Generation of light bullets

Abstract

Researchers have long sought to generate wave packets that are localized in all three dimensions (3D) as they propagate in space or evolve in time. Such wave packets theoretically exist in settings as diverse as condensedmatter physics, degenerate quantum gases, and nonlinear optics, but experimental observations are extremely rare. In a recent paper in Physical Review Letters, Stefano Minardi and co-workers at Friedrich Schiller University in Jena, Germany, report the generation of spatiotemporal solitons or “light bullets”—localized packets of electromagnetic energy that propagate without spreading out, despite diffraction and dispersion [1]. In addition to its intrinsic scientific interest, the study of spatiotemporal solitary waves should lead to ways to enhance light-matter interactions as well as to powerful optical information-processing systems. Diffraction causes light beams to spread in the transverse direction as they propagate. A temporal pulse of light analogously spreads out owing to material dispersion: the index of refraction varies with wavelength, so the different wavelengths that make up the pulse move at different speeds. Dispersion can be normal or anomalous. With normal dispersion, low frequencies move faster than high frequencies in a pulse (“red leads blue”), while with anomalous dispersion, the high frequencies lead the low frequencies. Thus a pulsed beam spreads in both time and space as it propagates. However, nonlinear effects can counteract the spreading. The index of refraction typically increases with the intensity of a light beam. A beam with a Gaussianshaped transverse intensity profile (which is what lasers usually produce) will undergo self-focusing as its center picks up a larger phase than its edges, as would occur in a positive lens. Self-focusing can nominally balance diffraction, to make a stable beam of fixed size. In the time domain, the intensity-dependent refraction can balance the effects of anomalous material dispersion to make a pulse that propagates indefinitely without spreading out. Stable localized wave packets that balance nonlinear and linear effects in these ways are called solitons. They are remarkable because either the linear or the nonlinear effects acting alone would cause the pulse or beam to decay, but in the right combination they lead to waves that propagate without spreading. Temporal solitons in optical fibers are of great interest as bits of information in telecommunications, for example. Silberberg suggested that it might be possible for a self-focusing nonlinearity to compensate both spatial and temporal spreading of a light pulse. The resulting packet of energy is a spatiotemporal soliton [2], which is referred to as a “light bullet” in recognition of its particlelike nature. However, spatiotemporal solitons are unstable in ordinary materials such as glass; a precise balance of the nonlinear and linear effects is required, so the slightest variation of pulse or material parameters destroys the wave packet. Over the past 20 years, researchers have explored a variety of alternative materials and techniques to generate light bullets. The first optical spacetime solitons were reported in 1999, but those had only one of the two transverse dimensions controlled—the beam was in the shape of a long narrow ellipse [3]. So-called X waves have profiles with long tails that accompany the main hump. These resist the effects of diffraction and dispersion to some extent [4] but are not localized. The propagation of light waves in media with properties that are modulated in the transverse dimension has also received much attention in the past two decades. The simplest example of this would be a onedimensional array of parallel optical waveguides, which are close enough that their evanescent fields overlap. That overlap can couple energy from one waveguide to its neighbors. Thus light injected into a waveguide will eventually transfer to the other waveguides in the array, in a process that can be thought of as discrete diffraction.