- Coherent 1-nm X-Rays Generated in Helium
Harmonic generation has been a workhorse of the photonics community for decades, creating coherent short-wavelength light from longer-wavelength lasers. Today, the market is awash with 532-nm lasers -- including green laser pointers -- whose output is the second harmonic of an infrared Nd laser. Recently, an Austrian-German team harnessed extremely high order harmonic generation to produce coherent 1-nm x-rays from the 700-nm output of an ultrafast Ti:sapphire laser.
Figure 1. The x-ray spectrum (red line), taken with a multichannel analyzer and a liquid-nitrogen-cooled silicon-lithium semiconductor detector, extends to 1 keV. The x-rays were filtered through a number of filters, whose overall transmission is represented by the green line. The gray line is the calculated spectrum emitted from the helium atoms. ©Nature Publishing Group.
Although the experiment, which represents the first demonstration of coherent x-rays in the 1-nm spectral range, produced x-rays of too low intensity for practical application, it points the way to a realistic source of coherent x-rays for many applications. Coherent x-rays, once extended to the wavelength range below 0.1 nm, would make possible x-ray images of much greater resolution -- and with much lower dosage levels for the patient -- than current techniques. This could lead, for example, to more sensitive cancer diagnoses, with significantly reduced patient risk. Already, at the currently demonstrated wavelength, the extremely short, coherent x-ray pulses hold promise for becoming a valuable tool in the investigation of atomic and molecular dynamics with near-atomic spatial and temporal resolution.
Figure 2. The purple light originates from helium atoms excited by intense laser radiation. The laser pulses propagate along the axis of the purple lobes through the gas, and the x-rays are radiated in the same direction in a beam several hundred microns in diameter. Image by Jozsef Seres, Technische Universität Wien.
Optical harmonic generation occurs when a driving field oscillates the electrons in a material beyond their linear range -- that is, beyond the point where they simply oscillate sinusoidally at the frequency of the driving field. The electrons' motion includes high-frequency components, and new fields are generated at these frequencies. These new fields are the harmonic radiation generated at harmonics of the driving field.
The overriding issue in creating significant quantities of radiation by harmonic generation is phase matching. Because the material is dispersive, the driving field and harmonic field get out of phase as they propagate. Thus, the harmonic generated at one point is not in phase with that generated at another point. For every point where harmonic radiation is generated, there exists another where it is generated exactly out of phase. The net effect is to cancel, or nearly cancel, the harmonic output.
In commercial lasers, using birefringent crystals such that the crystal's dispersion is exactly compensated by its birefringence solves the phase-matching problem. Crystals lack transparency in the x-ray region, however, so the European team, which included scientists from Technische Universität Wien and Femtolasers Produktions GmbH, both in Vienna, Austria, from Universität Würtzburg in Germany and from Max Planck Institut für Quantenoptik in Garching, Germany, used helium gas as the nonlinear material.
Researchers have used high-order harmonic generation in noble gases to generate coherent extreme-ultraviolet and soft x-ray outputs, but phase-matching problems have limited its extension to shorter wavelengths. High peak powers in the infrared pulse are required to generate x-rays, but they also ionize the helium and produce clouds of free electrons. These free electrons dramatically increase the dispersion between the infrared and x-ray wavelengths, to the point that virtually no phase matching occurs.
The team finessed this problem by pumping the helium gas with 5-fs pulses of 720-nm light, the shortest currently available at the necessary peak power level, from a pulse compressor seeded by a Ti:sapphire laser. Turning on the high laser field as quickly as this left a substantial fraction of the helium atoms nonionized, so the number of free carriers -- and thus the dispersion -- was reduced. The resulting small degree of phase matching allowed the buildup of a measurable output in the x-ray region (Figure 1).
The x-ray photon flux was very low, approximately 102 to 103 photons per second, according to team leader Ferenc Krausz. He explained that there still is a significant amount of dispersion in the helium and that better phase matching could increase the x-ray intensity by several orders of magnitude. The team is investigating the possibility of implementing quasi-phase matching by modulating the helium density along the propagation direction. In this technique, the phase mismatch is periodically reset as the two waves propagate through a medium.
- harmonic generation
- With relation to radiant energy, the conversion of electromagnetic radiation having a given frequency into radiation having a multiple of the frequency. This can occur when an intense directional light beam passes through a nonlinear optical medium.
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