Higher-Order Nonlinearity of Refractive Index: the Case of Argon

Higher-order dynamic Kerr effect (HOKE) is currently at the center of a controversy regarding the mechanisms of laser filamentation. A strong HOKE with a crossover from positive to negative nonlinear refractive index at intensities well below the ionization threshold, would engender plasma-free filamentation and exotic new effects in light propagation. Experimental evidence of HOKE crossover or lack thereof is being hotly debated. Motivated by this debate, we report the frequency-dependent nonlinear refractive index coefficients $n_{2}$ and $n_{4}$ for atmospheric-pressure argon gas, calculated via developed coupled cluster cubic response approach implemented in Dalton program. All calculations are performed at the CCSD level of theory with t-Aug-cc-PV5Z basis set. The benchmark dispersion curve for $n_{2}$ reproduces correctly the available experimental data and agrees well with previously-reported theoretical calculations. The nonlinear refractive index $n_{4}$ is obtained using the relations between different hyperpolarizability coefficients, and the latter are calculated via the auxiliary static electric field approach on the basis of $n_{2}$. We found that the higher-order nonlinear refraction index $n_{4}$ is positive over the wavelengths 300 nm-1500 nm. This result runs counter to the HOKE crossover hypothesis.