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Soviet Journal of Quantum Electronics

Role of multiphoton processes in four-photon scattering using high-intensity bichromatic pumping

Sergey K. Potapov, Vladimir Leonardovich Derbov, A. F. Bukatin

Published Jan 31, 1985• 0 citations
Publisher

Abstract

A theoretical analysis is made of the action of high-intensity bichromatic pump radiation on a system of vibrational–rotational molecular levels. The effective Hamiltonian approximation is used to reduce the problem to the solution of kinetic equations for the density matrix with a periodic external perturbation. These can be solved by adopting a basis of quasienergy states. The Raman susceptibility profile is obtained and investigated for an isolated vibrational resonance. It is shown that any change in the polarizability under excitation can be determined from the dependence of the population difference on the pump and scattered radiation intensities.

DOI
10.1070/qe1985v015n01abeh005873

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Soviet Journal of Quantum Electronics•Nov 30, 1979•1 citation
A theoretical analysis is made of the action of high-intensity bichromatic pump radiation on a system of vibrational–rotational molecular levels. The effective Hamiltonian approximation is used to reduce the problem to the solution of kinetic equations for the density matrix with a periodic external perturbation. These can be solved by adopting a basis of quasienergy states. The Raman susceptibility profile is obtained and investigated for an isolated vibrational resonance. It is shown that any change in the polarizability under excitation can be determined from the dependence of the population difference on the pump and scattered radiation intensities.
We introduce a theoretical framework to describe the interaction of an electromagnetic radiation field and a molecular system, such as a single molecule or a molecular crystal. By knowing in advance which electronic transitions are in resonance with the frequencies of the incident radiation, we propose a procedure to reduce the full problem to a description in terms of an effective Hamiltonian that fully takes into account the vibrational (nuclear) degrees of freedom, but that explicitly involves only those electronic states that meet the resonance condition. The influence of the rest of the electronic states appears as the polarizability of the system. We keep only those terms that give rise to Raman scattering but the scheme allows for a systematic inclusion of higher-order multiphoton processes. The resulting effective Hamiltonian is used to study the interaction of ultrashort laser pulses with a single molecule and with a molecular crystal. As applications, we study the interaction of a single ultrashort nonresonant pulse, and a train of such pulses, with a single molecule; we show that via Raman scattering the pulse impulsively transfers momentum to the molecule leaving it in a vibrational coherent state. We also study the interaction of two crossed laser pulses with a molecular crystal and show that a diffraction grating of lattice vibrations is impulsively created.
We have considered the Raman scattering in molecular media. Applying two laser fields in a two-photon resonance with vibrational transition, we have studied the role of rotational levels for excitation of vibrational coherence. It is shown that the molecular vibrational coherence strongly depends on the effect of coherent population trapping for rotational levels. The obtained results are important for applications of Raman spectroscopy to molecular detection in engineering, chemical, and biological applications.
A review is given of experimental and theoretical achievements in studies of multiphoton spontaneous scattering processes in atomic and molecular media. An analysis is made of integral multiphoton scattering, particularly of scattering in statistically inhomogeneous media with short-range quasiorder. A study of the intensity of the noncoherent multiphoton scattering component provides direct information on the nonlinear polarizability of atoms and molecules whilst the coherent component is associated with various atomic and molecular correlation mechanisms. An analysis of the spectra of elastic and inelastic multiphoton scattering processes yields information on the translational and rotational motion of the molecules. In particular, it is possible to measure the higher-order rotational relaxation times and to verify the adequacy of the various stochastic models of molecular motion. Observations of the spectral lines of three- or more-photon scattering, which obeys new selection rules, yield detail on the fine structure of the molecules and their linear and nonlinear vibrations. Examples are given of the most interesting spectra of three- or more-photon scattering in gases, liquids, and crystals obtained in singleand multichannel systems. The stochastic theory of multiphoton scattering in liquids is discussed, using the spherical tensor concept. The derived general expression reduces to known results for certain cases.
The temperature effect on the resonance Raman scattering from molecules is investigated. Considering a total system consisting of a molecular system, a heat bath, and the weak radiation field, a general expression for the relaxation processes is derived utilizing the Liouville operator technique for the time evolution of the density matrix of the total system. By using the perturbation method with respect to the radiation and matter up to second order, rate constants for zero photon (radiationless processes), one-photon and two-photon processes are derived after taking the long time limit in the Markoff approximation. Assuming a weak interaction between the molecular system and heat bath, a temperature-dependent resonance Raman scattering cross section is formulated in the adiabatic basis set for the molecular systems. In the displaced harmonic oscillator model, we obtain an analytical expression for the temperature-dependent Raman scattering cross section for the multimode case, which is suitable for both weak coupling and strong coupling cases. Analytical expressions for the Stokes and anti-Stokes bands of the jth order vibrational transition in the one oscillator model can easily be obtained from the general expression for the resonance Raman scattering cross section derived. An approximate Stokes to anti-Stokes ratio is given up to the second order of the dimensionless displacement Δ. The resonance Raman scattering cross section and the excitation energy profiles are numerically calculated as a function of physical constant such as temperature, molecular vibrational frequency and Δ. It is shown that the excitation profiles of the anti-Stokes band of the jth order vibrational transition have the similar envelope of the corresponding Stokes band shifted by jh/ω. The inverse Raman effect which is closely related to the ordinary Raman effect is also discussed.
A nonperturbative treatment of the dynamical behavior of a vibronic system in a resonant, coherent, driving light field is developed. The potential energy surfaces for the vibrational motion in the electronic ground and excited state are assumed to be displaced and distorted relative to one another. A system of three integrodifferential equations is derived from the infinite set of density-matrix equations. Both approximate analytical and numerical solutions are presented for the intensity and the intensity-correlation function of the scattered light. The results are valid for arbitrary ratios of the Rabi frequency to the relaxation rates. A system with fast vibrational relaxation behaves as a two-level system. For systems with slow vibrational relaxation, the applicability of perturbation theory requires pump fields that are weaker than those of a two-level system. The Rabi oscillations occurring in a strong pump field are damped less than those of a two-level system, and the intensity substantially decreases. The long-time behavior (determined by the vibrational relaxation time) is characterized by the increase of the intensity toward its stationary value.
It is shown that, in strong optical fields (~109 W/cm2), Raman lines may be excited due to transitions with changes by 3 and 4 in the rotational quantum number, which are forbidden in the linear approximation. This lifting of forbiddenness for Raman scattering is due to four-photon processes in which a pump photon is absorbed and a Stokes photon is emitted in an elementary event. Under quasiresonance pumping, this type of stimulated Raman scattering may be observed due to rotational transitions. Estimate are made of the conditions for observation of the spontaneous and stimulated processes in specific media.