Extreme and topological nonlinear optics of open systems

A review of results of an investigation of the theory of optical wave packets with extreme properties with respect to a controllable pulse shape or to the complexity of the internal structure of radiation beam pulses is presented. Special attention is paid to the manifestations of dissipative effects of the electromagnetic energy inflow and outflow. Precisely these factors lead to peculiar rules of conservation of purely electromagnetic quantities in dissipative media, in which the electromagnetic energy irreversibly decreases in the case of absorption and increases with gain. These rules impose certain restrictions on the possibility of transformation of the shape of pulses and allow one to qualitative describe their evolution. A higher efficiency of the action of unipolar or quasi-unipolar radiation pulses on classical and quantum microobjects is shown and possible ways of formation of these pulses are discussed. For bulk laser media with saturable absorption, the topological properties of localized radiation structures and their transformations with a smooth change in the parameters of the medium (pump level) are described. The preservation of the topological structure upon changes in parameters within the stability range yields the possibility of their distinguishing when coding information by topological solitons of the considered type.