, i.e. pump and probe, propagating along different directions. The coefficients of the nonlinear refractive index introduced in Eqs. (5) and (6) describe therefore the cross-Kerr refractive index experienced by the probe beam. It is possible to deduce from these terms the corresponding values for the Kerr effect as it would be observed in a single laser beam experiment. This can be achieved, in the case where the molecular alignment occurring during the laser pulse interaction can be neglected, by comparing the number of permutations between distinguishable fields in the case of one- and two-beam experiments. These permutation numbers appear as degeneracy factors in the different orders of the nonlinear polarization affecting the probe wave [2]. The extrapolation results in dividing each cross-Kerr coefficient n _2j reported in [1] by (j+1). The rectified results are presented in Table 1 and Fig. 1, and can be compared to those of the cross-Kerr effect published in [1].

Note that the approximation of neglecting the influence of the intrapulse alignment upon the electronic Kerr index is fully justified in present work. For instance, calculating the n ₂ coefficient of N₂ at a peak intensity of 45 TW/cm2, by making use of the elements of the hyper-polarizability tensor, results in an alignment contribution of less than 2%. For the higher order Kerr terms, the correction must be even smaller as the nonlinearity is larger.

Table 1. Measured coefficients of the nonlinear refractive index expansion of nitrogen, oxygen, argon, and air with I _inv the intensity leading to n _Kerr∥ = 0. The uncertainty corresponds to two standard deviations of the fitted values over a set of experimental records.

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Fig. 1. Nonlinear refractive index variation of air constituents versus intensity at room temperature and 1 atm. (a) N₂, (b) O₂, (c) Ar, and (d) air.

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