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Nonstationary CARS by Polaritons

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Journal of Applied Mathematics and Physics 2020年第9期8卷 1949-1958页

作者： vladimir feshchenko Galina feshchenko Dawson College Montreal Canada Vanier College Montreal Canada

One of the significant problems of molecular spectroscopy is the determination and detailed analysis of how molecular vibrations are dephased. The dephasing of infrared-active (IR-active) vibrations of molecules was investigated by IR absorption spectroscopy. Pulse methods were used to investigate IR-vibrations as well. These methods revealed such coherent nonstationary effects as optical nutation, damping of the free polarization, photon echo, etc. New means of studying dephasing processes were uncovered by the method of nonstationary (time-domain) coherent anti-Stokes Raman scattering (CARS) spectroscopy. However, there are some aspects of CARS that still are not fully covered. One of them is related to Raman scattering by polaritons in dipole-active crystals whereas the second one is the increase of efficiency of CARS (minimization of the wave mismatch, the relationship between pulse width and the relaxation time, etc.). The purpose of the present research to study the case of “extreme” coherency between all interacting pulses (the duration of each pulse is smaller than characteristic times and those pulses are traveling with the same speed) in dipole-active crystals. In this research, we analyzed the process of simultaneous propagation of three waves (anti-Stokes, Stokes, and the pump) under CARS by polaritons. We have found some solutions modeling such simultaneous propagation. We also found the expression for the gain factor for such scattering. The gain factor was evaluated under the assumption of a given stationary pump field. It was shown that the typical values of the relative intensities were consistent with the experimental results.

关键词： Coherent Anti-Stokes Raman Scattering Spectroscopy Polaritons Stimulated Raman Scattering

Computer Simulation of Transition Regimes of Solitons in Four-Photon Resonant Parametric Processes in Case of Two-Photon Resonance

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American Journal of Computational Mathematics 2016年第3期6卷 267-274页

作者： vladimir feshchenko Galina feshchenko Dawson College Montreal Canada Vanier College Montreal Canada

The transition regimes of solitons in four-photon resonant processes in the case of two-photon absorption of the fundamental radiation are numerically investigated. The standard system of equations for the amplitudes of probability of finding the system in state with certain energy is used to derive the expression for the induced polarization in the nonlinear medium. As for the equations for the amplitudes of the optical pulses, the general case is considered in which both the amplitudes and phases are space-time dependent. We focus on the finite difference methods and the case of simultaneously propagating solitons at all frequencies of the interacting waves (simultons). The obtained results indicate that upon certain threshold conditions all interacting pulses become the solitons of Lorentzian shape. The numerical analysis has also shown that the soliton amplitudes significantly depend on the ratio between the nonlinear polarizability at the fundamental frequency ω0 and that of combination of ω0 and the trigger-field frequency ω1(2ω0 + ω1). In the second part of the paper, we apply the method of phase planes to show that at typical values of parameters, the solitons are stable.

关键词： Solitons Transition Regime Stability

Polarization Simultons in Stimulated Raman Scattering by Polaritons

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Journal of Applied Mathematics and Physics 2021年第9期9卷 2193-2204页

作者： vladimir feshchenko Galina feshchenko Dawson College Montreal Canada Vanier College Montreal Canada

Expressions are obtained for the shortened Maxwell’s equations simulating the evolution of the ultrashort pulses propagating in anisotropic dipole-active crystals in stimulated Raman scattering (SRS) by polaritons. The developed theory considers the case of cubic crystals which become anisotropic due to the deformation of the dielectric constant by the linearly polarized pump wave. The pump field is approximated by a linearly polarized plane electromagnetic wave. The possibility of simultaneous propagation of pulses on both different frequencies (pump and Stokes) and different polarization (simultons) is theoretically shown. It is also shown that the expression for the gain factor g in SRS is consistent with the experimental results for the spectra of ZnS.

