Laser Solitons in 1D, 2D and 3D

We review research of spatial and spatiotemporal dissipative solitons and their complexes in laser with saturable absorption, beginning from geometrically one-dimensional (1D) and turning to two-dimensional (2D) and then to three-dimensional (3D) ones. We demonstrate evolution of features, including topological ones, with their enrichment, of the laser localized structures with increase of the scheme’s geometrical dimensionality

Extreme and Topological Dissipative Solitons with Structured Matter and Structured Light

Structuring of matter with nanoobjects allows one to generate soliton-like light bundles with extreme characteristics—temporal duration and spatial dimensions. On the other hand, structuring of light gives the possibility to form light bundles with complicated internal structure; their topology could be used for information coding similar to that in self-replicating RNA molecules carrying genetic code. Here we review the both variants of structuring. In the first variant, we consider a linear molecular chain and organic film interacting resonantly with laser radiation. Demonstrated are optical bistability, switching waves, and dissipative solitons, whose sizes for molecular J-aggregates can reach the nanometer range. We also discuss some theoretical approaches to take into account multi-particle interaction and correlations between molecules. In the second variant, light structuring in large-size laser medium with saturable amplification and absorption is achieved by preparation of the initial field distribution with a number of closed and unclosed vortex lines where the field vanishes. Various types of topological solitons, parameter domains of their stability, and transformation of the solitons with slow variation of the scheme parameters are presented

Three-dimensional structures in nonlinear cavities containing left-handed materials

We study the coupling between negative diffraction and direct dispersion in a nonlinear ring cavity containing slabs of Kerr nonlinear right-handed and left-handed materials. Within the mean field approximation, we show that a portion of the homogeneous response curve is affected by a three-dimensional modulational instability. We show numerically that the light distribution evolves through a sequence of three-dimensional dissipative structures with different lattice symmetry. These structures are unstable with respect to the upswitching process, leading to a premature transition to the upper branch in the homogeneous hysteresis cycle

Three-dimensional structures in nonlinear cavities containing left-handed materials

We study the coupling between negative diffraction and direct dispersion in a nonlinear ring cavity containing slabs of Kerr nonlinear right-handed and left-handed materials. Within the mean field approximation, we show that a portion of the homogeneous response curve is affected by a three-dimensional modulational instability. We show numerically that the light distribution evolves through a sequence of three-dimensional dissipative structures with different lattice symmetry. These structures are unstable with respect to the upswitching process, leading to a premature transition to the upper branch in the homogeneous hysteresis cycle