High-harmonic generation & ultrafast X-ray imaging


When a high-intensity laser pulse 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. One reason for the low efficiency is that the phase velocities of the driving laser and the generated radiation are different, which causes harmonics generated at different points in the gas to be out of phase. As a consequence the intensity of the harmonics decreases at distances just beyond the dephasing length, and at longer distances the harmonic intensity oscillates with the length of the gas cell. When generating very short wavelength harmonics (which are of most interest in applications) it is difficult to match the velocities of the driving and generated radiation -  a process known as phase-matching. However, an alternative approach is "quasi-phase-matching" (QPM), in which harmonic generation in out of phase zones is suppressed.

QPM can be achieved by a number of methods. These include using a counter-propagating train of laser pulses to suppress HHG; and modulating the intensity of the driving laser by exciting two or more modes of a waveguide. We have an extensive experimental programme on QPM, funded by EPSRC, which takes advantage of our high-power, femtosecond laser systems. This is backed up by numerical modelling of harmonic generation and quasi-phase-matching processes.

In its early stages of development, our imaging beamline was tested on simply binary transmissive apertures composed of a gold coated silicon nitride membrane. These apertures were fabricated using a Focussed Ion Beam that mills out prescribed patterns on the scale of nanometres to microns. During this process, calibration tests were performed to establish the length of time needed to mill through the gold coating and expose the transmissive substrate beneath - the video shows the final stages of the first calibration test in real time as the milling beam breaks through the substrate, causing the suspended feature to warp and fall out of the hole


Further reading

  1. M. Zepf, B. Dromey, M. Landremann, P. Foster & S. M. Hooker[/url], "Bright quasi-phase-matched soft-x-ray harmonic generation from argon ions," Phys. Rev. Lett. 99 14301 (2007). DOI: 10.1103/PhysRevLett.99.143901
  2. K. O'Keeffe, T. Robinson & S. M. Hooker, "Generation and control of chirped, ultrafast pulse trains," J. Opt. 12 015201 (2010). DOI: 10.1088/2040-8978/12/1/015201
  3. T. Robinson, K. O'Keeffe, M. Zepf, B. Dromey, & S.M. Hooker, "Generation and control of ultrafast pulse trains for quasi-phase-matching high-harmonic generation," J. Opt. Soc. Am. B 27 763 (2010). DOI: 10.1364/JOSAB.27.000763