Quantum-Mechanical Description of Ionization-Induced Generation of Tunable Mid-Infrared Pulses

Abstract

Abstract. The work is devoted to the analytical study of the excitation of low-frequency current density (with frequencies much smaller than the frequency of the optical wave) which radiates in mid-infrared band in the gas ionization by two-color laser pulses. We calculate the low-frequency current density using the analytical solution of time-dependent Schrödinger equation on the basis of strong-field approximation. Closed-form analytical formulas for the lowfrequency current density are obtained for laser-pulse parameters corresponding the tunneling and multiphoton ionization regimes. The features of excitation of low-frequency current density are analyzed in both regimes. IntroductionThe process of gas ionization by two-color laser pulses, containing the components with the frequency ratio close to two, is accompanied by excitation of the low-frequency current density (with frequencies much smaller than the frequency of the optical wave) [1][2][3][4][5]. The frequency detuning from the exact "synchronism" determines the frequency of the low-frequency current, which can be located in mid-infrared band [3][4][5]. This can be used to generate short pulses of mid-infrared radiation [4]. The low-frequency current density excited during gas ionization by a two-color laser pulse has been previously calculated analytically and numerically with the help of semiclassical and quantum-mechanical approaches [1][2][3][4][5][6][7][8][9]. The semiclassical approach is based on the solution of the hydrodynamic equation for the electron current density and the equation for the density of free electrons with a quasi-static probability of tunneling ionization per unit time [10]. The quantum-mechanical approach is based on the solution of the threedimensional time-dependent Schrödinger equation for the electron wave function [9,11]. The range of applicability of the semiclassical approach is limited by the laser pulse parameters corresponding to the tunneling ionization regime, at which the Keldysh parameter γ = I p /2U p [12] is much less than unity (here I p is the ionization potential of an atom, and U p is the ponderomotive energy of an electron in the laser field) [5,11,13]. For γ ≫ 1, the electron release occurs at a time of the order of the field period and greater, and to adequately calculate the low-frequency current density it is necessary to apply the quantum-mechanical approach.This work is devoted to the derivation of closed-form analytical expressions for the low-frequency current density on the basis quantum-mechanical approach using strong-field