A study of the relationship between high-harmonic generation and the length of the gas-filled waveguides in which it occurs promises researchers the tools to develop better sources of coherent extreme-UV and x-ray radiation. The collaboration behind the work from JILA in Boulder, Colo., and the University of Sofia in Bulgaria suggests that such sources will have applications in fundamental physics, materials science and biological imaging.In high-harmonic generation, ultrashort laser pulses are focused into an atomic gas, ionizing the atoms. It is believed that coherent short-wave radiation is released as the liberated high-energy electrons collide with the ions. Combining the target gas in a hollow waveguide with a periodically modulated diameter induces modulations in the phase and amplitude of the generated radiation that mitigate destructive interference. Previous work suggested this improves the efficiency of the process and enables the generation of shorter wavelengths.In the current study, the team sought to better understand the relationship between the length of the waveguide and the spatial coherence of the generated radiation. Using theoretical models and an experimental setup, it found that the spatial coherence of the extreme-UV radiation produced by an ultrafast Ti:sapphire laser in pressurized argon or helium gas reached a maximum in waveguides longer than 5 cm. For the work, the laser produced 20-fs pulses of 800-nm radiation at a repetition rate of 2 kHz, yielding peak intensities of 4 3 1014 W/cm2 at the center of the 150-µm-diameter waveguide and generating up to 29th-harmonic radiation.The scientists suggest that the improved coherence is the result of the interaction of the pump laser radiation and the gas. They calculated that the beam diameter of the pump laser oscillates with propagation length in 150-µm-diameter waveguides shorter than 5 cm and that it reaches a steady state in the longer waveguides. At the steady state, the maximum number of atoms in the target is excited and is done so uniformly, improving both the efficiency of the conversion process and the quality of the output.Henry C. Kapteyn, a professor of physics at the University of Colorado in Boulder and a member of the JILA team, said such discoveries also provide practical information for the design of an optimized high-harmonic-generation system. "The result is a 'tabletop' extreme-UV and soft x-ray laser source," he said. "Not yet cheap -- the equipment costs about $200,000 to $300,000 -- but at least it fits in a small lab.