Spontaneous Raman and fluorescence

SOLVATION EFFECTS IN FOUR-WAVE MIXING AND SPONTANEOUS RAMAN AND FLUORESCENCE LINESHAPES OF POLYATOMIC MOLECULES... 

V. Correlation Functions for Spontaneous Raman and Fluorescence Lineshapes... 

VIII. The Role of Vibrational Relaxation in Spontaneous Raman and Fluorescence Spectroscopy... 

Four-wave mixing (4WM) processes1-6 and spontaneous Raman and fluorescence (SRF) lineshapes7-12 provide a sensitive spectroscopic probe for polyatomic molecules in condensed phases. A 4WM process involves the interaction of three laser fields with wavevectors k, k2, and k3 and frequencies co, co2, and a>3, respectively, with a nonlinear medium. A coherently generated signal with wavevector ks and frequency cos is then detected (Fig. 1), where... 

Figure 2. The level scheme for spontaneous Raman and fluorescence (SRF) spectra. a>, c>, denote vibronic states belonging to the ground-state manifold, and h>, d),..., denote vibronic states belonging to the electronically excited manifold. In a SRF experiment, an to, photon is absorbed, and an to 2 photon is emitted.

V. CORRELATION FUNCTIONS FOR SPONTANEOUS RAMAN AND FLUORESCENCE LINESHAPES... 

In the previous sections, we derived general correlation function expressions for the nonlinear response function that allow us to calculate any 4WM process. The final results were recast as a product of Liouville space operators [Eqs. (49) and (53)], or in terms of the four-time correlation function of the dipole operator [Eq. (57)]. We then developed the factorization approximation [Eqs. (60) and (63)], which simplifies these expressions considerably. In this section, we shall consider the problem of spontaneous Raman and fluorescence spectroscopy. General formal expressions analogous to those obtained for 4WM will be derived. This will enable us to treat both experiments in a similar fashion and compare their information content. We shall start with the ordinary absorption lineshape. Consider our system interacting with a stationary monochromatic electromagnetic field with frequency w. The total initial density matrix is given by... 

We next turn to the spontaneous Raman and fluorescence lineshapes. In an SRF experiment, we have a single incident classical field (a ) and a single scattered mode (a>2). We shall use the Hamiltonian [Eq. (2)] with the only difference that the sum in Eq. (4) runs over j = 1,2, with El being the classical incident field and 2 being the scattered field, which will be treated quantum mechanically. In an SRF experiment, we monitor the scattered field with both time and frequency resolution. The operator representing the rate of emission of co2 photons is... 

In conclusion, in this section we presented the formal expressions for the absorption lineshape [Eq. (70)] and for spontaneous Raman and fluorescence spectroscopy. For the latter, we derived Liouville space expressions in the time and the frequency domain [Eqs. (74) and (75)], an ordinary correlation function expression [Eq. (76)], and, finally, the factorization approximation resulted in Eqs. (77) and (78). The factorization approximation is expected to hold in many cases for steady-state experiments and for time-resolved experiments with low temporal resolution. It is possible to observe a time-dependent shift of spontaneous emission lineshapes using picosecond excitation and detection [66-68]. This shift arises from the reorganization process of the solvent and also from vibrational relaxation that occurs during the t2 time interval. A proper treatment of these effects requires going beyond the... 

S. Mukamel, Solvatation effects in four-wave mixing and spontaneous Raman and fluorescence lineshapes of polyatomic molecules, Adv. Chem. Phys. 70 165 (1988). 

The inelastically scattered photons may or may not be scattered in phase. If they retain a phase relationship with one another the scattered radiation is coherent. If the inelastically scattered photons are emitted with random phases, as in spontaneous Raman and fluorescence, the radiation is said to be incoherently scattered. Because incoherent scattering seems to have the most immediate potential for applications in aerosol studies it will be emphasized in what follows. However, the case of coherent scattering by molecules embedded in particles is also of potential significance and will also be considered briefly in the next section. 

If the particle contains a number of dipoles and the scattering is incoherent (e.g., spontaneous Raman and fluorescence) the intensity of the light at the scattered frequency emerging from the particle is the sum of the contributions from each of the dipoles. The contribution from each dipole is different because the strength and direction of the exciting field varies with the location of the dipole with the particle. Moreover, the contribution from the dielectric medium of the particle necessary to satisfy the boundary conditions also depends upon the location of each dipole. 

Fig. 16.9 (a) Concept of higher photon confinement at the tip apex by a nonlinear optical process. Efficiency of a first-order process such as spontaneous Raman or fluorescence directly reflects the field distribution at the tip apex while the efficiency of a second-order process such as SHG or SFG and a third-order process such as CARS shows further confinement due to the nonlinear response of the material, (b) Energy diagram of CARS process... 

In the higher atmosphere the aerosol density decreases rapidly with altitude and other detection schemes may become more advantageous. Raman spectroscopy or detection of laser-induced fluorescence excited by frequency-doubled pulsed lasers has been utilized [14.22]. Both Raman and fluorescence intensities excited by the laser at a location x are proportional to the density n. (x) of scattering particles. However, because of the high pressure (p latm) the fluorescence is quenched if the collisional deactivation na v becomes faster than the spontaneous decay A. = 1/t. (see Sect. 12.2). Transition probabilities and quenching cross sections must therefore be known if quantitative results are to be obtained from measurements of the fluorescence intensity. 

Like spontaneous Raman microscopy, CARS microscopy does not rely on natural or artificial fluorescent labels, thereby avoiding issues of toxicity and artifacts associated with staining and photobleaching of fluorophores. Instead, it depends on a chemical contrast intrinsic to the samples. However, CARS microscopy offers two distinct advantages over conventional Raman microscopy ... 

The inelastic processes - spontaneous Raman scattering (usually simply called Raman scattering), nonlinear Raman processes, and fluorescence - permit determination of species densities as well as temperature, and also allow one, in principle, to determine the temperature for particular species whether or not in thermal equilibrium. In Table II, we categorize these inelastic processes by the type of the information that they yield, and indicate the types of combustion sources that can be probed as well as an estimate of the status of the method. The work that we concentrate upon here is that indicated in these first two categories, viz., temperature and major species densities determined from vibrational Raman scattering data. The other methods - fluorescence and nonlinear processes such as coherent anti-Stokes Raman spectroscopy - are discussed in detail elsewhere (5). 

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