Description
The generation of bright, coherent XUV light via frequency conversion of intense laser drivers is a problem of both fundamental and technological importance. Increasing the intensity of the generated high harmonics by raising the intensity of the driving field only works up to a point: at high intensities, rapid ionisation of the medium limits the conversion efficiency.
We identify the dominant limiting mechanism as the combined effect of phase matching and the blue shift of the driving field during its propagation through a rapidly ionising medium [1, 2]. We introduce the concept of a blue-shift length, which sets the upper bound for the quadratic intensity growth of the harmonics.
We study, analytically and numerically (by solving the propagation equation coupled with the TDSE), the behaviour of the macroscopic HHG signal with propagation distance. We show that its quadratic growth is limited by the shortest of three lengths: absorption, coherence, or blue-shift length. Thus, we define three regimes of HHG, corresponding to the dominant limiting mechanisms.
Moreover, we show that this seemingly fundamental restriction can be overcome by using an additional weak generating mid-IR field. For suitable combinations of the frequencies of the generating fields, the corresponding high-order frequency-mixing (HFM) process does not suffer from the blue shift of the drivers or phase mismatch [1], and thus its efficiency grows quadratically with propagation.
Our results open a new route for the highly efficient generation of XUV light, the first step of which has already been taken via the observation of high-order parametric generation [3]. Moreover, HFM offers new handles for XUV control, such as control over the carrier-envelope phase of the emitted attosecond XUV pulses [4, 5].
This work was carried out in close collaboration with Vasily Strelkov.
References:
[1] M. Khokhlova and V. Strelkov, “Highly efficient XUV generation via high-order frequency mixing,” New J. Phys. 22, 093030 (2020)
[2] M. Khokhlova and V. Strelkov, “Role of blue-shift length in macroscopic properties of high-harmonic generation,” New J. Phys. 26, 073013 (2024)
[3] O. Hort et al., “High-order parametric generation of coherent XUV radiation,” Opt. Express 29, 5982 (2021)
[4] V. Birulia et al., “Generation of attosecond pulses with a controllable carrier-envelope phase via high-order frequency mixing,” Phys. Rev. A 106, 023514 (2022)
[5] V. Birulia et al., “Macroscopic effects in generation of attosecond XUV pulses via high-order frequency mixing in gases and plasma,” New J. Phys. 26, 023005 (2024)
