Using Maxwell-Bloch equations, we analyze the response of a two-component medium of two-level atoms driven by a two-cycle optical pulse beyond the traditional approach of slowly varying amplitudes and phases. We show that the notions of carrier, envelope, phase, and group velocities can be generalized to this situation. For optical pulses of a given duration, we show that the optical field can form a temporal soliton.

We study solutions to second-harmonic-generation equations in two-dimensional media with anomalous dispersion. The analytical solution is obtained in an approximate form of the planar spatiotemporal two-component soliton by means of the averaged Lagrangian method. It is shown that a decrease in the amplitudes of both soliton components and an increase in the value of the transverse coordinate are accompanied by an increase in their temporal duration. Within this variational approach, we have managed to find a stability criterion for the light bullet and a period of oscillations of soliton parameters. Then, we use the obtained form as an initial configuration to carry out the direct numerical simulation of soliton dynamics. We demonstrate stable propagation of spatiotemporal solitons undergoing small oscillations predicted analytically for a long distance. The formation of a two-component light bullet is shown when we launch a pulse only at the fundamental frequency. In addition, we investigate the phase and group-velocity mismatch effects on the propagation of pulses.

The generalized sine-Gordon equation is obtained under the theoretical investigation of interaction of few-cycle pulses in a nonlinear medium modeled by a set of four-level atoms. This equation is derived without the use of the slowly varying envelope approximation and is shown to be integrable in the frameworks of the inverse scattering transformation method. Its solutions describing the propagation of the solitons and breathers and their interaction are investigated. In the case of different signs of the parameters of the equation considered, it is revealed, in particular, that the collision of solitons with opposite polarities can lead to an appearance of the short-living pulse having extraordinarily large amplitude, whose dynamics is similar to that of rogue waves. Also, the solitons of “rectangular” form and the breathers with rectangular oscillations exist in the case of the same signs of the parameters.

The possibility of the formation of metastable unipolar soliton-like electromagnetic objects in nonequilibrium dissipative media has been predicted. It has been shown that these objects propagating in a medium transfer it from a nonequilibrium to a short-lived metastable state, storing the information of input conditions at its lifetime scale.

The possibility of generating a terahertz spectral supercontinuum in the regime of the optical rectification of a femtosecond optical pulse is predicted. The transient and asymptotic stages of generation are distinguished. The supercontinuum consists of the soliton and nonsoliton components of a terahertz signal at the asymptotic stage. It is shown that the formation of supercontinuums is accompanied by a redshift of the median of the opticalpulse spectrum.

Various methods to increase the efficiency of the generation of broadband terahertz radiation based on optical rectification have been analyzed. The solutions of self-consistent optical terahertz equations have been studied using the inclined front technique. The effect of symmetric and asymmetric resonant impurity centers incorporated into a crystal has been examined. Transient and asymptotic stages of generation have been considered. Attention has been focused on the evolution of the spectra of both generated terahertz and input optic signals. One- and two-frequency generation modes have been discussed. Acoustic analogs that would provide the possibility of the generation of the gigahertz acoustic supercontinuum using subterahertz elastic signals in a solid have been analyzed. The main similarities and differences between terahertz optics and subterahertz acoustics have been revealed.