Stable autosolitons in dispersive media with saturable gain and absorption

We introduce the simplest one-dimensional model of a dispersive optical medium with saturable dissipative nonlinearity and filtering (dispersive loss) which gives rise to stable solitary pulses (autosolitons). In the particular case when the dispersive loss is absent, the same model may also be interpreted as describing a stationary field in a planar optical waveguide with uniformly distributed saturable gain and absorption. In a certain region of the model's parameter space, two coexisting solitary-pulse solutions are found numerically, one of which may be stable. Solving the corresponding linearized eigenvalue problem, we identify stability borders for the solitary pulses in their parametric plane. Beyond one of the borders, the symmetric pulse is destroyed by asymmetric perturbations, and at the other border it undergoes a Hopf bifurcation, which may turn it into a breather.Comment: A latex text file and four ps files with figures. Physics Letters A, in pres

Maxwell-Drude-Bloch dissipative few-cycle optical solitons

We study the propagation of few-cycle pulses in two-component medium consisting of nonlinear amplifying and absorbing two-level centers embedded into a linear and conductive host material. First we present a linear theory of propagation of short pulses in a purely conductive material, and demonstrate the diffusive behavior for the evolution of the low-frequency components of the magnetic field in the case of relatively strong conductivity. Then, numerical simulations carried out in the frame of the full nonlinear theory involving the Maxwell-Drude-Bloch model reveal the stable creation and propagation of few-cycle dissipative solitons under excitation by incident femtosecond optical pulses of relatively high energies. The broadband losses that are introduced by the medium conductivity represent the main stabilization mechanism for the dissipative few-cycle solitons.Comment: 38 pages, 10 figures. submitted to Physical Review

Discrete dissipative localized modes in nonlinear magnetic metamaterials

We analyze the existence, stability, and propagation of dissipative discrete localized modes in one- and two-dimensional nonlinear lattices composed of weakly coupled split-ring resonators (SRRs) excited by an external electromagnetic field. We employ the near-field interaction approach for describing quasi-static electric and magnetic interaction between the resonators, and demonstrate the crucial importance of the electric coupling, which can completely reverse the sign of the overall interaction between the resonators. We derive the effective nonlinear model and analyze the properties of nonlinear localized modes excited in oneand two-dimensional lattices. In particular, we study nonlinear magnetic domain walls (the so-called switching waves) separating two different states of nonlinear magnetization, and reveal the bistable dependence of the domain wall velocity on the external field. Then, we study two-dimensional localized modes in nonlinear lattices of SRRs and demonstrate that larger domains may experience modulational instability and splitting

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