Rayleigh radiation

In dispersive spectrometers, the Rayleigh radiation may produce stray radiation in the entire spectrum, the intensity of which may be higher than that of the Raman lines. Interferometers transform the Poisson distribution of the light quanta of the Rayleigh radiation into white noise, which overlays the entire Raman spectrum. Therefore, all types of spectrometers must have means to reduce the radiant power of the exciting radiation accompanying the Raman radiation. 

Wang and Lee [1] define the so-called Langevin and Rayleigh radiation pressures, respectively, as the mean excess pressures that either depend upon the sound wave only... 

Wang and Lee [1] define the so-called Langevin and Rayleigh radiation pressures, respectively, as the mean excess pressures that either depend upon the sound wave only (i. e., with C = 0), or on the sound wave together with a constraint which determines the constant C that contributes to the pressure. The concept of the radiation pressure enables the calculation of forces acting upon material surfaces, such as an interface between two fluids or the surface of a particle or a drop in a sound field. Strictly speaking, one should use the acoustic radiation stress tensor n to calculate such forces. However, in many situations, such as when the surface is rigid or when the velocity at a surface is normal to that surface, it is convenient to use the radiation pressure rather than the full stress. 

Immediately following the invention of optical lasers in the early 1960s, all instruments used lasers as the light source. Acquisition of spectra from samples with arbitrarily high Rayleigh radiation required some spectrometer developments as well as implementation of low-noise detectors. Curiously, the physics on which both laser and photomultiplier operation are based is derived from work of Albert Einstein. Photomultipliers operate by using the photoelectric effect for which Einstein received the Nobel Prize for work done in 1905. Laser action was a demonstration of stimulated emission that was predicted by Einstein in 1917. A discussion of laser action will not be included in this chapter, but the reader can refer to a text on optoelectronics such as Ref. 17. 

The field radiated into the coupling medium by such a distribution of sources may be obtained by means of the well-known Rayleigh integral. The field at the considered point r is computed by a simple integral over the whole radiating surface of the contributions of each elementary source acting as a hemispherical point source. 

This is known as the Stefan-Boltzmaim law of radiation. If in this calculation of total energy U one uses the classical equipartition result = k T, one encounters the integral f da 03 which is infinite. This divergence, which is the Rayleigh-Jeans result, was one of the historical results which collectively led to the inevitability of a quantum hypothesis. This divergence is also the cause of the infinite emissivity prediction for a black body according to classical mechanics. 

The first temi results in Rayleigh scattering which is at the same frequency as the exciting radiation. The second temi describes Raman scattering. There will be scattered light at (Vq - and (Vq -i- v ), that is at sum and difference frequencies of the excitation field and the vibrational frequency. Since a. x is about a factor of 10 smaller than a, it is necessary to have a very efficient method for dispersing the scattered light. 

Goldanskii V I and Krupyanskii Y F 1989 Protein and protein-bound water dynamics studied by Rayleigh scattering of Mdssbauer radiation (RSMR) Q. Rev. Biophys. 22 39-92... 

Figure 1-1 The Blackbody Radiation Spectrum. The short curve on the left is a Rayleigh function of frequency.

As Lord Rayleigh pointed out, the classical expression for radiation... 

Distribution of radiation for (a) Rayleigh scattering and (b) large-particle scattering. 

All three terms in this equation represent scattering of the radiation. The first term corresponds to Rayleigh scattering of unchanged wavenumber v, and the second and third terms correspond to anti-Stokes and Stokes Raman scattering, with wavenumbers of (v + 2v () and (v — 2v () respectively. 

Molecules initially in the J = 0 state encounter intense, monochromatic radiation of wavenumber v. Provided the energy hcv does not correspond to the difference in energy between J = 0 and any other state (electronic, vibrational or rotational) of the molecule it is not absorbed but produces an induced dipole in the molecule, as expressed by Equation (5.43). The molecule is said to be in a virtual state which, in the case shown in Figure 5.16, is Vq. When scattering occurs the molecule may return, according to the selection mles, to J = 0 (Rayleigh) or J = 2 (Stokes). Similarly a molecule initially in the J = 2 state goes to... 

The mechanism for Stokes and anti-Stokes vibrational Raman transitions is analogous to that for rotational transitions, illustrated in Figure 5.16. As shown in Figure 6.3, intense monochromatic radiation may take the molecule from the u = 0 state to a virtual state Vq. Then it may return to u = 0 in a Rayleigh scattering process or to u = 1 in a Stokes Raman transition. Alternatively, it may go from the v = state to the virtual state Fj and return to V = (Rayleigh) or to u = 0 (Raman anti-Stokes). Flowever, in many molecules at normal... 

Harada, Y. and Asakura, T. (1996) Radiation forces on a dielectric sphere in the Rayleigh scattering regime. Opt. Commun., 124, 529-541. 

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