Transverse-Pattern Formation in Photorefractive Optics

Abstract

The propagation of a light beam through a nonlinear medium is the simplest scenario that one could imagine for light-matter interaction, but it is accompanied by a series of dramatic and fascinating changes in the spatio-temporal structure of the beam. Among these are light-induced scattering which may result in asymmetric beam fanning; the formation of spatial distributions of the electromagnetic fields that results in back reflection; phase-conjugation; and the possibility to prevent the beam from spreading and to enable selftrapping of the beam profile. Therefore, the spatial evolution of a single light beam is a central topic of nonlinear optical dynamics. A theoretical interpretation of this complex phenomenon and its experimental verification are of key importance for gaining insight into the nonlinear properties of a particular medium, on the one hand, and for contributing to our understanding of more general questions about the complex spatio-temporal behavior of nonlinear systems on the other hand. This is the reason why we have chosen this simple propagation of light through a nonlinear medium as the starting point for our investigations.The topic is not a completely new one. Initial investigations on the selftrapping of light beams in nonlinear media were already performed in the early 1960s [1, 2]. The most important task, since the beginning of this research, was to find the conditions for the stability and nonlinear evolution of solitary-wave solutions of the nonlinear propagation equations associated with the propagation of the beam in the nonlinear material. This is one of the most crucial parts of the problem of self-trapping of optical beams and promises applications in waveguiding, information processing and, most simply, propagation without spreading losses.In general, these effects may occur in all materials that display a nonlinear response that may act in such a way that diffraction effects due to the propagation of the beam can be compensated exactly. The balance between beam broadening on the one hand and self-focusing on the other hand gives rise to the formation of a solitary wave. In this case the envelope of the light wave does not change its profile during propagation. This wave is often called a soliton for short.Solitons are waves that do not spread or disperse like all familiar waves, but retain their size and shape indefinitely -they are dynamically and struc-

Dancing Light: Counterpropagating Beams in Photorefractive Crystals

“…Theory capable of capturing such dynamics is introduced and linear stability analysis (LSA) performed. Numerical simulations are found in qualitative agreement with the experiment and LSA [3]. Spontaneous symmetry breaking of head-on Gaussian beams is demonstrated as the coupling strength is increased, resulting in the splitup transition of CP components.…”

Quantum criticality in photorefractive optics: Vortices in laser beams and antiferromagnets

“…Before entering the crystal, the laser beams can be given any desirable pattern of both intensity and phase. In particular, one can create vortices (winding of the phase) making use of the phase masks [3] or other, more modern ways.…”

“…Nonlinear and pattern-forming systems [1][2][3] have numerous analogies with strongly correlated systems encountered in condensed matter physics [4,5], and on the methodological level they are both united through the language of field theory, which has become the standard language to describe strongly correlated electrons [6,7] as well as nonlinear dynamical systems [8]. In the field of pattern formation, some connections to condensed matter systems have been observed, see e.g.…”

“…However, this topic is far from exhausted and we feel many analogies between quantum many-body systems and pattern-formation dynamics remain unexplored and unexploited. In particular, nonlinear optical systems and photonic lattices are flexible and relatively cheap to build [3] and they can be used to "simulate" a broad spectrum of phenomena concerning band structure, spin ordering and conduction in strongly correlated electron systems; some of the work in this direction can be found in [14,15].…”

Localized Structures in Broad Area VCSELs: Experiments and Delay-Induced Motion

“…In particular, LSs could be used as bits for information storage and processing. Several overviews have been published on this active area of research [31,9,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48].…”