Abstract A practical approach to understanding light scattering processes in the condensed phase is presented. First a theoretical discussion of the various parameters in resonance light scattering is given and there is a special emphasis on our simplified approach to this question. As with other approaches the two level density matrix in association with a quantum regression theorem leads to two types of emission from an ensemble of molecules at finite temperature (T2 ≠ 2T1). We have called one of these fluorescence and the other sharper emission Raman scattering because it results directly from the presence of a coherent polarization in the medium. A brief discussion of time dependent scattering is also given. An experiment that reproduces the main features of the theory is described for resonance scattering from azulene in naphthalene at 30 K. For all values of the laser frequency (near resonance) both a sharp (Raman) and diffuse (fluorescent) component occurs in the emission spectrum. These spectra when interpreted by the simplified theory yield a value of T2 = 0.7 ps from fluorescence linewidth, and T2 = 0.8 ps from the incoherent to coherent scattering ratio, for the 0–0 two level system of azulene in naphthalene. A discussion of practical aspects of the influence of inhomogeneous line broadening is also presented.
Abstract A practical approach to understanding light scattering processes in the condensed phase is presented. First a theoretical discussion of the various parameters in resonance light scattering is given and there is a special emphasis on our simplified approach to this question. As with other approaches the two level density matrix in association with a quantum regression theorem leads to two types of emission from an ensemble of molecules at finite temperature (T2 ≠ 2T1). We have called one of these fluorescence and the other sharper emission Raman scattering because it results directly from the presence of a coherent polarization in the medium. A brief discussion of time dependent scattering is also given. An experiment that reproduces the main features of the theory is described for resonance scattering from azulene in naphthalene at 30 K. For all values of the laser frequency (near resonance) both a sharp (Raman) and diffuse (fluorescent) component occurs in the emission spectrum. These spectra when interpreted by the simplified theory yield a value of T2 = 0.7 ps from fluorescence linewidth, and T2 = 0.8 ps from the incoherent to coherent scattering ratio, for the 0–0 two level system of azulene in naphthalene. A discussion of practical aspects of the influence of inhomogeneous line broadening is also presented.
The review deals with various variants of classification of the types of secondary emission of light by molecules; cases are distinguished in which the secondary emission occurs without additional processes that find their way between photon emission and absorption; the advisability of differentiating between the cases of resonance fluorescence and resonance scattering is noted. Reference is made to papers that have made contributions to the development of quantum-mechanical and classical theory of Raman scattering and to the development of the concepts of the relations between electron-vibrational absorption spectra, fluorescence spectra, and scattering excitation near and near and far resonance. Conditions are considered of excitation of the spectrum at different relations between the electronic-oscillator damping constant, the atom vibration frequency, the rotational frequencies, and the difference between the frequency of the incident light and the frequency of the electronic transition. The conditions for the excitation of typical light scattering, typical resonance fluorescence, and certain intermediate types, in which individual features of scattering are combined with certain features of fluorescence (phenomena of the transition type) are noted. The results of investigations of different models of the scattering centers, their advantages, shortcomings, and limits of applicability are compared. The most interesting results of the experimental investigations of resonant scattering of light by molecules and crystals are noted.
Abstract This chapter focuses on spectroscopic applications of time dependent quantum mechanics focusing on molecular spectroscopy in condensed phases. (1) Molecular spectroscopy in the dressed state picture. (2) Resonance Raman scattering. (3) Resonance energy transfer. (4) Collective excitation and emission. (5) Thermal relaxation and dephasing (the Bloch equations, relaxation of a prepared state, dephasing (decoherence), the absorption lineshape, homogeneous and inhomogeneous broadening, motional narrowing, thermal effects in resonance Raman scattering). (6) A case study: Resonance Raman scattering and fluorescence from Azulene in a Naphthalene matrix. (7) Probing inhomogeneous bands (hole-burning spectroscopy, photon echoes, single-molecule spectroscopy. (8) Optical response functions.