关键词： Nonstationary Stimulated Raman Scattering Polaritons Phonons Solitons Polarization

Nonstationary Stimulated Raman Scattering by Polaritons in Cubic Crystals

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Journal of Applied Mathematics and Physics 2019年第9期7卷 2122-2129页

作者： vladimir feshchenko Galina feshchenko Dawson College Montreal Canada Vanier College Montreal Canada

The purpose of this article is to consider two aspects of the nonstationary stimulated Raman scattering by polaritons in cubic crystals. The first feature is related to the pump field, which, by deforming the permittivity of the medium, changes its symmetry. As a result, for example, the cubic crystal becomes anisotropic. The second one results from the possibility of exciting anomalous longitudinal waves at the frequency of the mechanical phonons which is the fundamental difference between scattering by dipole-active (polar) phonons and that of by dipole-inactive (nonpolar) ones. When the phonon frequency is approached, the amplitude of the transverse polariton wave decreases due to increased absorption and the wave mismatch. The polariton wave becomes practically longitudinal. Such a wave is maintained by the pump field and exists only in a pumped medium. The system of four shortened nonstationary equations (two for the Stokes waves with perpendicular polarizations and two for both transverse and longitudinal polariton waves) is obtained. The analysis is carried out for a given stationary pump field which is assumed to be a linearly polarized plane electromagnetic wave. Principal attention was paid to the calculation and analysis of the gain factor which defines the intensities of both stimulated (SRS) and spontaneous Raman scattering. The expressions for two proper gain factors gμ are obtained for Stokes waves in nonstationary case. It was shown that the pumped cubic crystal becomes anisotropic. It is also shown that the values of intensities calculated by using the expression for gμ are consistent with the experimental results for spectra of ZnS.

关键词： Nonstationary Stimulated Raman Scattering Polaritons Phonons

Computer Simulation of Transition Regimes of Solitons in Stimulated Raman Scattering with Excitation of Polar Optical Phonons

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American Journal of Computational Mathematics 2015年第3期5卷 336-344页

作者： Galyna feshchenko vladimir feshchenko Vanier College Montreal Canada Dawson College Montreal Canada

The system of nonlinear equations modeling the process of nonstationary stimulated Raman scattering (SRS) in noncentrosymmetric crystals for the waves on laser, Stokes, polariton, and phonon frequencies is investigated by using the numerical methods. The general case for amplitudes of waves that resulted in doubling of the number of equations is considered. It is shown that the application of the methods of finite differences to the computer simulation of transition regimes is completely consistent with the analytical results found for the asymptotical solutions in form of solitons. The obtained results also indicate that the laser pulses of Gaussian shape appearing at the boundary of nonlinear medium tend to become solitons of Lorentzian shape. It was also found that the formation of solitons occurs when the vibrations of optical phonons and that of electromagnetic wave were either in or out of phase. It is shown that all electromagnetic waves entering the medium with different speeds become solitons having the same speed. In the second part of the paper we considered the computer simulation of soliton stability with respect to small (weak) perturbations of all interacting waves. In the present paper we considered the case of evolution of those disturbances in the vicinity of peaks of solitons. The numerical analysis showed that in wide range of parameters the solitons were stable.

关键词： Finite Differences Method Abbreviated Maxwell’s Equations Stimulated Raman Scattering Stability

Nonstationary Stimulated Raman Scattering by Polaritons in Continuum of Dipole-Active Phonons

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Journal of Applied Mathematics and Physics 2018年第2期6卷 405-417页

作者： vladimir feshchenko Galina feshchenko Dawson College Montreal Canada Vanier College Montreal Canada

The system of equations simulating the processes of nonstationary stimulated Raman scattering (SRS) with the excitation of polar optical phonons is obtained. This system is found by applying such standard methods as the nonstationary theory of perturbations, which resulted in the equations for the amplitudes of probabilities to find the discrete system in certain state, and slowly-varying amplitudes for the electromagnetic waves. It has been shown that the obtained system includes, as extremes, the case of classical interaction between electromagnetic field and resonant medium (including the “area theorem”), and the one related with SRS on optical phonons. We have conducted both theoretical and numerical investigation of simplified system assuming that the amplitudes of all electromagnetic waves (laser, Stokes, and polariton) were real (there was no destructive spatial-temporal phase modulation). Only low-order nonlinear processes are considered. It is shown that this system can be reduced to Sine-Gordon equation. This system can also be simplified to the equation that simulates the motion of physical pendulum from upper equilibrium position. The numerical study of nonstationary SRS when the electromagnetic field of laser radiation and Stokes excite both polariton emission and the continuum of dipole-active phonons has been carried out. The evolution of the intensity of the polariton wave as function of the length of nonlinear medium has been numerically analyzed.

关键词： Nonstationary Stimulated Raman Scattering Polaritons