Daniel Sebastian Steingrube

Research interests:

  1. Basics
  2. In particular
See also my PhD thesis:
High-order harmonic generation with ultra-short pulses from filamentation.

High-order harmonic generation

three step model: 1. tunnel-ionization, 2. acceleration, 3. recombination High-order harmonic generation (HHG) is a highly non-linear process driven by a strong field of an intense laser field. Therefore, laser amplifier systems based on the chirped-pulse amplification (CPA) technique are commonly applied delivering pulses in the millijoule range with pulse durations in the femtosecond regime. HHG can be explained by the three-step model by Corkum, et.al. [1,2] where an electron is ionized in the first step due to the strong field of a laser. In the second step, the electron is accelerated in the laser field and returns in the case of linearly polarized light to the ion. When ion and electron recombine in the third step, a high energy photon in the extreme-ultraviolet (XUV) spectral region is emitted. Due to the periodic nature of this generation process and its coherence, only odd harmonics of the fundamental photon energy are emitted, since other photon energies from every half-cycle of the laser field interfere destructively.
[1] P.B. Corkum, Phys. Rev. Lett. 71: 1994 (1993)
[2] M. Lewenstein et al., Phys. Rev. A 49: 2117 (1994)

Phase matching

phase matching: single atoms emit harmonic photons with different phases The previously described generation process of high-order harmonic radiation describes only the microscopic view or the single-atom response of HHG. However, in order to understand a real measurement of this phenomenon, the coherent sum of all single atom contributions must be considered [1]. Thereby, single atoms at different locations can contribute with different phases due to a spatial phase or intensity distribution of the fundamental field. The yield of harmonic radiation accounting for all phase-effects is called the macroscopic response.
[1] A. L'Huillier et al., J. Phys. B 24: 3315 (1991)

Semi-infinite gas cell

semi-infinite gas cell (SIGC) The semi-infinite gas cell (SIGC) [1-3] consists of an entrance window and an exit pinhole and is filled with a gas medium for HHG. For high-order harmonic generation, a laser is focused through the entrance window close to the exit pinhole. The exit pinhole is usually realized by a thin metal plate where the laser drills the pinhole by itself. Thus, the SIGC is a simple geometry, free of alignment. The entrance is far away from the focus region to avoid non-linear effects in the entrance region.
In particular, my research interest are the phase-matching effects in this geometry (see below) [3].
[1] N. Papadogiannis et al., App. Phys. B 73: 687 (2001)
[2] J. Peatross et al., J. Mod. Opt. 51: 2675 (2004)
[3] D.S. Steingrube et al., Phys. Rev. A 80: 043819 (2009)


filament: balancing effect due to self-focusing and defocusing due to ionization An intense laser beam in a medium experiences self-focusing due to an intensity dependent refractive index of the medium (Kerr effect). The spatial intensity profile causes a refractive index distribution acting as a focusing lens. Due to this focusing the beam collapses and gives rise to high intensities which lead to ionization of the medium. The resulting distribution of the free electrons, however, leads to a refractive index profile acting as a defocusing lens. Both effects, focusing and defocusing, are balancing in a filament resulting in a self-guiding channel of light [1].
Beside self-focusing, other self-action-effects occur in a Kerr-medium. Due to self-phase-modulation, the spectral shape of the fundamental laser pulse is broadened and new frequencies are generated. This effect can be used to shorten the pulse duration yielding few-cycle laser pulses from multi-cycle pulses [2].
My research interest is the combination of laser filamentation with high-order harmonic generation (see below) [2,3] with the prospects of single attosecond pulse generation.
[1] A. Couairon et al., Phys. Rep. 441: 47 (2007)
[2] E. Schulz et al., App. Phys. B 95: 269 (2009)
[3] D.S. Steingrube et al., Opt. Exp. 17: 16177 (2009)

Attosecond pulse generation

single attosecond pulse generation For tracking of electron motion, light pulses of durations in the range of attoseconds (10-18s) are necessary. These short attosecond pulses can be generated in the XUV spectral region by the coherent process of HHG [1]. Using a multi-cycle driver pulse, only discrete harmonics spaced by two fundamental photon energies are generated which would, at best, yield a train of attosecond pulses emitted at each half cycle of the driving laser field. When generating high-order harmonics with few-cycle driver pulses, the highest harmonics in the cutoff-region are only produced by a single half-cycle. Due to a missing counterpart of harmonics generated from another half-cycle for destructive interference, a continuous spectral shape is observed in the cutoff. When filtering this continuous spectrum, a single attosecond pulse can be obtained.
[1] A.L. Cavalieri, New J. Phys. 9, 242 (2007)

Phase matching of high-order harmonics in a semi-infinite gas cell

phase matching of high-order harmonics in a semi-infinite gas cell In particular, we have investigated HHG and its phase matching in a SIGC [1]. Systematically, we have investigated the HHG conversion efficiency in xenon and helium in dependence on experimental parameters, such as the focus position, the gas pressure, and the focal length of the focusing lens. The figure shows exemplarily the harmonics intensity (encoded by the color) obtained in helium versus the focus position, defined as sketched on the left. The red points indicate the maximum conversion efficiency for a particular harmonic order. The experimental results were reproduced well by numerical simulations on phase matching [1].
[1] D.S. Steingrube et al., Phys. Rev. A 80: 043819 (2009)

HHG with ultra-short pulses from a femtosecond filament

high-order harmonic generation with ultra-short pulses from a femtosecond filament Filamentation is a promising technique for ultra-short pulse generation with application to attosecond pulse generation. We have demonstrated that pulse compression in a femtosecond filament can be applied to produce a supercontinuum in the extreme ultraviolet (XUV) spectral region via HHG [1]. Thereby, a continuous XUV-spectrum up to 124 eV was obtained which is comparable to results achieved with the traditional hollow-core fiber technique. We have applied the few-cycle pulses from the filament to HHG in different noble gases, as shown in the figure. A massive spectral broadening is observed for HHG with the few-cycle pulses, while distinct harmonics order with narrow bandwidth are obtained using 30-fs pulses from the amplifier, as shown in black for the sake of comparison.
[1] D.S. Steingrube et al., Opt. Exp. 17: 16177 (2009)

HHG by intensity spikes in a femtosecond filament

intensity spikes in a femtosecond filament Recently, we have experimentally demonstrated the occurrence of intensity spikes in a femtosecond filament, which are intense enough for the generation of high-order harmonics [1]. According to theoretical predictions [2], an intensity spike emerges due to an ultrafast refocusing process which cannot be compensated by nonlinear absorption or plasma defocusing. In a filament, due to free electrons which are generated on the leading part of the pulse, the trailing part of the pulse is defocused into the off-axis reservoir surrounding the filament core (see figure). Due to the self-focusing, this radiation is then refocused onto the axis in a non-equilibrium process giving rise to the intensity spike.
high-order harmonic generated by intensity spikes in a femtosecond filament We have demonstrated that intensity spikes can be exploited for HHG directly in the filament. Thereby, one of these spikes (A) produces an XUV-spectrum of well-resolved harmonic orders, while another spike (B) produces an XUV-supercontinuum. Numerical simulations, which are in excellent agreement with the experiment, predict that the continuous spectrum can be used to produce an isolated attosecond pulse of 500 as duration. This suggests a innovative and simple attosecond pulse source combining spectra broadening, dispersion compensation and HHG in a single stage.
[1] D.S. Steingrube et al., New J. Phys. 13: 043022 (2011)
[2] M.B. Gaarde and A. Couairon, Phys. Rev. Lett. 103: 043901 (2009)