The propagation of the solitary waves in the resonant birefringent amplifier with linear losses is considered. The birefringent
optical linear medium contains two-level atoms with the upper state degenerated over projection of angular moment. It
is assumed that population of resonance levels of atoms is inverted. The steady state pulse of polarized radiation that is vectonal
generalization of the known π-pulse was analytically found. Numerical simulations demonstrate the formation dynamics
solitary waves originated in birefringent amplifier.
We derive nonlinear evolution equations describing parametric up- and down-conversion under the conditions when either of the two interacting waves is in resonance with a material transition, e.g., with plasmonic oscillations. Using perturbation theory in the limit of the large wave-number mismatch we drive analytical expressions for two families of quasi-solitonic solutions. If material transition is in resonance with the second-harmonic then the quasi-solitons are of the Nonlinear-Schrodinger type. If the fundamental frequency is in resonance then the reduced system is the paraxial wave equation coupled to the nonlinear classical oscillator. The latter system is integrated analytically and localized solutions are presented.
The propagation of an extremely short (one cycle) pulse of an electromagnetic field in a medium with two equilibrium states is considered theoretically. The analysis is based on the set of Maxwell equations and the Landau-Khalatnikov equation, in which the approximations of the slowly varying envelopes are not used. The solutions of this set that describe the steady-state propagation of a solitary polarization wave and electromagnetic pulse are found. In the approximation of unidirectional wave, a numerical simulation of the solitary waves propagation and interaction is performed in terms of the model considered. The switching phenomena in thin ferroelectric films were considered in framework of the numerical simulation.
We study the interaction of a Bose-Einstein condensate in an optical lattice with additional electromagnetic fields under Raman resonance condition. System of evolution equations describing ultra-short optical pulse propagation and photo-induced transport of cold atoms in optical lattice is derived. The steady state solution of these equations was found. There are new kinds of polaritonic solitary waves propagating.
Second harmonic generation was considered with regard to dispersion of nonlinear susceptibility, and second- and third- order dispersion of the group-velocities. The case of a finite phase mismatch is analyzed and analytically. The steady state pulses of the fundamental and second harmonic waves were found. Modulation instability of the continuous wave solution is considered. The correction terms for MI thresholds, which are resulted from dispersion of non-linear susceptibility, were found.
System of evolution equations describing ultra-short optical pulse propagation in quadratic non-linear medium is derived with taking into account the dispersion of the non-linear susceptibility and second-order group-velocity dispersion. Both type I and type II of phase matching were considered. The case of a finite phase mismatch was analyzed by an analytical method. The steady state pulses of the fundamental and second harmonic waves were found. There are new kinds of ultra-short pulses propagating in quadratic medium in the anomalous and normal dispersion regime.
Propagation of the ultrashort pulses of the electromagnetic wave was considered in framework of the anharmonic oscillator model. For the quasi-harmonic waves, the model leads to the description of quadratic parametric processes, e.g., sum-frequency and difference-frequency mixings. Unipolar steady state pulse was obtained by analytical method. In numerical simulations it was shown that these steady state pulses are stable under collisions and small harmonic perturbations. However, these pulses are not solitons in the strict sense. Multipolar pulses demonstrate the stable regime of propagation too if these pulses exhibit a few oscillation of the electric field and the energy of these impulse is fairly high.