Stokes hyper-Raman scattering

When the sample is illuminated by a giant pulse of frequency v, the scattered radiation contains frequencies of 2v (hyper-Rayleigh scattering) and 2v vm (Stokes and anti-Stokes hyper-Raman scattering), where vM is a frequency of a normal vibration of the molecule. Clearly, this is Raman scattering caused by two incident photons (2v) of the laser. Experimentally, this... 

Fig. 3.23 Hyper-Rayleigh scattering (a), Stokes hyper-Raman (b), and anti-Stokes hyper-Raman scattering (c)...

The hyper-Raman effect is a three-photon process involving two virtual states of the scattering system. The level scheme for Stokes hyper-Raman scattering is presented in Figure 1. 

Figure 7 Hyper-Raman spectra of CeHeexcited with a Nd YAG laser (Aq = 1.064 nm) Q-switched at 1 kHz (A) and of CgDe in the lower spectrum with the laser Q-switched at 6 kHz (B). Reproduced by permission of Elsevier Science from Acker WP, Leach DH and Chang RK (1989) Stokes and anti-Stokes hyper Raman scattering from benzene, deuterated benzene, and carbon tetrachloride. Chemical Physics Letters 155 491-495.

Acker WP, Leach DH and Chang RK (1989) Stokes and anti-Stokes hyper Raman scattering from benzene, deu-terated benzene, and carbon tetrachloride. Chemical Physics Letters 155 491-495. 

Hyper Raman scattering is at a wavenumber 2vq v r, where Vq is the wavenumber of the exciting radiation and —v r and +V[jr are the Stokes and anti-Stokes hyper Raman displacements, respectively. The hyper Raman scattering is well separated from the Raman scattering, which is centred on Vq, but is extremely weak, even with a 0-switched laser. 

The methods of nonlinear Raman spectroscopy, i. e. spontaneous hyper Raman scattering (based on the hyperpolarizability) and coherent nonlinear Raman scattering (based on the third-order-nonlinear susceptibilities) are discussed in detail in Sec. 3.6.1. In Sec. 3.6.2 the instrumentation needed for these types of nonlinear spectroscopy is described. In this section we present some selected, typical examples of hyper Raman scattering (Sec. 6.1.4.1), coherent anti-Stokes Raman. scattering (Sec. 6.1.4.2), stimulated Raman gain and inverse Raman spectroscopy (Sec. 6.1.4.3), photoacoustic Raman spectroscopy (Sec. 6.1.4.4) and ionization detected stimulated Raman spectroscopy (Sec. 6.1.4.5). 

Nonlinear vibrational spectroscopy provides accessibility to a range of vibrational information that is hardly obtainable from conventional linear spectroscopy. Recent progress in the pulsed laser technology has made the nonlinear Raman effect a widely applicable analytical method. In this chapter, two types of nonlinear Raman techniques, hyper-Raman scattering (HRS) spectroscopy and time-frequency two-dimensional broadband coherent anti-Stokes Raman scattering (2D-CARS) spectroscopy, are applied for characterizing carbon nanomaterials. The former is used as an alternative for IR spectroscopy. The latter is useful for studying dynamics of nanomaterials. 

This quantity plays an important role in other multi-photon processes, such as two-photon absorption, second harmonic generation and hyper-Raman scattering as three-photon processes, and coherent anti-Stokes Raman scattering (CARS), a four-photon process (Table 1.5). The two-photon absorption can be treated theoretically from Eq. (1.115) in the same way as the Raman scattering process discussed above. Thus, the transition rate for two-photon absorption is given by Eq. (1.161). 

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. 

Figure 1 Schematic level diagram for Stokes and hyper Raman scattering.

Nonlinear scattering is exemplified by hyper-Raman scattering, induced Raman scattering, coherent anti-Stokes Raman scattering (CARS). 

In Eq. (1) it was assumed that the induced dipole varied in a linear fashion with the electric field. However, for electric field intensities above 10 V/m, as are often produced by pulsed lasers, the linear dependence breaks down. New spectroscopic phenomena arise from the nonlinear interaction of a system with intense monochromatic radiation. Each of the four examples considered here involves changes in wavelength of the radiation as a result of interaction with the system and can be considered to be a variant of the Raman effect. The four examples are the hyper-Raman scattering, the surface-enhanced hyper-Raman scattering, stimulated Raman scattering, and coherent anti-Stokes Raman scattering (CARS). 

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.)... 

Coherent Raman spectroscopy Coherent Raman spectroscopy is a term that refers to a series of closely related nonlinear Raman techniques in which the scattered Raman radiation emerges from the sample as a coherent beam -coherent meaning that the photons are all in phase with one another. The coherent techniques include Stimulated Raman Scattering (SRS), Coherent anti-Stokes Raman Spectroscopy (CARS), Coharent Stokes Raman Spectroscopy (CSRS), and Stimulated Raman Gain Spectroscopy (SRGS). Although most of the nonlinear Raman techniques are also coherent techniques, there is one incoherent nonlinear Raman process called Hyper Raman. 

It is not in the scope of the present chapter to review all possible experimental setups for the various types of Raman scattering classical, microprobe, Fourier transform (FT), coherent anti-Stokes (CARS), surface enhanced (SERS), hyper (HRS), photo-acoustic (PARS), and so forth (see, e.g.. Refs. 29-31). A basic Raman-scattering instrument requires a laser-light source, an appropriate sample holder, a sample illumination optical unit, a scattered-light collection optical unit (these two may be combined in one system), a disperser (spectrometer) or an interferometer, a light detection unit, a recorder, and an appropriate microcomputer able to drive, control, and record all of the experimental parameters as well as the results and their processing. 

The introduction of lasers therefore has indeed revolutionized this classical field of spectroscopy. Lasers have not only greatly enhanced the sensitivity of spontaneous Raman spectroscopy but they have furthermore initiated new spectroscopic techniques, based on the stimulated Raman effect, such as coherent anti-Stokes Raman scattering (CARS) or hyper-Raman spectroscopy. The research activities in laser Raman spectroscopy have recently shown an impressive expansion and a vast literature on this field is available. In this chapter we summarize only briefly the basic background of the Raman effect and. present some experimental techniques which have been developed. For more thorough studies of this interesting field the textbooks and reviews given in [9.1-4] are recommended. 

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