INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF OPTICS B: QUANTUM AND SEMICLASSICAL OPTICS J. Opt. B: Quantum Semiclass. Opt. 7 (2005) R53–R72 doi:10.1088/1464-4266/7/5/R02 REVIEW ARTICLE Spatiotemporal optical solitons Boris A Malomed 1 , Dumitru Mihalache 2 , Frank Wise 3 and Lluis Torner 4 1 Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel 2 Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest, Romania 3 Department of Applied Physics, 212 Clark Hall, Cornell University, Ithaca, NY 14853, USA 4 ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, Barcelona 08034, Spain Received 1 December 2004, accepted for publication 1 February 2005 Published 15 April 2005 Online at stacks.iop.org/JOptB/7/R53 Abstract In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic–cubic or cubic–quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose–Einstein condensates supported by full or low-dimensional optical lattices. Keywords: Bose–Einstein condensation, collapse, dispersion management, Gross–Pitaevskii equation, group-velocity dispersion, light bullet, matter-wave soliton, modulational instability, nonlinear optics, nonlinear Schr¨ odinger equation, optical lattice, optical vortex, second-harmonic generation, self-focusing, solitary wave, spatial soliton, spatiotemporal soliton, variational approximation, vortex soliton (Some figures in this article are in colour only in the electronic version) List of acronyms used in the text 1D one dimensional 2D two dimensional 3D three dimensional BC boundary conditions BEC Bose–Einstein condensation BG Bragg grating CQ cubic–quintic (nonlinearity) FF fundamental frequency GVD group-velocity dispersion GVM group-velocity mismatch LB light bullet MI modulational instability NLS nonlinear Schr¨ odinger (equation) OL optical lattice 1464-4266/05/050053+20$30.00 © 2005 IOP Publishing Ltd Printed in the UK R53