The theory of resonant Raman scattering in the presence of intense incident and scattered light waves has been developed, using the quantum-mechanical master-equation approach. When the optical matrix elements between the resonant intermediate state and the initial and final states of the atomic system are larger than the relevant relaxation frequencies, it is shown that instead of the usual power broadening and shift of the Stokes or anti-Stokes line, each line can split into as many as five or seven lines, depending upon whether both the fields are exactly at resonance or otherwise.
The theory of resonant Raman scattering in the presence of intense incident and scattered light waves has been developed, using the quantum-mechanical master-equation approach. When the optical matrix elements between the resonant intermediate state and the initial and final states of the atomic system are larger than the relevant relaxation frequencies, it is shown that instead of the usual power broadening and shift of the Stokes or anti-Stokes line, each line can split into as many as five or seven lines, depending upon whether both the fields are exactly at resonance or otherwise.
The general method developed in a previous paper (see ibid., vol.10, p.345 (1977)) is applied to the problem of resonance Raman scattering in very intense laser fields. At very low intensities the spectrum consists of three monochromatic lines (Rayleigh, Raman Stokes and anti-Stokes) which split into a triplet and two doublets when the laser light, tuned on one of the two transitions connecting the upper state to the two lower sublevels, has a sufficiently high intensity to saturate this transition but not the second one. The Raman and Rayleigh lines are completely mixed when the intensity becomes so high that both transitions are saturated. The corresponding evolution of the spectrum is determined. Optical-pumping effects leading to asymmetries in the fluorescence spectrum are taken into account.
The resonant Raman scattering in a three level system produces an optical pumping of molecules from the initial to the final states which are radiatively coupled to the intermediate resonant state. We consider the pumping that is produced by an intense, pulsed, monochromatic radiation field that is near-resonant with the initial resonance frequency. The Heitler–Ma damping theory is solved exactly for the case when the resonance fluorescence is weak compared to the Raman scattering, or any other processes which might cause irreversible decay of the resonant state. In particular, we examine the usefulness of dressed states to describe the intense field limit. The spectral line shape for the Raman scattering is obtained. The transient behavior following the onset of the laser pulse is examined and a careful analysis of the pumping rate and its relationship to both weak and strong field theories is presented.
Stimulated Raman scattering (SRS) from a system that is both Raman active and infrared active has been investigated theoretically when a strong coherent resonant infrared light field, in addition to a pumping field, is applied. In the density matrix formulation, it is found that the gain function in steady state is redistributed as a result of the modulation on the populations and transition probabilities by the presence of the strong resonant field. The redistribution curve shows Rabi frequency splitting for the Stokes component and a new origin of anti-Stokes components of SRS that is anticipated in the present mechanism.
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.
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 theory of optical birefringence is discussed from the point of view of the scattering of polarized photons by molecules using the framework of formal scattering theory and quantum electrodynamics. In Part One, those features from noncovariant quantum electrodynamics relevant to the molecular scattering of photons are reviewed. Chapter One contains an outline of classical electrodynamics in the Coulomb gauge, including the Stokes parameter and density matrix formulations of polarization. Chapter Two deals with the quantization of the radiation field, and the occupation number representation is defined. The quantum mechanical description of polarized light is outlined in Chapter Three: operator equivalents of the density matrix and Stokes parameters are invoked, the parameters themselves being obtained from the expectation values of the Stokes operators with the state vector of the photon. The Stokes parameter and density matrix are then applied to the polarization of a general beam containing an arbitrary number of photons, and some new methods are developed. The interaction of the electromagnetic field with bound electrons is formulated in Chapter Four in terms of a canonically transformed interaction Hamiltonian in which the multipole terms are explicit. Since each term is then gauge-invariant, this Hamiltonian is particularly suited to the application of diagrammatic perturbation theory which follows from the iteration of the scattering matrix in the interaction representation (Chapter Five). Also the extension of the theory to multiphoton processes is facilitated "because the field strength is explicit in the transformed Hamiltonian. The S-matrix connects the initial and final asymptotic states of the scattering system, and in Chapter Six the state vector and density operator of the scattered photon beam are obtained from those of the incident beam. Part Two contains the application of the above methods to a variety of linear and nonlinear optical birefringence effects in the absence or presence of external fields. In Chapter Seven, general equations are obtained for the polarization changes imposed on a forward scattered photon in terms of matrix elements of the reaction operator between plane polarized photon base states; whereas Chapter Eight extends this treatment to an n-photon beam, thereby encompassing the hyperpolarizability contributions to the polarization changes of the forward scattered beam. It is then demonstrated that the fundamental process in optical birefringence can be interpreted as an infinitesimal unitary transformation of the polarization spinor. Also the S-matrix approach to birefringence is compared with the methods used in crystal optics, and with the classical treatments of the scattering of polarized light by molecules. The general equations obtained for the polarization changes of the forward scattered beam are subsequently interpreted in the light of the physical circumstances appropriate to the bire- fringence effect of interest. In Chapters Nine, Ten, and Eleven, diagrammatic perturbation theory is used to obtain explicit expressions, in terms of molecular polarizability and rotation tensors, for the linear and nonlinear contributions to the polarization changes involved in natural optical activity, and in birefringence phenomena induced by static and optical electric and magnetic fields. The nonforward scattering of polarized photons by molecules is discussed in Part Three. General equations are calculated in Chapter Twelve for the azimuth, ellipticity, and depolarization ratio of the Rayleigh beam at any scattering angle and for any polarization of the incident beam. Explicit expressions in terms of molecular quantities are then obtained for the polarization at scattering angles of 90° and almost zero from both optically inactive and optically active molecules. It is demonstrated that a determination of the precise polarization state of the scattered beam can provide useful molecular information additional to that obtained from depolarization ratios alone. This is because the depolarization ratio depends on only the diagonal elements of the polarization density matrix and so does not convey all the information about the system. Raman scattering processes are contained in the formulation and the polarization of the Raman light at any scattering angle can be obtained. This is shown to be particularly useful for predicting the polarization of stimulated Raman light for any Raman-active liquid placed within a laser cavity. By extending the nonforward scattering formulation to incorporate multiphoton processes, equations are obtained in Chapter Thirteen for the ellipticity, azimuth, and depolarization ratio of the second harmonic wave at any scattering angle as a function of the incident polarization. Several specific situations are subsequently investigated. Finally, it is shown in Chapter Fourteen that the near-forw- ard Rayleigh and Raman scattering formulations provide an explanation for the observed polarization, as a function of the initial polarization, of the self-trapped filaments that arise from the self-focusing of an intense laser beam.