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Attosecond pulse measurement techniques
We are working as part of the UK Research Councils Attosecond Technology programme which is developing sources, metrology and applications of attosecond pulses. The role of our group at Oxford is to develop methods and equipment for fully characterising attosecond pulses produced by high harmonic generation (HHG). To this end, we are extending the technique of spectral phase interferometry for direct electric field reconstruction (SPIDER) into the extreme ultraviolet, sub femtosecond region.
This extension involves directly measuring extreme ultraviolet (XUV) photons with a spectrometer and is thus more efficient and considerably less complex than methods which measure the photoelectron spectra emitted when the XUV pulse is mixed in a gas with longer optical pulses that have been used previously to measure the duration of attosecond pulses. SPIDER involves the mixing of two fields that are replicas of each other except that one of the replicas is spectrally shifted, or sheared, with respect to the other and delayed in time. The detection of these pulses in a spectrometer yields an interferogram from which the spectral phase can be extracted directly.
Creating sheared pulses
To create the sheared pulses we use the fact that the XUV radiation produced via HHG depends on the mean frequency of the driving pulse. Specifically, this means that a harmonic pulse train generated by a pulse of mean frequency ω and one generated by a pulse of mean frequency ω + δω will be spectrally sheared with respect to one another by nδω at the nth harmonic. These can be overlapped in an XUV spectrometer to produce a SPIDER interferogram.
Fig. 1 shows the interferogram obtained in this way from a pair of harmonic pulses generated in argon by two 30 fs pulses, separated by 77 fs, with mean wavelengths of 800 nm and 804 nm. The peak intensity of each pulse is 1.7 x 1014 W/cm-2, which ensures that ionisation due to the first pulse does not significantly distort the XUV burst generated by the second pulse. The total ionisation yield is about 103, and the interferogram can be inverted using Fourier processing methods to give the spectral phase of the XUV radiation over several harmonic orders as shown in Fig. 2.
A drawback to this configuration is that the intensity of the first driving pulse is limited by the requirement that the ionisation it produces does not distort the XUV pulse generated by the second driving pulse. This can be avoided if the geometry of the nonlinear interaction is altered so that the interferogram has a spatial, rather than spectral, carrier imposed. This is shown in figure 3.
The two driving pulses now generate two spectrally sheared harmonic pulses in spatially separated regions. The harmonic radiation propagates to a single spectrometer, which records the spatial interference pattern as a function of XUV wavelength. The encoding of the phase information in this geometry is achieved by interfering the energy-shifted XUV pulses in the spatial domain after they have propagated away from the generation region. The spatial fringes allow the useful interferometric component to be isolated using the same Fourier techniques as conventional SPIDER. The advantages of this approach are that there is no need to resolve any spectral fringes, which relaxes the constraint on the resolution of the spectrometer, there is no time delay between the interfering pulses to calibrate and the XUV pulses are created in separate regions of the HHG source. Fringes from simulated spatially encoded attosecond SPIDER (SEA SPIDER) data are shown in figure 4, and the phase reconstructed from this data in figure 5.
 Self-referencing, spectrally or spatially encoded spectral interferometry for the complete characterization of attosecond electromagnetic pulses Eric Cormier, Ian A. Walmsley, Ellen M. Kosik, Adam S. Wyatt, Laura Corner and Louis F. DiMauro, Physical Review Letters 94, 033905 (2005)
 Spectral phase interferometry for complete reconstruction of attosecond pulses E. Cormier, I. A. Walmsley, E. M. Kosik, A. S. Wyatt and L. Corner, Laser Physics 15, 909 (2005)
 Complete characterisation of attosecond pulses E.M. Kosik, L. Corner, A.S. Wyatt, E. Cormier, I.A. Walmsley and L.F DiMauro, Journal of Modern Optics 52 361 (2005)