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Annalen der Physik

Zur Theorie der stimulierten Resonanz‐R AMAN ‐Streuung

Joachım Herrmann, J. Wienecke

Published Jan 1, 1974• 6 citations
Publisher

Abstract

Abstract The gain of the stimulated resonance RAMAN scattering (SRRS) and stimulated fluorescence is obtained by means of an analytical solution of the density matrix equation and MAXWELL's equations for laser‐ und STOKES‐radiation. The transient effects, which are caused by the population change of the molecule levels, and the influence of the resonance absorption on the pumping and the STOKES radiation are studied. The strong laser absorption yields a maximal gain, which shows, why the stimulated resonance RAMAN scattering could not be observed in many substances. As a result of our paper we give a possible interpretation of the experimentally observed relation between the stimulated fluorescence and the resonant RAMAN scattering.

DOI
10.1002/andp.19744860306

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Stimulierte Resonanz‐Raman‐Streuung an angeregten und nicht angeregten Molekülen

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Abstract A review of the theory of the stimulated resonance Raman scattering (SRRS) is given. The calculation of the gains for the SRRS with the ground level (SRRS I) or an excited one (SRRS II) as initial states shows that there are some restrictions for their appearance. Due to the strong resonance absorption of the pumping wave and the disturbing influence of stimulated fluorescence the SRRS I is not observable in a Franck‐Condon excitation and in an absorption of Lorentzian line shape. The SRRS II has a sufficiently large gain on the condition τel ≪vib (τel, τvib – transversal relaxation time of the electronic or vibronic transition). In case of a strong deviation of the wings of the absorption profile from the Lorentzian shape, however, the SRRS I is favoured rather than the two other processes. Another possibility to avoid the resonance absorption of the pumping wave exists for the transversal excitation of the SRRS. Thereby the limit of application of the SRRS may be extended to other substances which are no saturable absorbers. Apart from the saturable absorption and the transversal excitation the self‐induced transparency is the third possibility to generate SRRS of ultrashort light pulses.

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Acta Optica Sinica•Jan 1, 1989•0 citations
Abstract The gain of the stimulated resonance RAMAN scattering (SRRS) and stimulated fluorescence is obtained by means of an analytical solution of the density matrix equation and MAXWELL's equations for laser‐ und STOKES‐radiation. The transient effects, which are caused by the population change of the molecule levels, and the influence of the resonance absorption on the pumping and the STOKES radiation are studied. The strong laser absorption yields a maximal gain, which shows, why the stimulated resonance RAMAN scattering could not be observed in many substances. As a result of our paper we give a possible interpretation of the experimentally observed relation between the stimulated fluorescence and the resonant RAMAN scattering.
Abstract A review of the theory of the stimulated resonance Raman scattering (SRRS) is given. The calculation of the gains for the SRRS with the ground level (SRRS I) or an excited one (SRRS II) as initial states shows that there are some restrictions for their appearance. Due to the strong resonance absorption of the pumping wave and the disturbing influence of stimulated fluorescence the SRRS I is not observable in a Franck‐Condon excitation and in an absorption of Lorentzian line shape. The SRRS II has a sufficiently large gain on the condition τel ≪vib (τel, τvib – transversal relaxation time of the electronic or vibronic transition). In case of a strong deviation of the wings of the absorption profile from the Lorentzian shape, however, the SRRS I is favoured rather than the two other processes. Another possibility to avoid the resonance absorption of the pumping wave exists for the transversal excitation of the SRRS. Thereby the limit of application of the SRRS may be extended to other substances which are no saturable absorbers. Apart from the saturable absorption and the transversal excitation the self‐induced transparency is the third possibility to generate SRRS of ultrashort light pulses.
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 passage of strong monochromatic laser radiation through a resonance medium consisting of three-level atoms is investigated. It is shown that if collisions are taken into account in the scattered waves the resonances at combination frequencies occur to first order in the laser field intensity. A numerical analysis of the dependence of the stimulated electronic Raman scattering (SERS) components' gain factors on the pump frequency is carried out. The dispersion curves of the SERS components' gain (absorption) factors for fixed values of pump frequency and intensity are plotted.
The influence of a strong field resonant to the Raman transition on the behavior of the Stokes harmonic in saturated two-wave stimulated Raman scattering is theoretically considered based on the description of a gas of three-level atoms by medium density matrix equations. The vibrational mode of energy redistribution between laser and scattered radiation, threshold with respect to the resonant field intensity, is predicted. The action of optical fields on the absorption and amplification of the resonant field in a Raman medium is described.
A model is developed for the description of stimulated Raman scattering. This model allows for changes in the level populations due to radiative transitions and it can be used also for an arbitrary detuning of the pump radiation from the center of a line of an atom in the active medium. A study is made of the conversion of wide-band laser radiation into a Stokes signal. It is shown that this conversion is quite efficient and the Stokes signal gain corresponds to coherent scattering. This result is related to the matching of the phases of the pump and Stokes signals. Numerical investigations carried out using this model under the experimental conditions described elsewhere give results in agreement with the experimental data.
Strong stimulated radiations at wavelengths 3740 A have been observed when PbCl2 molecules are photodissociated by 2660 A ultraviolet laser. Dependences of these radiations on the pump laser intensity and PbCl2 molecular density have been studied experimentally. A theoretical model to describe these processes is put forward. These two raditions are identified as resonant laser radiation and stimulated Raman scattering originated from bhe population of the metastable level 6p23P2 of atomic Pb, which is produced by two-photon dissociation of PbCl2. When molecular density of PbCl3 is 6.21×1016cm-3, the maximum populations on the two metastable levels, 6p23 P2 and 6p21D2, of atomic Pb are almost same, which equals 2.0×1016cm-3.