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Annalen der Physik

Solitons in Stimulated Raman Scattering

Heinz Steudel

Published Jan 1, 1977• 32 citations
Publisher

Abstract

Abstract The semiclassical equations of SRS are derived by the following method: The many‐level molecule is described by the Schrödinger equation and subsequently all amplitudes but those of the essential two levels are eliminated by approximate integration. Especially the case of equal group velocities for pump and Stokes wave is considered. Terms describing a frequency shift due to dynamical Stark effect and a change of refraction index by vibrational excitation can be removed by a suitable transformation. Under various, physically different, assumptions the system of molecular and field equations is reduced to the equations describing a quasimonochromatic pulse propagating in a resonant two‐level system, and in this way we can find a rich manifold of solutions. E.g., the 2π‐pulse of self‐induced transparency can be transferred to SRS. By other assumptions we are led to equations defining the Bäcklund transformation for the sine‐Gordon equation. For this case also soliton type solutions can be constructed.

DOI
10.1002/andp.19774890307

Related papers

a Theoretical Study on the Stimulated Raman Scattering Modulated by the Flopping Frequency Arising from the Interaction Between a Strong Resonant Field and the Medium.

C. J. Hsu

The stimulated Raman scattering (SRS), arising from the interaction between molecules of a medium and two strong light fields - a resonant field and a pumping field - is studied theoretically. The transitions of molecules between a given pair of levels is assumed to be both Raman active and infrared active. A semiclassical approach, in which the density matrix method is used for the quantum mechanical description for the medium, is employed. We expand the density matrix in various orders within which the zeroth-order is referred to as the solution of the equation of motion of the density matrix when only the resonant field is applied. -- We obtain a set of equations in second order of the density matrix element p₁₀⑵ (ω) from which the gain function can be derived. This set of equations in the special case of steady state is accidentally similar to those obtained by Mollow in his study of the power spectrum of a strong driven two-level system. We have shown that the SRS in the steady state under the resonant field interaction, is drastically reduced in general. When the flopping frequency is larger than the relaxation constants (Ω > r), we find there appears both weak positive and weak negative gains on both sides of the ordinary SRS components. Since we retain our second-order equations in a general form rather than the form for steady state, we are able to take account of the dependence on the transient zeroth solution. By employing the Laplace transform technique with the help of convolution products, we are able to solve for ρ₁₀⑵(ω) in the stationary flopping state. When the intensity of the resonant field is high, we have found theoretically that both the Stokes and anti-Stokes component become doublets and equally displaced by the amount of the flopping frequency, Ω, on the opposite sides of ordinary Stokes and anti-Stokes components, respectively. The gain maxima are approximately the order of Ω/4r times the ordinary gain of the Stokes component, where Ω/r >> 1 if the flopping exists. The gains are therefore large in comparison with the ordinary gain for SRS in the steady state.

•Jan 1, 1978•0 citations

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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.

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We study the stimulated Raman scattering (SRS) of light from an atomic system embedded in a photonic crystal and coherently pumped by a laser field. In our study, the electromagnetic field is treated classically and the atomic system is described quantum mechanically. Considering a decomposition of the pump and Stokes fields into the Bloch modes of the photonic crystals and using a multiscale analysis, we derive the Maxwell-Bloch equations for SRS in photonic crystals. These equations contain effective parameters that characterize the SRS gain, the nonlinear atomic response to the electromagnetic field, and the group velocity and that can be calculated in terms of the Bloch modes of the unperturbed photonic crystal. We show that if the pump laser frequency is tuned near a photonic band edge and the atomic system is carefully chosen such that the Stokes mode matches another photonic band edge, low-threshold, enhanced Raman amplification is possible. Possible physical realizations of SRS in photonic crystals are also discussed.

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Similarity reduction and perturbation solution of the stimulated-Raman-scattering equations in the presence of dissipation

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Similarity and other group-invariant solutions of stimulated Raman scattering (SRS) in the presence of dissipation are studied. The group-theoretical analysis reduces the SRS equations to ordinary differential equations which in the most interesting cases, i.e., in the case of the self-similar and soliton solutions, are studied perturbatively to derive the effect of dissipation.

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Victor P. Kochanov

Abstract The theory of multifrequency stimulated Raman scattering (SRS) of light on rotational transitions of molecules, which are simulated by a three-level quantum system, is developed. It is shown that the application of bichromatic pumping increases the scattered radiation spectrum width. The exact algebraic solution for the wave amplitudes is obtained in the simplest version of synchronous SRS on transitions with a negligibly low eigenfrequency. It is found that an increase in the ratio of the Raman transition frequency to the pump radiation frequency leads to predominance of the anti-Stokes scattering branch. The effect of wave asynchronism emerging due to linear and nonlinear dispersion of the medium as well as the phase difference of the pump waves on SRS is considered. All types of asynchronism narrow generated frequency spectrum and suppress the anti-Stokes scattering branch. Nonlinear dispersion ensures positive values of wave amplitudes due to phase jumps by π during the propagation of waves in a medium.

