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Nonlinear optics and attosecond source in the extreme-UV spectral range

As above mentioned, studies of ultrafast dynamics based on pump-probe experiments requires at least two ultrashort light pulses, moreover perfectly synchronized at the attosecond time scale. Again, this is ideally provided by a nonlinear process called high harmonic generation (HHG) which may be driven by a strong laser field in a large variety of physical systems, from a gas medium [Salières99] to a solid material [Ghimire11] or a plasma [Thaury10]. HHG in a gas medium has been first reported in the eighties simultaneously at Michigan University and at CEA-Saclay  [McPherson87, Ferray88]. In the years 2000, it has been demonstrated that HHG actually led to the emission of attosecond pulses, perfectly synchronized with the laser driving field. In the last ten years, nonlinear optics focused on HHG has developed into a new and vast domain of research, explored by several tens of laboratories worldwide.

HHG and attosecond emission refer to the same physical process, which may be equivalently described either in the “spectral domain” or the “temporal domain”. Let us consider the temporal description of HHG in a gas medium, that is within the interaction of isolated atoms or molecules with a strong laser field – usually in the infra-red spectral range, i.e., wavelength λ between 0.8 µm and 3 µm and period T=λ/c between 2.7 and 10 femtosecond - at intensity above 1013 W/cm2. Following Paul Corkum’s picture [Corkum93], one may understand the interaction as a sequence of three steps within only one half-period of the laser electric field (1.3-5 fs):

  • step 1: the system is ionized by field ionization which frees an electronic wavepacket (EWP) in the energy continuum, in the immediate vicinity (a few 10 to 100 Å) of the atomic or molecular,

  • step 2 : the free electronic wavepacket is accelerated by the laser field and, for given initial conditions in step1, it may return to the ionic core with a high kinetic energy,

  • step 3: upon return, the electronic wavepacket can recombine radiatively with the ionic core; the energy in excess is released in the form of an ultra-short, attosecond burst of light (of a few 10 to 100 as duration), whose wavelength is centred in the extreme-UV spectral range.

The 3-step process reproduces at every of the 5-20 half-cycles usually contained in the driving laser pulse, so that a temporal “train” of attosecond pulses is produced [Paul01, Mairesse03]. Emission in the temporal domain corresponds to the usual two levels of structure in the conjugated spectral domain:

  • The single isolated attosecond pulse of duration ~100 as is associated with a broad continuum of several 10 eV (~20 eV for 100 as), thus extending in the extreme-UV referred to as the XUV spectral range.

  • The train of attosecond pulses is associated with a discrete harmonic structure which modulates the above broad continuum.

Note that, besides the above 3-step scattering of the recolliding electron in the HHG radiative channel, another 3-step scattering takes place in the so-called “ionization” or “electron diffraction” channel where, in step 3, the recolliding electronic wavepacket is scattered – with momentum exchange – by the ionic core. The “electron diffraction” channel in the atom/molecule interaction with a strong field offers another tool to ultrafast dynamics in pump-probe experiment.

 

[1] note that this is not trivial since the duration of the excitation, e.g., using a light pulse, determines the spectral width of the electronic/nuclear wavepacket which is excited and therefore determines partially the characteristic time of its coherent evolution, independently of the dynamical process under study – see, e.g., A. H. Zewail, Chemistry at the Uncertainty Limit, Angew. Chem. 40, 4371 (2001).

 

Figure : schematic description of the « recollision » between an electronic wavepacket and a molecular ion of the presence of a strong laser field. The diatomic molecular ion is schematized by the four-lobe electronic valence orbital and a two-center Coulomb potential; the strong field linearly polarized is schematized on the right; the free electronic wavepacket is driven by the laser field into a three-step process, field ionization, acceleration and recollision with the molecular ion. This leads to either electron scattering (“diffraction”) or emission of an attosecond light burst. The emitted light encodes information on the molecular system: it provides the basis for harmonic spectroscopy, an efficient tool for studying ultrafast dynamics available in ATTOLAB (courtesy Thierry Ruchon, CEA/LIDyL).

 

[Corkum93]

Plasma perspective on strong-field multiphoton ionization, Corkum, P. B., Phys. Rev. Lett. 71, 1994–1997 (1993).

[Ferray88]

Multiple-harmonic conversion of 1064 nm radiation in rare gases, Ferray, M.; L'Huillier, A.; Li, X. F.; Lompre, L. A.; Mainfray, G., Manus, C., J Phys B: At Mol Phys 21, L31 (1988)

[Ghimire11]

Observation of high-order harmonic generation in a bulk crystal, S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, D. A. Reis, NATURE PHYSICS 7, 138 (2011) - DOI: 10.1038/NPHYS1847

[Mairesse03]

Attosecond Synchronization of High-Harmonic Soft X-rays, Mairesse, Y.; de Bohan, A.; Frasinski, L. J.; Merdji, H.; Dinu, L. C.; Monchicourt, P.; Breger, P.; Kovacev, M.; Taïeb, R.; Carré, B.; Muller, H. G.; Agostini, P. & Salières, P., Science 302,1540-1543 (2003)

[McPherson87]

Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases, McPherson, A; Gibson, G; Jara, H; Johann, U; Luk, T S; McIntyre, I A; Boyer, K; Rhodes, C K, JOSA B 4, 595 (1987)

[Paul01]

Observation of a Train of Attosecond Pulses from High Harmonic Generation, Paul, P. M.; Toma, E. S.; Breger, P.; Mullot, G.; Augé, F.; Balcou, P.; Muller, H. G. & Agostini, P., Science 292,1689-1692 (2001)

[Salières99]

Study of the Spatial and Temporal Coherence of High-Order Harmonics, Salières, P.; L'Huillier, A.; Antoine, P. & Lewenstein, M., in Advances in atomic, molecular, and optical physics, eds. B. Bederson and H. Walther, Academic Press, vol. 41, pp. 83-142 (1999)

[Thaury10]

High-order harmonic and attosecond pulse generation on plasma mirrors: basic mechanisms, C Thaury, F Quéré, J. Phys. B: At. Mol. Opt. Phys. 43, 213001 (2010) - doi:10.1088/0953-4075/43/21/213001

 

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