Hyper-Raman effect

The higher-order terms /9EE,7EEE in the expansion (8.14) of p(E) represent the hyper-Raman effect. Analogous to (8.3) we can expand in a Taylor series in the normal coordinates q = q ocos(w t) 

Assume that two laser waves Ej = EoiCos(wit-kiz) and 3 = Eqj xcos(w2t-k2t) are incident on the Raman sample. From the third term in (8.14) we then obtain with (8.36) contributions to p(E) due to Pq 

The intensity of hyper-Raman lines can be considerably enhanced when the molecules under investigation are adsorbed at a surface [8.61] because the surface lowers the symmetry and increases the induced dipole moments. 

Similar to the induced Raman effect the hyper-Raman effect can also be used to generate coherent radiation in spectral ranges where no intense lasers exist. One example is the generation of tunable radiation around 16 /xm by stimulated hyper-Raman effect in strontium vapor [8.62]. 

Since the coefficients (dp/dq)o are very small, one needs large incident intensities to observe hyper-Raman scattering. Similar to second-harmonic generation (Vol. 1, Sect. 5.8), hyper-Rayleigh scattering is forbidden for molecules with a center of inversion. The hyper-Raman effect obeys selection rules that differ from those of the linear Raman effect. It is therefore very attractive to molecular spectroscopists since molecular vibrations can be observed in the hyper-Raman spectrum that are forbidden for infrared as well as for linear Raman transitions. For example, spherical molecules such as CH4 have no pure rotational Raman spectrum but a hyper-Raman spectrum, which was found by Maker [357]. A general theory for rotational and rotational-vibrational hyper-Raman scattering has been worked out by Altmann and Strey [358]. 

For large electric field amplitudes E, such as can be achieved with pulsed lasers, the linear relation (9.2) between induced dipole moment p and electric field E is no longer a satisfactory approximation and higher order terms have to be included. We then obtain instead of (9.2) 

The coefficients 3, y,. .. which are tensors of rank 3,4. are called hyperpolarizabilities. Analogous to (9.3) we can expand 3 in a Taylor series in 

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Vibrations allowed in the infrared are also allowed in the hyper Raman effect. 

Some vibrations which are both Raman and infrared inactive may be allowed in the hyper Raman effect. Indeed, the occasional appearance of such vibrations in Raman spectra in a condensed phase has sometimes been attributed to an effect involving the hyperpolarizability. 

Cyvin, S. J., Rauch, J. E. and Decius, J. C. (1965) Theory of hyper-Raman effects (nonlinear inelastic light scattering) selection rules and depolarization ratios for the second-order polarizability. 

High-power pulsed lasers offer the possibility of studying nonlinear phenomena such as stimulated Raman scattering, the inverse Raman effect and the hyper-Raman effect. These investigations have contributed much to our knowledge of the solid-state and liquid stucture of matter and its higher order constants. 

When the power of the exciting radiation is raised into the megawatt range, nonlinear Raman effects are observed, namely the stimulated Raman effect, the inverse Raman effect (Stoicheff absorption), and the hyper-Raman effect. The results of such experiments with single crystals will be discussed in the last chapter, with special emphasis on stimulated Raman scattering from polaritons. 

The selection rules for fi hyper-Raman scattering were derived by Cyvin, Rauch, and Decius, 02) and those for y hyper-Raman scattering, which has not yet been detected experimentally, by Christie and Lockwood 103>. From their tables one can see that silent modes become 3-active for such important point groups as C6, D6, C3v, C6v, C. D, 0 and Oh. Examples of additional 7 activity can be found in the point groups C4v, C. D. D, and Oh. Long and Stanton 104) have derived a quantum-mechanical theory of the hyper-Raman effect which indicates several possibilities for resonance enhancement of hyper-Raman intensities. Iha and Woo 105) extended the theory of nonlinear... 

Here, E is the strength of the applied electric field (laser beam), a the polarizability and / and y the first and second hyper-polarizabilities, respectively. In the case of conventional Raman spectroscopy with CW lasers (E, 104 V cm-1), the contributions of the / and y terms to P are insignificant since a fi y. Their contributions become significant, however, when the sample is irradiated with extremely strong laser pulses ( 109 V cm-1) created by Q-switched ruby or Nd-YAG lasers (10-100 MW peak power). These giant pulses lead to novel spectroscopic phenomena such as the hyper-Raman effect, stimulated Raman effect, inverse Raman effect, coherent anti-Stokes Raman scattering (CARS), and photoacoustic Raman spectroscopy (PARS). Figure 3-40 shows transition schemes involved in each type of nonlinear Raman spectroscopy. (See Refs. 104-110.)... 

The importance of the hyper Raman effect as a spectroscopic tool results from its symmetry selection rules. These are determined by products of three dipole moment matrix elements relating the four levels indicated in Fig. 3.6-1. It turns out that all infrared active modes of the scattering system are also hyper-Raman active. In addition, the hyper Raman effect allows the observation of silent modes, which are accessible neither by infrared nor by linear Raman spectroscopy. Hyper Raman spectra have been observed for the gaseous, liquid and solid state. A full description of theory and practice of hyper-Raman spectroscopy is given by Long (1977, 1982). 

In this section we first discuss the principles of resonance Raman and surface-enhanced Raman scattering and give some specific examples. Since the hyper Raman effect and the coherent nonlinear Raman effects have been described in Sec. 3.6, we only add some typical applications of the methods. 

In addition the reader may find tables with selection rules for the Resonance Raman and Hyper Raman Effect in the book of Weidlein et al. (1982). Special discussions about the basics of the application of group theory to molecular vibrations are given in the books of Herzberg (1945), Michl and Thulstrup (1986), Colthup et al. (1990) and Ferraro and Nakamoto (1994). Herzberg (1945) and Brandmiiller and Moser (1962) describe the calculation of thermodynamical functions (see also textbooks of physical chemistry). For the calculation of the rotational contribution of the partition function a symmetry number has to be taken into account. The following tables give this number in Q-... 

Nonlinear Raman processes 163 Spontaneous scattering hyper Raman effect 163 Stimulated Raman effect 164... 

The high intensity and coherence of laser radiation can lead to more elaborate photon scattering processes than those involved in the conventional Raman effect. The simplest example is second harmonic generation (hyper-Rayleigh scattering) and the associated hyper-Raman effect in which two laser photons of frequency interact simultaneously with the molecule to produce a scattered photon at frequency (hyper-Rayleigh), or at XiOi.-tO (Stokes hyper-Raman) or at (antiStokes hyper-Raman). As illustrated in figure 1.3, these processes involve two virtual intermediate excited states. 

Much more important for gas phase spectroscopy than the hyper-Raman effect are the various coherent Raman effects, so we shall develop the theory of coherent Raman scattering in rather more detail. The usual starting point is the bulk polarization of the medium expressed as a function of the electric field vectors of the various light waves present simultaneously in the medium (SI)... 

S.J. Cyvin, J.E. Rauch, J.C. Decius, Theory of hyper-Raman effects. J. Chem. Phys. 43, 4083 (1965)... 

K. Altmann, G. Strey, Enhancement of the scattering intensity for the hyper-Raman effect. Z. Naturforsch. A 32, 307 (1977)... 

J. Reif, H. Walther, Generation of Tunable 16 om radiation by stimulated hyper-Raman effect in strontium vapour. Appl. Phys. 15, 361 (1978)... 

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