Journal of Experimental and Theoretical Physics•Jan 1, 2019•1 citation

Raman Solitons and Raman spikes

Jérôme J.-P. Leon, А. В. Михайлов

Stimulated Raman scattering of a laser pump pulse seeded by a Stokes pulse generically leaves a two-level medium initially at rest in an excited state constituted of static solitons and radiation. The soliton birth manifests as sudden very large variations of the phase of the output pump pulse. This is proved by building the IST solution of SRS on the semi-line, which shows moreover that initial Stokes phase flips induce Raman spikes in the pump output also for short pulse experiments.

arXiv:solv-int/9703007•Mar 10, 1997•1 citation
Abstract The semiclassical equations of SRS are derived by the following method: The many‐level molecule is described by the Schrödinger equation and subsequently all amplitudes but those of the essential two levels are eliminated by approximate integration. Especially the case of equal group velocities for pump and Stokes wave is considered. Terms describing a frequency shift due to dynamical Stark effect and a change of refraction index by vibrational excitation can be removed by a suitable transformation. Under various, physically different, assumptions the system of molecular and field equations is reduced to the equations describing a quasimonochromatic pulse propagating in a resonant two‐level system, and in this way we can find a rich manifold of solutions. E.g., the 2π‐pulse of self‐induced transparency can be transferred to SRS. By other assumptions we are led to equations defining the Bäcklund transformation for the sine‐Gordon equation. For this case also soliton type solutions can be constructed.
The stimulated Raman scattering (SRS), arising from the interaction between molecules of a medium and two strong light fields - a resonant field and a pumping field - is studied theoretically. The transitions of molecules between a given pair of levels is assumed to be both Raman active and infrared active. A semiclassical approach, in which the density matrix method is used for the quantum mechanical description for the medium, is employed. We expand the density matrix in various orders within which the zeroth-order is referred to as the solution of the equation of motion of the density matrix when only the resonant field is applied. -- We obtain a set of equations in second order of the density matrix element p₁₀⑵ (ω) from which the gain function can be derived. This set of equations in the special case of steady state is accidentally similar to those obtained by Mollow in his study of the power spectrum of a strong driven two-level system. We have shown that the SRS in the steady state under the resonant field interaction, is drastically reduced in general. When the flopping frequency is larger than the relaxation constants (Ω > r), we find there appears both weak positive and weak negative gains on both sides of the ordinary SRS components. Since we retain our second-order equations in a general form rather than the form for steady state, we are able to take account of the dependence on the transient zeroth solution. By employing the Laplace transform technique with the help of convolution products, we are able to solve for ρ₁₀⑵(ω) in the stationary flopping state. When the intensity of the resonant field is high, we have found theoretically that both the Stokes and anti-Stokes component become doublets and equally displaced by the amount of the flopping frequency, Ω, on the opposite sides of ordinary Stokes and anti-Stokes components, respectively. The gain maxima are approximately the order of Ω/4r times the ordinary gain of the Stokes component, where Ω/r >> 1 if the flopping exists. The gains are therefore large in comparison with the ordinary gain for SRS in the steady state.
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.
We study the stimulated Raman scattering (SRS) of light from an atomic system embedded in a photonic crystal and coherently pumped by a laser field. In our study, the electromagnetic field is treated classically and the atomic system is described quantum mechanically. Considering a decomposition of the pump and Stokes fields into the Bloch modes of the photonic crystals and using a multiscale analysis, we derive the Maxwell-Bloch equations for SRS in photonic crystals. These equations contain effective parameters that characterize the SRS gain, the nonlinear atomic response to the electromagnetic field, and the group velocity and that can be calculated in terms of the Bloch modes of the unperturbed photonic crystal. We show that if the pump laser frequency is tuned near a photonic band edge and the atomic system is carefully chosen such that the Stokes mode matches another photonic band edge, low-threshold, enhanced Raman amplification is possible. Possible physical realizations of SRS in photonic crystals are also discussed.
Abstract The theory of multifrequency stimulated Raman scattering (SRS) of light on rotational transitions of molecules, which are simulated by a three-level quantum system, is developed. It is shown that the application of bichromatic pumping increases the scattered radiation spectrum width. The exact algebraic solution for the wave amplitudes is obtained in the simplest version of synchronous SRS on transitions with a negligibly low eigenfrequency. It is found that an increase in the ratio of the Raman transition frequency to the pump radiation frequency leads to predominance of the anti-Stokes scattering branch. The effect of wave asynchronism emerging due to linear and nonlinear dispersion of the medium as well as the phase difference of the pump waves on SRS is considered. All types of asynchronism narrow generated frequency spectrum and suppress the anti-Stokes scattering branch. Nonlinear dispersion ensures positive values of wave amplitudes due to phase jumps by π during the propagation of waves in a medium.