Attosecond Nonlinear Optics

Extreme Nonlinear Optics - A New Era for X-Rays

High harmonic generation (HHG) from a single atom can be explained using semi-classical (top and middle) or quantum pictures (bottom). In the semi-classical picture (top left), an atom is ionized in a strong laser field. The free electron then oscillates away from the ion, sometime recombining with it, and emitting any excess energy as a higher energy photon. The right image shows the more-realistic, fully quantum, calculation of the extended wavefunction of an electron as it is accelerated in a strong laser field.

Phase-matched signal growth ensures that harmonic emission from many atoms over an extended medium adds together coherently to generate a bright coherent (laser-like) output beam. 


Ever since the invention of the visible laser 50 years ago, scientists have been striving to create lasers that generate coherent beams at shorter wavelengths i.e. the x-ray region of the spectrum. This quest has led to the construction of large facilities, such as kilometer-scale x-ray free-electron lasers, to reach the keV photon energy region. X-rays are unique in their ability to view the nano world. Their wavelengths are well matched to nanoscale objects, and they span characteristic inner-shell absorption edges whose position depends on the local element, charge and spin state. Ultrafast x-rays can capture all coupled electron-ion motion relevant to function at the nanoscale. Ultimately however, to be broadly accessible for science, medicine and industry, laser-like (i.e. coherent) x-ray sources need to be much smaller and cheaper.

Fortunately, high harmonic generation (HHG)—the coherent equivalent of the x-ray tube—represents a unique new technique for producing ultrafast coherent beams from the EUV to keV regions of the spectrum. Instead of boiling electrons off a hot filament, in HHG a femtosecond laser plucks an electron from an atom, coherently accelerates it away from, and then back to, its parent ion. When the electron recombines with the ion, its kinetic energy is coherently converted into a high harmonic photon. However, a grand challenge has been how to generate bright harmonics, particularly at the high photon energies needed for many applications imaging and spectroscopy. To generate bright beams of high harmonic x-rays, the laser and x-ray waves must propagate in phase throughout a medium to ensure that the signal from many atoms adds coherently. This is challenging at the high laser intensities required to accelerate the electron to high kinetic energy – the laser ionizes the gas, which causes the laser wave to outrun the x-ray waves, leading to severe destructive interferences.

In recent breakthrough work in collaboration with the Baltuska group at the Technical University Vienna, we showed that by using ultrafast lasers with long wavelengths in the mid-infrared region of the spectrum (≈ 4 microns), bright x-ray beams can be generated spanning from the UV to > 1.6 keV. This corresponds to wavelengths less than 8 Å from a tabletop apparatus! These bright x-ray beams span a region of the x-ray spectrum that includes the “water window” (between 0.3 – 0.6 keV) that is useful for taking ultrahigh-resolution x-ray images of single cells or nano structures. They also span regions of the spectrum important for element-specific imaging of magnetic materials (around 70 eV and 0.8 keV). Furthermore, we now understand that this technique is not limited to the soft x-ray region of the spectrum, and may make coherent hard x-ray source feasible. Thus, the laser-like, coherent, tabletop, version of the Roentgen x-ray tube that HHG corresponds to may well become a feasible alliterative to the x-ray tube that is still ubiquitous in medical imaging even a century after Roentgen’s discovery.

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