Advances in table-top femtosecond lasers have made routine the generation of optical pulses containing terawatts of power with peak intensities of 10¹⁶ - 10¹⁸ W cm^-2, raising the possibility of new types of small-scale short-wavelength lasers and miniature particle accelerators.

Short-wavelength lasers, laser wakefield acceleration, and so-called high-harmonic generation require laser pulses with intensities of order 10¹⁶ - 10¹⁸ W cm^-2 to propagate tens of millimetres through moderately dense plasmas. However, the laser-plasma interaction length is fundamentally limited by diffraction to distances of order the Rayleigh range, which for spot sizes of a few tens of microns is only a few millimetres. Refractive de-focusing often restricts the interaction length still further.

We have recently developed a new type of waveguide which is able to overcome such de-focusing. The 'gas-filled capillary discharge waveguide' operates by running a simple pulsed discharge in a gas contained by a narrow-bore capillary. Within the plasma which is formed, radial heat conduction to the walls of the capillary causes the temperature to be greater, and hence the density to be lower, along the axis of the capillary than at the capillary walls. Since the refractive index of a plasma decreases as the electron density increases, this radial electron density profile acts as a positive lens which continuously re-focuses a propagating optical pulse. We have used this approach to achieve guiding of laser pulses with a peak intensity of 10¹⁷ W cm^-2 over lengths of up to 50 mm with the lowest losses yet reported for such intensities.

The gas-filled capillary discharge waveguide is being further developed in order to allow channelling over longer plasma lengths, as well as tailoring the properties of the plasma channel to the particular requirements of short-wavelength lasers, laser driven accelerators, and high-harmonic generation.

New types of lasers operating in the so-called extreme ultraviolet (XUV: 30 - 100 nm) and soft x-ray spectral region (1 - 30 nm) may be driven by a process known as 'optical field ionization' (OFI). This occurs for intensities greater than approximately 10¹⁶ W cm^-2, when the electric field associated with an electromagnetic wave is greater than that which binds the valence electrons of an atom. The threshold nature of this ionization process enables considerable control over the ion species generated, through the laser intensity, and by adjusting the polarization of the driving radiation the final energy of the ionized electrons may also be varied. The plasmas formed by this method are promising media for creating population inversions at short wavelengths via either collisional excitation or electron-ion recombination. However, whilst several lasers in the extreme ultraviolet and soft X-ray spectral regions have been demonstrated with this approach, progress has been hampered by the difficulty in achieving sufficiently long gain lengths.

The development by the group of waveguides for high-intensity laser pulses offers the prospect of greatly increasing the gain length of OFI-driven lasers, greatly increasing their output energy and allowing lasing to be achieved on many new laser transitions. In the first experiment of its type, we recently demonstrated lasing at 41.8 nm on a transition of Xe8+ driven by OFI in a gas-filled capillary discharge waveguide. We intend to build on this success and investigate a wide variety of OFI lasers driven within plasma channels.

It was observed some years ago that when a pulse of light with an intensity of order 10¹⁵ W cm^-2 interacts with a gas, radiation with frequencies equal to the odd harmonics of the frequency of the driving laser are generated. The harmonics can be of very high order, as high as several hundred, corresponding to generated wavelengths in the soft x-ray region. Further, this high-harmonic generation (HHG) produces beams of short-wavelength radiation of good spatial and temporal coherence. As such, HHG is now commonly used as a simple and reliable source of tunable short-wavelength radiation in a wide range of scientific disciplines.

However, the efficiency with which harmonics can be generated is very low, of order 10^-7. In order to improve this it is necessary to (i) increase the efficiency with which harmonics are generated per atom; (ii) phase-match the harmonic generation process; (iii) increase the length over which harmonics are generated by guiding the driving laser beam over long lengths. Further, it would be desirable to be able to generate shorter wavelengths.

It should be possible to increase the efficiency of harmonic generation per atom by using driving laser pulses of shorter wavelength. Further, it is expected that generation of shorter wavelengths would be possible by generating harmonics in ions, rather than neutral atoms, and by using driving laser pulses of higher intensity.

The plasma waveguide developed by the group offers allows very high intensity laser pulses to interact with a long length of plasma. However, in order for HHG to occur over the length of the waveguide, techniques for overcoming the mismatch in phase velocity of the driving and generated radiation must be employed. A possible solution to this phase-matching problem would be the development of plasma channels with longitudinal structure, which would allow operation in the so-called 'quasi phase-matching' regime.

The group has an active theoretical programme of research in this area, using computer codes to calculate the single-atom response and incorporating this into numerical models of the propagation of the driving and generated radiation through plasma channels. We also undertake experiments on HHG in plasma channels and gas jets using the group's high-power femtosecond laser facility.

When an intense laser pulse propagates through a plasma, electrons are pushed away from the front and back of the pulse leading to the formation of a longitudinal plasma wave that propagates at the group velocity of the optical pulse. The longitudinal electric field in the plasma wave can be as high as 100 GV m^-1, more than three orders of magnitude larger than that found in conventional RF accelerators such as those used at CERN. Particles injected into the correct phase of the plasma wave can be accelerated to energies of order 1 GeV in only a few tens of millimetres (compare this with the rest mass of the electron which is only 0.5 MeV). This 'laser wakefield accelerator' is particularly promising for generating beams of short pulse, high-energy electrons for applications in femtosecond electron diffraction, medical imaging, and miniature free-electron X-ray lasers.

The successful implementation of laser-driven accelerators requires the driving laser pulse to be guided over tens of millimetres. The guiding technique developed by the group is ideally suited to this application. As reported in Nature Physics, we have used this approach to generate electron beams with energies of 1 GeV — a beam energy comparable to that used in today's synchrotron machines. We are now developing techniques for increasing the shot-to-shot stability and energy of laser accelerated electron beams. We have also formed a Leverhulme International Network to explore the prospects of using the high-energy electron pulses to drive free-electron lasers operating at X-ray wavelengths.