Analytical theory of resonant highorder harmonic generation
M. A. Khokhlova1,2, V. V. Strelkov1
1. Theoretical Department, General Physics Institute of Russian Academy of Sciences,119991, 38 Vaviliva str., Moscow, Russia
2. Department of Physics, M. V. Lomonosov Moscow State University, 119991, Leninskie gory str., Moscow, Russia
Properties of resonant highorder harmonics generated in intense laser field are actively studied both
experimentally  and theoretically . Very efficient generation of the harmonic resonant with the
transition from the bound to the autoionizing state was demonstrated in the experiments using plasma plumes
[1,2] and Xe jet .
We suggested analytical quantummechanical theory describing the effect of quasistationary state on HHG
. We start with the timedependent Schrodinger equation for an atom or ion in an external laser field. The
wave function is presented as a sum of the ground state, unperturbed continuum and the quasistationary state.
To solve the Schrödinger equation we derived the perturbation method in which the solution obtained in the
absence of the quasistationary state by Lewenstein et al. in Ref.  is taken as an unperturbed solution.
Assuming that (i) the ionization rate is low, (ii) the quasistationary state population is low, (iii) the quasi
stationary state is not affected with the laser field, and (iv) the quasistationary state width * is much less than
the quasistationary state energy, we find the following equation for the spectral complex amplitude of the
microscopic response at the frequency Z
(atomic units are used):
P ( Z ) P nr ( Z ) F (Z )
* / 2 o
F (Z )
« 1 Q »
'Z i* / 2 1⁄4
where is the
spectrum of the nonresonant contribution, * is the resonance width, Q is a complex
defined by the properties of the generating atom or ion, but not
depending on the laser field. So the resonant harmonic line is presented as a product of the F (Z ) Fanolike
 factor and the harmonic line which would be emitted in the absence of the AIS.
Our theory allows calculating not only the resonant harmonic intensity, but also its phase. We show that there
is a rapid variation of the phase in the vicinity of the resonance. Our calculations reasonably agree with recent
harmonic phase measurements .
The other direction of our research is the study of the phase properties of the cutoff harmonics. We study the
harmonic phase dependence on the laser intensity both analytically and numerically. Moreover, we investigate
the dephasing between adjacent harmonics to study the emission time of the attosecond pulses. Thus, the
optimum conditions for the shortest attosecond pulse generation using the cutoff harmonics are suggested.
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