We have studied the nonstationary transmission of two ultrashort laser pulses incident on a thin film. The radiation frequency of one of these pulses is in resonance with the two-photon transition from the ground state of the crystal to the biexciton state, while the other pulse coherently mixes the exciton and biexciton states, leading to strong renormalization of the energy spectrum of the crystal. We have obtained a system of nonlinear equations describing the time evolution of the exciton and biexciton amplitudes and the fields of three pulses transmitted through the film. We have analyzed the effect of amplitudes and widths of incident pulsed and of the time delay between them on the peculiarities of film transmission of these pulses. We have predicted the effect of a substantial time delay in the generation of the pulse transmitted through the film relative to the incident pulse, which is in resonance with the exciton–biexciton transition frequency. The possibility of generation of a precursor, viz., a pulse transmitted through the film sooner than the peak of the incident pulse reaches the film, as well as possibility of generation of a reflected pulse in the absence of the incident pulse, has been proven.

The effects of laser beam propagation in a coupler composed of two parallel optical-fibre arrays are studied by the coupled-mode method taking into account the interaction of a given fibre with the nearest neighbours and the linear dependence of the propagation constant on the fibre number. It is shown that, due to the complex structure of each subsystem, the structure of light intensity spatial distribution becomes significantly complicated in the system under study. The occurrence of space limited transverse light diffraction is predicted.

The results of investigation of the photodissociation dynamics of triatomic Bose-condensed ultracold molecules (trimers) with the formation of atoms and diatomic (dimer) pairs are presented. The interaction Hamiltonian is proposed, and a system of nonlinear equations is constructed that describes the evolution of atoms and molecules. Integrals of motion are obtained, and a nonlinear differential equation is derived for the time evolution of the atomic density with the use of these integrals. The solutions of this equation in various approximations imply that, depending on the initial conditions, different regimes of time evolution of the system are possible: periodic and aperiodic regimes.

The bound states of two interacting two-dimensional magnetoexcitons with electrons and holes on the lowest Landau levels (LLLs) moving in-plane of the layer with equal but opposite oriented wave vectors and forming a molecular-type structures with the resultant wave vector →k = 0 were investigated. Four possible spin structures of two electrons and of two holes forming the bound states were considered. Two of them lead to the formation of the para and ortho magnetoexcitons in the presence of the electron-hole (e-h) Coulomb exchange interaction. In this case we have studied the interaction of two para magnetoexcitons and of two ortho magnetoexcitons with the resultant spin equal to zero. Another two variant, are actual when the Coulomb exchange e-h interaction is negligible small and the spin of two electrons separately and the effective spin of two holes are interconnected and forms the singlet or the triplet states with zero spin projections on the magnetic field direction. The spin states of the four particles were constructed combining the singlet two electron state with the singlet two hole state as well as the triplet two electron state with the triplet two hole state. Only the bound states of two electrons and of two holes with singlet-singlet and with triplet-triplet spin structures were studied. It was shown that the spin structure of the type singlet-triplet and triplet-singlet do not exist due to the hidden symmetry of the magnetoexcitons. The orbital structure of the 2D magnetoexciton with wave vector →k ≠ 0 is similar with an in-plane electric dipole with the dipole moment perpendicularly oriented to the wave vector. The bimagnetoexciton with resultant wave vector →k = 0 is composed from two antiparallel oriented electric dipoles moving with antiparallel wave vectors →k ≠ 0. Their relative motion in the frame of the bound states is characterized by the variational wave functions φn(→k) depending on the modulus →k. It was shown that the stable bound state in the lowest Landau levels approximation do not exist in four investigated spin combinations. Instead of them a deep metastable bound state with an activation barrier comparable with the ionization potential of the magnetoexciton with →k = 0 was revealed in the triplet-triplet spin configuration. Its orbital structure in the momentum space representation is characterized by the maximal exciton density on the in-plane ring and with zero density in the center.

The possible existence of the bound states of the interacting two-dimensional (2D) magnetoexcitons in the lowest Landau levels (LLLs) approximation was investigated using the Landau gauge description. The magnetoexcitons taking part in the formation of the bound state with resultant wave vector k= 0 have opposite in-plane wave vectors and look as two electric dipoles with the arms oriented in-plane perpendicularly to the corresponding wave vectors. The bound state of two antiparallel dipoles moving with equal probability in any direction of the plane with equal but antiparallel wave vectors is characterized by the variational wave function of the relative motion depending on the modulus | k |. The spins of two electrons and the effective spins of two holes forming the bound states were combined separately in the symmetric or in the antisymmetric forms for electrons and holes. In the case of the variational wave function the maximum density of the magnetoexcitons in the momentum space representation is concentrated on the in-plane ring. The stable bound states of the bimagnetoexciton molecule do not exist for both spin orientations. Instead of them, a deep metastable bound state with the activation barrier comparable with the ionization potential of the magnetoexciton with k =0 was revealed.

The dynamics of optical parametric excitonpolariton oscillations in semiconductor microcavities was studied taking into account the conversion processes of the two pump polaritons into signal and idler polaritons and vice versa. The system of nonlinear evolution equations was obtained for describing the time evolution of densities of pump, signal and idler polaritons.

