Nonperturbative low harmonics generation in low-frequency laser field

TL;DR

Solving the 3D TDSE for a SAE Argon atom in a low-frequency laser field, the study reveals a quasi-static response captured by a semi-phenomenological dipole–field relation that accurately reproduces ab initio results for intensities up to $1.4\times 10^{14}$ W/cm$^2$ and frequencies up to about $1$ eV. This approach enables efficient evaluation of linear and non-linear susceptibilities, including Kerr-like behavior, third-harmonic generation, and optical rectification in two-color fields, by inverting a simple implicit relation between $E$ and the dipole moment and performing Fourier analysis of the quasi-static dipole. The key contributions are the fitted quasi-static model parameters, demonstration of non-perturbative growth of $\tilde{\chi}^{(1)}(\omega)$ and $\tilde{\chi}^{(3)}(3\omega)$, and the phase dependence of the two-color-induced rectification, providing a practical bridge between ab initio simulations and analytical descriptions in strong-field physics.

Abstract

Solving numerically three-dimensional non-stationary Schrödinger equation, we find the atomic response to the quasi-static electric field We suggest a semi-phenomenological approximation of this response which describes well the {\it ab initio} numerical calculation result both for low and high intensities (up to $1.4 \cdot 10^{14}$ W/cm$^2$). In particular, this approximation describes the nonperturbative increase or the third harmonic generation efficiency with the laser intensity, as well as the dependence of the optical ratification signal in the two-color field on the phase difference between the fields. Making the calculations for the realistic laser frequencies, we find that our approach is applicable up to fundamental frequencies of about 1 eV.

Figures (3)

• Figure 1: The dependence of effective susceptibility $\tilde{\chi}^{(1)}(\omega_0)$ on intensity for different frequencies (a) and on intensity for $\omega_0=3.1~eV$ for different pulse durations (b).
• Figure 2: The dependence of effective susceptibility $\tilde{\chi}^{(3)}(3\omega_0)$ on intensity for different frequencies.
• Figure 3: The dependence of effective susceptibility $\tilde{\chi}^{(3)}(\omega=2\omega_0-\omega_0-\omega_0)$ on intensity for different phase differences for two-color field given by Eq. (\ref{['two-color']}) for $\omega_0=1 eV$ with equal amplitudes ($\alpha=1$) (a) and for $\alpha=1/\sqrt{2}$ (b).