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Ultrashort pulses

Phase in focus

Ultrafast, nonlinear light–matter interactions such as high-harmonic generation take place at the focus of a beam of laser pulses and rely strongly on the phase of the optical carrier field with respect to the pulse envelope's maximum — the carrier-envelope phase (CEP). For a focused monochromatic beam, it has long been known that the on-axis spatial dependence of the phase around the focus is described by the Gouy phase, which follows a simple arctangent curve. However, the situation for focused, ultrashort broadband pulses is more complex and recent theoretical studies have suggested a significant deviation from the Gouy phase.

Now, Dominik Hoff and co-workers from Germany and Israel have experimentally performed three-dimensional mapping of the CEP evolution of a focused broadband Gaussian laser beam (pictured) and elucidated its complex behaviour (Nat. Phys.; 2017).

The experimental system was composed of a nanotip-based focus characterization set-up and a xenon-gas-based, stereographic, above-threshold ionization CEP meter. A train of 4-fs-duration, 700-nm central wavelength pulses from a laser system with a hollow-core fibre compressor was split into two paths: one path for individual characterization of the random CEP of each shot and the other for recording electron spectra from the laser–nanotip interaction. The beam of laser pulses was focused using a 90° off-axis parabolic mirror onto a metal (tungsten or gold) nanotip placed inside an ultrahigh-vacuum chamber (10−9 mbar).

Credit: Macmillan Publishers Ltd

The key point for success in the three-dimensional mapping is the capture of ejected photoelectrons from the nanotip: the large kinetic energy obtained by these electrons strongly depends on the CEP. A time-of-flight spectrometer recorded the flight time of photoelectrons using a microchannel plate and determined their kinetic energy. In the other path, the CEP meter measures the randomly varying CEP of each and every shot.

The metal nanotip was positioned at several points in the beam path. Strong-field-induced photoemission happened almost exclusively in the enhanced optical near-field region at the apex of the sharp tip, with a radius of 10 nm. The spatial and CEP resolutions were consequently obtained as 10 nm and 80 mrad (corresponding to 60 as), respectively.

The measured CEP showed extrema (darkest red and darkest purple regions) at 1.7 times the Rayleigh length (zR) both before and after the focus (z is the laser-propagation direction and r the radial position). Although the phase evolution exhibited a much more complex spatial dependence than the Gouy phase, it opens the opportunity for novel ways to improve phase matching in high-order harmonic and attosecond pulse generation.


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Horiuchi, N. Phase in focus. Nature Photon 11, 541 (2017).

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