Attosecond pulse generation and detection

The conjecture of producing a train of attosecond pulses using high-order harmonic generation (HHG) has been put forward almost 10 years ago. More recently, detailed theoretical investigations have confirmed this possibility and shown that it is indeed conceivable to generate a train or even a single attosecond pulse. The method utilizes the coherent properties of the high harmonics produced in the interaction of laser light with atoms in a manner analogous to the short pulse production in mode-locked lasers.  Nonetheless, it is only now that experimental evidence has started accumulating, indicating that the femtosecond barrier towards attosecond pulses might have fallen. Provided that they are well characterized, they may serve as the fastest camera, able to record frozen snapshots of ultra fast electron dynamics.  Consequently, they are of great interest to a variety of scientific areas including atomic, molecular, solid state and plasma physics, as well as to material science. The challenging problem is to find a measuring technique that unequivocally verifies the existence of attosecond pulses and it provides a  precise temporal characterization.

In principle, one should be able to apply the well known techniques from femtosecond pulse metrology like successive optical auto-correlations of increasing order to obtain the answer, i.e., characterize the attosecond pulse and ultimately measure its exact duration.  The difficulty arises from the fact that, in contrast to femtosecond, the attosecond pulses are necessarily in the UV-XUV spectral range, they are orders of magnitude weaker and spectrally much broader. In case of femtosecond pulses with frequencies in the visible spectral region, an amplitude splitting interferometer (Michelson or Mach-Zehnder) in conjunction with a second harmonic crystal is commonly used. Both basic components, interferometer and detector, have to be appropriately modified or adapted for operation in the XUV spectral region. In this case,  a beam splitting interferometer using a free-standing transmission grating, adapted for operation in the 10 - 100 nm spectral region is ideally suited for the temporal characterization of attosecond pulses. In conjunction with focusing mirrors, this interferometer can be made to exhibit dispersion characteristics that allow measurement of pulses with few as duration [(see: E. Goulielmakis et al.,  Appl. Phys.  B 74, 197(2002)] .

The idea of utilizing a grating as a beam splitter is based on the natural splitting of an incident beam through dispersion into different orders. This is depicted in the figure above where a monochromatic beam incident on the grating is diffracted into one zeroth order and two first orders (for simplicity, only one is shown). Two mirrors reflect the zeroth order and one of the first orders straight back through the grating. In the second passage through the grating, the first order of the primary zeroth order automatically propagates in the same direction as the zeroth order of the primary first order. Because of the equal number of dispersions into the first and zeroth order involved, the splitting of the original beam in the two arms of the interferometer is exactly 50% independently of the efficiency of the grating. The transmission grating interferometer exhibits an additional feature, namely it spectrally analyzes the incident radiation. This property is especially desirable in case of gas harmonics produced by relatively long laser pulses where the spectrum is discrete.  Then, the isolation of a single harmonic or a group of harmonics can be easily implemented by simple geometrical obstacles like apertures or knife-edges.

The first experimental utilization of this grating based interferometer was the characterization with respect to its duration and spatial coherence of the third harmonic of a 1kHz repetition rate Ti:sapphire laser system delivering ~50fs pulses . The harmonic was generated in an Ar gas cell and its temporal characterization was performed by measuring the second order interferometric as well as the intensity AC traces in a second cell containing gaseous Toluene (C7H8). The results are depicted in the figure below along with the Fourier spectrum of the autocorrelation trace.

To assess the overall performance of the grating Michelson interferometer, a measurement  was undertaken of the TH pulse duration  using a conventional Michelson interferometer with a 1mm thick fused silica beam splitter. The total optical path from source to detector through optical components and air was nearly the same for both interferometers. Within the accuracy of the measurement, both interferometers gave the same value for the TH pulse duration. This demonstrate the applicability of this  new type of interferometer in the XUV spectral region and therefore its appropriateness for higher harmonics autocorrelation measurements [see: N. A. Papadogiannis et al. Opt. Lett., 27, 1561(2002)]

The observation of a non-linear process, e.g. multiphoton ionization or inner-shell transition, induced by short-pulse coherent XUV radiation, such as the high-order harmonics of fs-laser radiation from rare gases, has been a challenging problem for a long time now. This is not only because of the interesting new physics inherent to the process, but also because it opens up the possibility of applying well established approaches in fs-laser pulse metrology to short pulses in the XUV wavelength region by providing an appropriate non-linear detector. Thus, second or higher order auto-correlation techniques can be appropriately modified for XUV radiation and utilized for the temporal characterization of individual higher-order harmonics or of a harmonic superposition.

In an experiment performed with the first module of the 10 Hz Ti:sapphire laser system at Max-Planck-Institut für Quantenoptik, ATLAS, delivering 130 fs long pulses,  two-photon ionization of He induced by a broadband XUV spectrum consisting of the 7th harmonic (~113 nm) to the 13th harmonic (~61 nm) of a Ti:sapphire laser was observed. In terms of the perturbation theory, this is a second order processes induced by the shortest wavelength and broadest bandwidth ever reported so far.  A schematic of the experimental set-up used is shown in the previous figure. The laser beam is focused with a 1.5 m lens into a Xenon gas-jet in which the harmonics are generated. A Kirckpatrick-Baez focusing system is introduced in the propagation axis of the XUV radiation. This comprises two gold-coated spherical mirrors of 5 m radius of curvature one fixed in the x-y plane and the other in the x-z plane. The fundamental is filtered out by a 0.16 µm thick Indium filter, which also selects the 7th to 13th harmonic. At focus of the Kirckpatrick-Baez system, the XUV light interacts with  a second pulsed He gas-jet. The ions resulting from two-photon ionization by the harmonic beam are detected by a  time of flight energy analyzer as shown in the figure of the setup. The harmonics are monitored simultaneously with the ionization signal by means of an XUV monochromator coupled to the exit of the ionization chamber. The He+ ion signal was thus measured as a function of the total XUV intensity and the results of this measurement in a log-log scale are shown in figure to the left.   The slope of a fitted straight line is 2.3±0.3. Further, solving the Time Dependent Schrödinger Equation for He in a coherent polychromatic field, the He+ ion yield was calculated as a function of the total XUV intensity and found to be in reasonable agreement with its measured value.  These results establish the feasibility of a second order auto-correlation measurement of superposition of harmonics and thus open up the prospect of conducting second order auto-correlation measurements of coherent superposition of higher harmonics aiming at the unambiguous quantitative temporal characterization of attosecond pulse trains.