Stimulated Raman scattering in the approximation of unidirectional propagation in a medium with static dipole moments

The evolution equations of two-frequency stimulated Raman scattering in a molecular quasithree- level medium with static dipole moments have been derived in the approximations of the nondepletion of the pump field and the unidirectional propagation of the Stokes field. Completely integrable particular cases of the resulting system of equations have been found. New mechanisms of controlling the parameters of microwave pulses generated in such a system have been studied within this model. The numerical analysis and particular exact solutions demonstrate the possibility of switch between the regimes of generation of narrow Stokes field pulses and nearly rectangular pulses.     

Mass transfer mechanism and chemical stability of strongly basic anion-exchange membranes under overlimiting current conditions

The dynamics of changes in overall and partial voltammetric characteristics with respect to chloride and hydroxide ions is studied by the method of rotating membrane disk (RMD) under the conditions of stabilized diffusion layer thickness for the original strongly basic MA-41P and homogeneous AMX membranes and also for the modified heterogeneous MA-41P-M membrane at high current densities. For unmodified anion-exchange membranes at currents exceeding the limiting value, the hydrolysis of fixed ammonium bases produces secondary and ternary amino groups which are catalytically active in the reaction of water molecule dissociation. The hydrolysis of amino groups in the membrane surface layer is the mechanism of degradation of electrochemical characteristics of strongly basic membranes. This results in the increase of transport numbers with respect to hydroxide ions and weakening of mass transfer with respect to salt ions. For the surface-modified heterogeneous anion-exchange membranes, no degradation of electrochemical characteristics is observed. The characteristics of the surface-modified MA-41P-M membrane remain stable: after long-term operation of the energized membrane, the partial currents with respect to hydroxide ions are close to zero and the mass transfer with respect to salt ions is considerably intensified. The dependences of the thickness of the hydrolyzed layer of a strongly basic anion-exchange membrane on the time of its exposure to solutions of high pH are determined. An original method is developed for determination of the hydrolyzed layer thickness for strongly-basic anion-exchange membranes, which is based on the copper ability to form stable complex compounds with weakly basic amino groups of anion-exchange membranes.     

Self-induced transparency in a dispersive medium

The evolution of the electromagnetic field in a two-level medium occurring in a matrix with finite response time has been studied. An integrable variant of the Maxwell-Bloch equations with allowance for nonlinear dispersion is derived and solved using the inverse scattering problem. It is shown that the nonlinear dispersion caused by the finite response time of the matrix yields a new possibility of controlling soliton parameters. A particular case of the constructed model can be used to describe field pulses in the parameter domain that occurs between the regions of applicability of the quasi-monochromatic approximation and the approximation of unidirectional propagation of pulses with durations on the order of the oscillation period.     

Mass Transfer of Salt Ions in an Electromembrane System with Violated Electroneutrality in the Diffusion Layer: The Effect of a Heterolytic Dissociation of Water

The effect of water dissociation on the mass transfer of salt ions is studied with allowance for the space charge. The Kharkats problem, which considers exaltation of the limiting diffusion current, and the Rubinstein problem, which accounts for violation of the electroneutrality condition in a membrane system, are generalized.     

Radiative asymptotic behavior of stimulated Raman scattering

This paper uses an integrable model to study an asymptotic solution describing the transformation of energy occurring in stimulated Raman scattering. The model allows for motion of populations and for the nonlinear Stark effect. Initial conditions leading to a radiative solution are discussed. The boundary conditions reflect the injection into the medium of high-power pulses of constant-amplitude pump and Stokes fields. It is shown that the radiative asymptotic behavior of this problem in the limit of weak medium excitation and in the limit of rapidly varying intense fields is determined by the kernels of Marchenko equations that are proportional to functions depending only on a self-similar variable. Analytic solutions are found for these cases. Detailed numerical calculations carried out for weak fields corroborate the analytic results. The role of the soliton part of the continuous spectrum of the problem is also studied. It is found that a high-power soliton of the Stokes field can be generated at the leading edge of a wave packet. Zh. éksp. Teor. Fiz. 115, 1168–1195 (April 1999)     

Exciton self-trapping in molecular media with an elastic dipole moment

Exciton self-trapping in a molecular medium is considered within a self-consistent model taking into account the change in the dipole moment as a result of a displacement of molecules and the resonance interaction with an electromagnetic field. New mechanisms and specific features of the formation of localized structures in quasi-one-dimensional molecular structures are investigated. It is shown that the dependence of the dipole moment on molecular vibrations leads to new conditions for exciton self-trapping and intrinsic optical bistability, as well as for the formation of electromagnetically induced transparency. The theory proposed is used to explain the specific features of exciton self-trapping in a conjugated polymer and J aggregates of dyes under the action of an external laser field.     

Generation of acoustic solitons by a single-mode electromagnetic field

Mechanisms of acoustic pulse generation by a single-mode electromagnetic field propagating in a photoelastic material are analyzed. The anisotropy induced by acoustic excitations in an isotropic medium leads to nonlinear coupling between the polarization components of a single-mode electromagnetic field. For different conditions, it is shown that the acoustic-electromagnetic wave interaction due to mixing of the polarization components of light and acoustic waves can give rise to soliton-like coherent acoustic excitations in a thin crystal plate. When spatial dispersion is ignored, the governing system of equations for unidirectional acoustic solitons can be reduced to an integrable model. It is shown that qualitatively different scenarios of formation of acoustic solitons are possible, depending on the directions of deformation and field polarization.     

Self-localization of excitons and nonlinear optical properties of J-aggregates in a periodically modulated thin film

Nonlinear optical properties of dye J-aggregates embedded in a one-dimensional periodic medium are analyzed theoretically and numerically. The effect of strain-induced exciton self-localization in a chain of monomers on nonlinear optical properties of the system is investigated for weakly and highly ordered J-aggregates. It is found that exciton self-localization in a periodic medium enhances light absorption and effective optical susceptibility. Optical bistability thresholds are examined for weakly and strongly excited dye J-aggregate thin films. It is shown that the threshold intensity of incident electromagnetic field is lower by more than an order of magnitude as compared to that for a homogeneous medium.     

Strongly regular growth of entire functions of order zero

For entire functions of order zero we introduce a new concept of regularity of growth, which is shown to possess properties similar to those which characterize the concept of totally regular growth of entire functions of finite order in the sense of Levin-Pflüger. Translated fromMatematicheskie Zameiki, Vol. 63, No. 2, pp. 196–208, February, 1998. This research was partially supported by the International Science Foundation under grant No. UCR000.