Microscopic nature of macroscopic nonlinearity: analytical calculation of gas susceptibilities

An analytical formula for the non-resonant nonlinear susceptibility of an arbitrary order in a gaseous medium is obtained by successive quantum-mechanical calculation of the response of an atom in the laser field and summation of these response fields from all atoms in a coherent manner. Based on this formula, the transition from domination of a single nonlinear susceptibility term at a given harmonic to comparable contributions of multiple high-order susceptibilities at mid-infrared wavelengths is observed. It occurs at the accessible laser intensities (10¹⁰-10¹² W/cm²), which decreases with the laser wavelength. The proposed composite approach can be used to find promising gaseous media, including gas mixtures, with improved harmonic generation efficiency.