Phase properties of resonant high-order harmonics |
|
| Margarita Khokhlova | |
| General Physics Institute of Russian Academy of Sciences | |
| Properties of resonant high-order harmonics generated in intense laser field are actively studied both experimentally (see review [1] and references therein) and theoretically (see [2,3] and references therein). Very efficient generation of the harmonic resonant with the transition from the bound to the autoionizing state of the generating ion was demonstrated recently in the experiments using plasma plumes [1] and Xe jet [4]. In this paper we develop an analytical model for resonant HHG. We use the single-active electron approximation, and the role of the other electrons is reproduced with a model potential of the parent ion. We use double-barrier structure with a gap between the barriers as an approximation of this potential. This potential has one bound state and one quasi-stationary state, which reproduce the ground and the autoionizing states of the real atom (or ion), respectively. We derive analytically the wave function (both in the discrete and continuum spectrum) in such potential. Further, we find the matrix element of the dipole moment of the continuum- ground-state transition. When the continuum state energy is close to that of the quasi-stationary state, the absolute value of the matrix element has a maximum corresponding to the strong enhancement of the harmonic generation efficiency; the phase of the matrix element varies rapidly in the vicinity of the resonance. This phase describes the additional phase shift of the harmonic close to the resonance. The described harmonic phase properties are important in the attosecond pulse generation with resonantly-enhanced harmonics, recently demonstrated experimentally [5]. Moreover, our results show ways to control the resonant harmonic phase via controlling the detuning from the resonance. [1] R. A. Ganeev, J. Phys. B , 40, R213 (2007). [2] V. Strelkov, Phys. Rev. Lett. 104, 123901 (2010). [3] M. Tudorovskaya and M. Lein, Phys Rev A 84, 013430 (2011). [4] Shiner, et al., Nature Physics, 7, 464 (2011). [5] Elouga Bom, et al., Opt Express, 19, 3677 (2011). |