Using the coupled-mode method, the effects of propagation of laser radiation in a coupler of two parallel waveguide arrays are studied. It is shown that due to the composite spatial structures of each of the subsystems, the structure of the spatial distribution of radiation intensity in the subsystems is substantially complicated in the investigating system.

A dispersion law for the system of three-level atoms with an equidistant energy spectrum interacting with resonant laser radiation has been obtained taking into account two successive optically allowed one-photon transitions and an optically allowed two-photon transition between the lower and upper levels. It has been shown that the dispersion law consists of three polariton branches. The effects of repulsion and attraction of branches of the dispersion law and their intersection, as well as the self-consistent variation of the photon–atom coupling constant, have been predicted.

We studied the dynamics of polaritons in a microcavity in the parametric oscillator mode, when the pump is carried out by two laser pulses with close frequencies. Analytical solutions of a system of nonlinear differential equations are found for equal damping constants

Using the coupled-wave method, we consider anharmonic Bloch oscillations of light in an array of waveguides, taking into account the coupling between waveguides up to the third order. It is shown that the beam trajectory is periodic, with the trajectory oscillating within a single period.

AbstractThe double-pulse interaction with excitons and biexcitons in semiconductors is studied theoretically. It is shown that the dispersion law of carrier wave has three branches under the action of a powerful pumping in the region of the M -band of luminescence. Values of parameters at which the dispersion law branches can intersect due to the degeneration of the exciton level energy have been found. The effect of a significant change in the force of coupling between the exciton and photon of a weak pulse with a change in the pumping intensity is predicted.

The double-pulse interaction with excitons and biexcitons in semiconductors is studied theoretically. It is shown that the dispersion law of carrier wave has three branches under the action of a powerful pumping in the region of the M-band of luminescence. Values of parameters at which the dispersion law branches can intersect due to the degeneration of the exciton level energy have been found. The effect of a significant change in the force of coupling between the exciton and photon of a weak pulse with a change in the pumping intensity is predicted.

The possible formation of two-dimensional (2D) magnetic bi-excitons composed of two 2D magnetoexcitons with electrons and holes on the lowest Landau levels (LLLs), with opposite center of- mass wave vectors k and and with antiparallel electric dipole moments perpendicular to the corresponding wave vectors was investigated. Two spinor structures of two electrons and of two holes were considered. In the singlet-singlet state the spins of two electrons as well as the effective spins of two holes create the combinations with the total spin S=0 and its projection on the magnetic field The triplet-triplet state corresponds to S=1. Two orbital Gaussian variational wave functions depending on | k | and describing the relative motion of two magnetoexcitons inside the molecule were used. It is shown that in the LLLs approximation the stable bound states of bimagnetoexcitons do not exist. A metastable bound state for the triplet-triplet spin configuration a metastable bound state with the orbital wave function, having the maximum on the in-plane ring was revealed. The metastable bound state has an energy activation barrier comparable with the magnetoexciton ionization potential and gives rise to the new luminescence band due to the metastable bi-exciton-para exciton conversion with the frequencies higher than those of the para magnetoexciton luminescence line.

The possible formation of two-dimensional (2D) magnetic biexcitons composed of two 2D magnetoexcitons with electrons and holes on the lowest Landau levels (LLLs) with opposite center-of-mass wave vectors k→ and −k→ and with antiparallel electric dipole moments perpendicular to the corresponding wave vectors was investigated. Two spinor structures of two electrons and of two holes were considered. In the singlet-singlet state the spins of two electrons as well as the effective spins of two holes create the combinations with the total spin S=0 and its projection on the magnetic field Sz=0. The triplet-triplet state corresponds to S=1 and Sz=0. Two orbital Gaussian variational wave functions depending on |k→| and describing the relative motion of two magnetoexcitons inside the molecule were used. Analytical calculations show that in the LLLs approximation the stable bound states of bimagnetoexcitons do not exist, but there is a metastable bound state with the orbital wave function, having the maximum on the in-plane ring for the triplet-triplet spin configuration. The metastable bound state has an energy activation barrier comparable with the magnetoexciton ionization potential and gives rise to the new luminescence band due to the metastable biexciton-para exciton conversion with the frequencies higher than those of the para magnetoexciton luminescence line.

The dynamics of polaritons in a microcavity in the parametric oscillator mode, when two pump polaritons turn into the signal and idler polaritons and vice versa, has been studied. The pumping is carried out using two lasers with close frequencies. Analytical solutions of the system of nonlinear differential equations have been obtained. The periodic and aperiodic modes of the transformation of a pair of pump polaritons into signal and idler polaritons have been found.

Exact analytical solutions have been obtained to the system of nonlinear differential equations for the intensities of the waves propagating in a three-channel nonlinear directional coupler with a Kerr nonlinearity and different coupling constants between the optical waveguides.

The pump-probe method of studying of the optical properties of a semiconductor in the exciton region of a spectrum is considered theoretically taking into account the exciton–photon and elastic exciton–exciton interactions. It is shown that the concentration of excitons, and the susceptibility of the medium are mainly determined by the detuning from the exciton resonance and the magnitude of the pump field. The values of the parameters corresponding to the observed parametric resonance are obtained and the dynamic analysis of the found solutions is carried out.