18.11 N&v 281 Mh

widely used to generate coherent light at frequencies at which laser light is unavailable. Standard devices can have a very high efficiency (close to 100%), but they employ pure, sizeable — and hence expensive — nonlinear single crystals, and require careful adjustments. On page 374 of this issue, Baudrier-Raybaut et al. show that efficient optical frequency conversion can be achieved in disordered polycrystalline materials, which are, by contrast, rather cheap to fabricate and require hardly any control. This finding is likely to mark a significant step towards large-scale applications of nonlinear optics in everyday life. Suppose that light of some frequency (say, the red light of a ruby laser, at 4.3 10 hertz) is shone onto a nonlinear crystal (a material that is not centrosymmetric). The vibrating electric field of the laser beam excites oscillations of the electrons bound in the atoms of the material. The electrons, in their turn, re-emit light at the ‘fundamental’ (original) frequency but also at a frequency that is double the original value (8.6 10 hertz, in this example; ultraviolet light). This ‘second harmonic’ appears because of the anharmonicity and the asymmetry of the electric potential seen by the electrons in the crystal. This is the simplest optical frequency converter. But nonlinear frequency conversion is efficient only if the second-harmonic waves generated by different atoms interfere constructively — or, at least, do not extinguish each other because they are out of phase (Fig. 1a). This ‘phase-matching’ condition is a manifestation of momentum conservation and is of paramount importance for all nonlinear wave-mixing processes. In the first report of the generation of optical harmonics by Franken et al., for example, the nonlinear process was not phase-matched and the resulting signal was weak — so weak, it is said,that the editorial staff of Physical Review Letters mistook it for irrelevant noise and carefully removed the tiny spot it produced on the photographic plate. The condition of phase matching requires that the two waves, the fundamental and the second harmonic, should travel with the same velocity. But the speed of a wave is a monotonically decreasing function of frequency (for so-called normal dispersion), so phase matching cannot be obtained ‘for free’. The most common approach has been to news and views