Attosecond Nonlinear Optics for Creating Bright X-Ray Beams

Nature Physics

Fig. 1. Optimal suppression of the emission from out-of-phase zones is accomplished when the effective counterpropagating pulse width and pulse separation correspond to one and two coherence lengths, respectively (see inset). The inset corresponds to a frame co-moving with the forward propagating beam. In the lab frame, the pulse width and separation are twice as large. Nature Physics 3, 270-275 (2007)

Fig.2. Measurement of harmonic intensity as a function of harmonic order and intersection point between the forward and counter propagating beams, with respect to the exit of the waveguide.
Nature Physics 3, 270-275 (2007)

Fig. 3. An artist's conception of high harmonic generation in a hollow capillary.

Ever since laser was invented and bright, directed, beams of light could be generated, scientists have used nonlinear-optics to convert light from one color to another. This is fortunate because lasers simply do not exist in many regions of the spectrum - in particular in the x-ray region. As a result, new methods that can convert laser light efficiently from the visible to shorter wavelengths are a "grand challenge" in laser science. In a breakthrough experiment published in Nature Physics, we used a train of light pulses to artificially fabricate a nonlinear crystal to efficiently convert laser light efficiently to x-rays.

In this experiment, we first used a powerful visible laser to pluck an electron from an atom of argon (Ar). Then, the electron was slammed violently back into the same atom, generating an X-ray. This process creates a directed, but weak, beam of x-rays. The challenge is to add together the different x-ray waves emitted from a large number of atoms. Because the visible waves and x-ray waves travel at different speeds in the gas, usually the generated x-ray waves do not all add constructively. What is needed is to eliminate x-ray emission from regions that cause destructive interference. This was accomplished by sending some weak pulses of a visible light into the gas in the opposite direction to the laser beam generating the x-rays. The weak laser beam scrambles the electrons plucked from the atoms, suppressing x-ray emission from regions that are out-of-sync with the main beam. Using three counter-propagating pulses, the x-ray flux was increased by > 700 at selected photon energies around 70 eV. In theory, it should be possible to extend this technique all they way into the hard x-ray region, where this technology could improve current x-ray imaging resolution by a thousandfold, with impacts in medicine, biology, and nanotechnology.

"Optics in 2007. Nonlinear Optics."
Optics and Photonics News, pp 32 (Dec. 2007).

Phase Matching at keV Photon Energies - Coherent Hard X-Rays!


	Fig. 1. (a) Schematic of grating-assisted phase matching (GAPM) in high harmonic generation (HHG) by quasi-cw counterpropagating light. (b) The combination of the medium phase mismatch and the optically-induced sinusoidal oscillation in the phase of the emitted harmonics results in a partial correction of the phase mismatch associated with the frequency conversion process. Cohen et al. PRL 99, 53902 (2007)
	All-optical QPM also solves the phase matching problem even at keV energies! In recent work, we proposed a new and experimentally feasible technique for phase-matched frequency conversion into the x-ray region of the spectrum. A weak quasi-CW counter-propagating field induces a sinusoidal modulation on the phase of the generated harmonics, which is formally equivalent to a modulation in the refractive index for the driving laser. For harmonics with photon energies ~keV, the coherence lengths in the micron range are well matched to the wavelength of the IR field. The induced phase modulation is akin to a frequency modulation of the harmonics - in contrast with the amplitude modulation induced by a counter propagating pulse. This is the first technique that appears to be feasible for phase matching very high-order harmonics over extended distances in plasma waveguides, to generate bright, tunable, and narrow bandwidth x-ray beams at keV photon energies. This approach can work over long distances, since gases are transparent in keV region. Although there are many technical challenges - there is no fundamental roadblock.