Extreme Nonlinear Optics: Coherent X Rays from Lasers

coherent light with controllable properties—is one of the most significant enabling achievements of 20thcentury science. Because atoms interact through the electromagnetic force, researchers can probe—and in some cases control—the properties and dynamics of atomic, molecular, or condensed matter systems with unprecedented precision simply by applying external, controlled electromagnetic fields. In recent years, nonlinear-optical techniques that convert one frequency of light to another have played an increasingly pivotal role in that technology—a role second in significance only to that of the laser itself. Optical frequency doubling or parametric amplification, for instance, converts laser light into coherent radiation tunable over the near-IR, visible, and near-UV regions of the spectrum. Recent years have also seen the development of ultrashortpulse technologies. The uncertainty principle DEDt \/2 dictates that a very short pulse of light must have broad spectral bandwidth. However, generating such a short pulse also requires that the colors in that broad spectrum have a well-defined phase relationship with each other; that is, the coherence must span the entire spectrum. More generally, control over broad-spectrum coherence makes it possible to implement the optical analog of an arbitrary waveform generator, a device that can sculpt the shape of a light pulse over time and precisely manipulate atomic or molecular dynamics. By taking concepts of nonlinear optics and ultrashort pulse generation to an extreme limit, one can generate coherent light at even shorter wavelengths using a process called high-harmonic generation (HHG). This process shifts femtosecond laser light from the near-IR (1–2 eV) to the extreme-UV (tens to hundreds of eV) and soft x-ray (up to a keV) regions of the spectrum. The EUV is a difficult region of the spectrum for nonlinear optics because traditional frequency-conversion techniques generally rely on crystalline solids as the nonlinear medium, and solids are not transparent in the EUV. Nevertheless, good reasons are driving the development of new light sources in that spectral range: Short-wavelength light is ideal as a structural and chemical spectroscopic probe and as a tool for nanoscale lithography. Synchrotron sources were originally developed to address such applications, but those machines are large and have limited access. High-harmonic generation produces tunable, laserlike light with high spatial and temporal coherence from an assembly of components small enough to sit on a tabletop. Moreover, the physics of the process differs radically from traditional nonlinear optics because it is intimately linked to the attosecond time domain. The quantum dynamics of the atom–field interaction determines the wavelength range, efficiency, coherence properties, and pulse duration of the generated light (see PHYSICS TODAY, April 2003, page 27).