High-order harmonic generation of H atom in elliptically polarized laser field

Abstract

The ellipticity of a laser field provides an additional control parameter for laser-atom interactions and introduces some special features in nonlinear photo-processes. For example, high-order harmonic generation (HHG) in gases is the most important method for generating extreme ultraviolet (XUV) attosecond pulses from intense infrared laser field. Some alternative methods to generate isolated attosecond pules are known as polarized gating (PG), double optical gating (DOG), and generalized double optical gating (GDOG), each of them making use of the strong dependence of the HHG on the ellipticity of the driving pulse. The ellipticity dependence of the yield in HHG as a function of the driving laser wavelength, intensity, target atom, and harmonic order, should be very useful for designing polarization gating-based schemes for isolated attosecond pulses. As was shown in numerical and experimental studies, HHG is very sensitive to the driving field ellipticity. In particular, the harmonic yield rapidly decreases with increasing ellipticity. According to the semiclassical three-step model, after tunneling ionization, the electron oscillates quasifreely driven by the laser field and acquires additional kinetic energy, finally it can recombine with the parent ion and emit a harmonic photon, whereas for an elliptically polarized laser field, a small ellipticity e = E 0 y /E 0 x (here E 0 x is the electric field component along the major polarization axis and E 0 y is the minor axis) can displace the electron along the minor polarization axis, which leads to a rapid decrease of the recombination efficiency with the increasing ellipticity. The decrease of the HHG efficiency can be attributed to the fact that the electron wave packet misses the parent ion due to lateral shift driven by the transverse component of the elliptically polarized field. However, the high-order harmonic generation could still occur owing to spreading of the electron wave packet after the tunnel ionization which can compensate for the lateral shift. By solving the two dimensional Time-dependent Schrodinger equation numerically using the Crank-Nicolson method, we study high-order harmonic generation of model H atom in an elliptically polarized laser field with different wavelengths. We use laser pulses with wavelengths of 800, 1000, 1300, 1500, and 1800 nm, respectively. The peak intensities are 1.5×1014 and 2.5×1014 W/cm2. We show that the numerical calculated wavelength scaling of elliptical-polarization dependence are in good agreement with a function ( e 1/2 ∝ λ - 1), where e 1/2 is the ellipticity required to suppress the harmonic yield by a factor 2. For the same wavelength, the ellipticity dependence of the HHG becomes stronger with increasing laser peak intensity. Furthermore, the wave packet spreading rates obtained from ADK model are 17% smaller than our numerical result, that is in good agreement with experimental measurement. So, it is two dimensional model of H atom that in the elliptical polarized laser field is an effective method to study the HHG spectrum.