Two-dimensional lattice solitons

Through a balance between linear and nonlinear processes, periodic nonlinear systems can produce a self-localized state: a lattice soliton. Such systems include, for example, “breather” states in biological α-helixes and quantum vortex pairs in linear arrays of current-driven Josephson junctions. Now, Mordechai Segev (Technion-Israel Institute of Technology), Demetri Christodoulides (University of Central Florida), and their colleagues have created such a system in two dimensions. The physicists used light both as the means for creating the lattice—by interfering pairs of plane waves within a photorefractive, anisotropic crystal—and as the “probe” beam to form the optical lattice soliton. The degree of nonlinearity was set by a tunable electric field and by adjusting the ratio between the probe beam and the lattice waves. At a low voltage, the probe propagated linearly through the 6-mm-long crystal and showed a “discrete diffraction” pattern (left image, above). At a higher voltage, however, self-trapping occurred and a soliton formed (right image). When the probe intensity was lowered, even at the high voltage, the diffraction reappeared. The researchers say that their methods allow them to dynamically reconfigure the lattice into various geometries, and that further possibilities include studying lattice solitons with angular momenta, vortex lattice solitons, and 3D collisions of lattice solitons. They also say that these ideas can be implemented in other media, such as atomic lattices for Bose–Einstein conden-sates. (J. W. Fleischer et al., Nature 422, 147, 2003 . See also J. W. Fleischer et al., Phys. Rev. Lett. 90, 023902, 2003 .)