One of the fundamental properties of the laser is its ability produce spatially coherent beams that can be focused to a very small spot size comparable to the wavelength lambda, or to record complex images such as holograms. However, to date the generation of fully-spatially-coherent light has been limited to the visible/UV and longer wavelength regions of the spectrum. Short-wavelength light sources such as electron impact sources, synchrotron sources, and x-ray lasers do not use resonators, and as a result generate only partially coherent light. High harmonic generation (HHG) is a useful way of generating coherent light in the ultraviolet and extreme ultraviolet (EUV) regions of the spectrum. In HHG, pulses of short-wavelength light with extremely short duration can be produced by focusing a high-intensity femtosecond laser into a gas. Odd harmonics of the exciting laser frequency (i.e. 3w, 5w, etc.) are produced in a directed, narrow-divergence beam, with photon energies that can extend up to > 1keV (corresponding to harmonic orders > 1000). This process thus up-shifts a femtosecond pulse from the visible into the XUV.

In 2002 we demonstrated that "laser-like" harmonic EUV beams could be generated by focusing a femtosecond laser into a hollow waveguide filled with gas. The waveguide guides the laser beam, and ensures that the EUV beam that emerges is well collimated and truly "laser-like". Such an EUV source, with good beam quality and high spatial coherence, can be used for experiments in femtosecond holography, high-precision metrology, inspection of optical components for EUV lithography, and for microscopy with nanometer resolution. Furthermore, the time duration of the EUV radiation is femtoseconds - attoseconds.

Generating fully coherent x-ray beams requires that the conversion process be phase matched. To build-up coherently over an extended propagation distance, the EUBVand laser light must travel with the same phase velocity; i.e. the process must be phase-matched. In this case, the nonlinear response from the medium continues to add constructively to the signal beam, leading to a bright output signal at a new wavelength. Use of a hollow waveguide allows the velocity of the laser to be adjusted to match that of the EUV light by tuning the gas pressure.

Fig. 2. Phase-matched generation of fully coherent EUV beams.
Science 280, 1412 (1998); Science 297, 376 (2002);Optics Letters 29, 1357 (2004).

Microscopy has been a critical enabling technology for understanding materials and biological systems since its invention. One of the most promising alternative approaches for high-resolution, high-contrast, imaging of thick samples is to use short wavelength light, in the soft-x-ray region of the spectrum. Lensless imaging is a relatively new coherent imaging technique that requires spatially coherent beams. This technique eliminates lenses by replacing them with a computerized phase retrieval algorithm. By obviating the need for lenses, lensless imaging is well-suited to the x-ray region, where optical elements are very limited. This technique was first demonstrated in 1999 by John Miao and co-workers using spatially-filtered light from a synchrotron source.

High harmonic generation in gas-filled waveguide generates spatially coherent EUV beams and is ideally suited for lensless imaging. In recent work, we performed the first experimental demonstration of lensless imaging using a tabletop source of coherent soft-x-rays. By taking multiple exposures while blocking small-angle scattered light using beam blocks of varying size, we obtain very high dynamic range diffraction patterns which successfully reconstruct to images with resolution near 200 nm. Moreover, no low spatial frequency information is missing from the reconstructions. This work thus demonstrates that lensless diffractive imaging can be successfully implemented using tabletop light sources, with broad potential application in nanoimaging and biological imaging.

Nature News and Views: Harmonic pictures in a flash.
Nature 449, 553 (2007)