Lineshapes of three-level resonance Raman scattering and two-level resonance fluorescence, homogeneously broadened by collisions, in the presence of arbitrarily strong coherent radiation, are studied by means of a tetradic (density-matrix) scattering theory. In the case of medium coupling strength V L to the radiation field (where T 2 -1 <or=V L << tau c -1 , with T 2 and tau c being the coherence damping and collision times, respectively) the Mollow lineshape (1977) for resonance fluorescence is rederived, with proper T 2 and population cross-relaxation effects included. In particular it is shown that relaxation through intermediate non-resonant levels can considerably alter the lineshape in resonance fluorescence. In the case of strong coupling (V L >or approximately= tau c -1 ) the collision rates are modified by the applied field (optical collisions). It is shown that, whereas in self attenuation spectra optical collision rates can be obtained only from line intensity or line wing measurements, in resonance scattering these rates are directly obtained from linewidth measurements.
The nature of resonance emission of light, which appears as a mixture of (coherent) resonance scattering and (incoherent) resonance fluorescence, is considered. The basic conceptual elements which distinguish the scattering and fluorescence components for the linear excitation limit are developed in terms of a simple formulation whereby a molecule interacts with a coherent Lorentzian light pulse which increases exponentially with time for t<0 and is turned off at t = 0. These results together with the ideas, currently existing in the literature, that stochastic modulation of a molecule by its medium is essential for the appearance of fluorescence provide the basis for the further formulation of a theory which does not require the ad hoc introduction of a random potential. The theory developed considers the microscopic origins of manifest stochastic modulation effects in terms of a bath potential for the molecule–medium (bath) degrees of freedom. This potential, termed the sudden potential, is associated with the change in interaction with the medium that a molecule experiences upon intramolecular state transitions which are induced by external interactions (e.g., by light). Development of the reduced molecule–field density operator leads naturally to a separation of terms which describes scattering and (the propensity for) fluorescence. Critical to the theory is a four-time correlation function for the bath (sudden) potential. The difficulties inherent in defining absorption (spectrum) resonances and the corresponding distinctions between resonance and relaxed emission are discussed. Implications are considered for the further understanding of experimental results on molecular excitation dynamics in the gas phase and in supersonic jets. Sources of stochastic modulation other than material media are mentioned. In particular, the possibility is suggested of the pervasive existence of stochastic modulation through interaction of a molecule with the vacuum state of the radiation field. This raises questions concerning the fundamental relations between quantum mechanics and thermodynamics.
Time dependent description of resonance Raman scattering is performed for a general system, by a density matrix reformulation of damping theory originally used for resonance fluorescence of atom. Radiative damping in the intermediate states can be described in terms of "damping operator" in realistic situations. In large ergodic systems, the scattering reduces to luminescence if the relaxation time within the excited states is much shorter than the radiative lifetime. In a typical case, time resolved emission spectra consist of various stages (i) scattering complex where absorption and emission are inseparable, (ii) dynamical and then (iii) kinetic relaxations giving rise to the hot luminescence, which finally converges to (iv) the ordinary luminescence from relaxed excited states. Hot luminescence does not appear within a motionally narrowed line. The interpretation of spectra depends also on the method of observation.
In this paper we apply the T matrix formalism of scattering theory to derive general expressions for the absorption cross sections, the cross sections for resonance fluorescence and the emission quantum yields from large molecules in the statistical limit. In the simple case of an isolated molecular resonance both the absorption line shape and the photon scattering cross section exhibit a Lorentzian distribution on the photon energy, the emission quantum yields are distributed among the ground state vibronic levels according to their radiative widths and, most important, the emission quantum yields are independent of the photon energy and of the spectral width of the exciting light. We were able to derive general expressions for the resonance scattering from a pair of overlapping resonances, including radiative corrections to infinite order. The absorption cross section does not vanish in the region of destructive interference but assumes a finite value which depends on the radiative widths. A sharp maximum in the partial and in the total emission quantum yields is exhibited in the destructive interference regions. This general scheme was applied to a pair of zero order discrete states, one of which is optically active, which interact with an optically inactive quasicontinuum. The energy dependent quantum yield depends on the total width of the radiatively impotent state and may exhibit a minimum. We have demonstrated that when interference effects are involved the decay characteristics of this system will differ for coherent and for narrow band excitation. The general formalism was utilized to derive approximate relations for the resonance fluorescence cross sections and for the quantum yield in the case of a Fano absorption line shape which are valid away from the interference region. Finally, we have applied the general theoretical scheme to the case of the direct photodissociation spectrum of molecules. We have demonstrated that a finite energy dependent emission quantum yield will be observed when a molecule is optically pumped into a dissociative continuum.