Colloquium: Optimal control of high-harmonic generation

High-harmonic generation provides an attractive light source of coherent radiation in the extreme-ultraviolet (XUV) and soft-x-ray regions of the spectrum and allows for the production of single attosecond pulses or pulse trains. This Colloquium covers the control of high-harmonic spectra by temporal and spatial pulse shaping of the driving laser pulses and its implications on time-resolved XUV spectroscopy and attosecond pulse shaping. It summarizes important steps for extending existing pulse shaping techniques and control schemes from the near-infrared or visible part to shorter wavelengths. Using adaptive pulse shaping of the driving laser pulses, several groups have demonstrated control of the high-harmonic spectrum, including the author’s work on the complete control over the XUV spectrum of high-order harmonics, generated in a gas-filled hollow fiber. It is possible to achieve both the enhancement and the suppression of single or several selected harmonic orders. These arbitrarily shaped soft-x-ray spectra will allow for important modifications of the resulting harmonic pulses in the temporal domain. This constitutes first steps towards direct attosecond pulse shaping in the soft-x-ray domain. Moreover, high-harmonic generation in a hollow-core fiber can be enhanced by coupling into a single fiber mode using a feedback-controlled adaptive two-dimensional spatial light modulator.