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4 - Rayleigh and Raman Scattering from Linear Molecules

Published online by Cambridge University Press:  24 February 2022

Chiao-Yao She  and
Jonathan S. Friedman
Chiao-Yao She
Affiliation:
Colorado State University
Jonathan S. Friedman
Affiliation:
Universidad Ana G. Mendez
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Summary

In Chapter 4, we look at nonresonant scattering, specifically Rayleigh and Raman scattering from linear molecules. We continue with the semiclassical (quantum) treatment, leading to the induced dipole moment and associated differential scattering cross section. Explicitly adding vibrational and rotational manifolds of the ground state, we show the results for all three regimes: Rayleigh, rotational Raman, and vibrational Raman scattering. We then apply these results to nitrogen and oxygen molecules and associate the results with macroscopic quantities, such as the index of refraction of an ensemble, or gas. From this point, we focus specifically on Rayleigh + vibrational Raman spectra of O2 and N2, determining vibrational and rotational constants and the thermal populations of the states, based on their molecular energies, which leads to the spectral strengths of individual lines. We finish this chapter with a description of the Cabannes spectrum and the effect of the density fluctuations on its lineshape, considering the success of theoretical models in reproducing these spectra in Knudson (low-density), kinetic (medium-density) and hydrodynamic (high-density) regimes.

Keywords

Rayleigh scatteringRotational Raman scatteringvibrational Raman scatteringRayleigh cross sections for nitrogen and oxygenRaman cross sections for nitrogen and oxygenpolarizability and macroscopic propertiesRayleigh spectra for nitrogen and oxygenRaman spectra for nitrogen and oxygendensity perturbationsand Cabannes spectra
Type
Chapter
Information
Atmospheric Lidar Fundamentals
Laser Light Scattering from Atoms and Linear Molecules
 , pp. 50 - 93
Publisher: Cambridge University Press
Print publication year: 2022

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References

Shen, Y. R. (1984). The Principles of Nonlinear Optics. Wiley-Interscience, ISBN: 0 471-88998-9.Google Scholar
Long, D. A. (2002). The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules. John Wiley & Sons, Ltd., ISBN 0-471-49028-8 (Hardback); 0-470-84576-7 (Electronic).CrossRefGoogle Scholar
Placzek, G. (1934). Rayleigh-Streuung und Raman-Effekt. In Handbuch der Radiologie, Marx, E., ed., 6, 205–374, Academische Verlag: Leipzig.Google Scholar
Edmonds, A. R. (1957). Angular Momentum in Quantum Mechanics. Princeton University Press.Google Scholar
She, C.-Y. (2001). Spectral structure of laser light scattering revisited: Bandwidths of non-resonant scattering lidars. Appl. Optics 40(27), 4875–4884.CrossRefGoogle Scholar
Placzek, G., and Teller, E.. (1933). Die Rotationsstruktur der Ramanbanden mehratomiger Moleküle. Zeitschrift für Physik 81, 209–258. doi: https://doi.org/10.1007/BF01338366Google Scholar
Altmann, K., and Strey, G.. (1972). Application of spherical tensors and Wigner 3-j symbols to the calculation of relative intensities of rotational lines in Raman bands of molecular gases. J. Mol. Spectroscopy, 44(3), 571–577.CrossRefGoogle Scholar
Wandinger, U. (2005). Raman lidar. Chapter 9 in Lidar Range-Resolved Optical Remote Sensing of the Atmosphere. Weitkamp, C., ed., Springer.Google Scholar
She, C.-Y., Chen, H., and Krueger, D. A.. (2015). Optical processes for middle atmospheric Doppler lidars: Cabannes scattering and laser induced resonance fluorescence. Jour. Opt. Soc. Am. B 32(9), 1575–1592, and Erratum, ibid., p. 1954.Google Scholar
Young, A. T. (1982). “Rayleigh scattering.” In Physics Today (January), pp. 42–48.Google Scholar
Griffith, D. J. (1998). Introduction to Electrodynamics. 2nd ed. Prentice Hall.Google Scholar
King, L. V. (1923). On the anisotropic molecule in relation to the dispersion and scattering of light. Proc. R. Soc. London, A104(726), 333–357.Google Scholar
Tomasi, C., Vitali, V., Petrov, B., Lupi, A., and Cacciari, A.. (2005). Improved algorithm for calculations of Rayleigh-scattering optical depth in standard atmospheres. Appl. Optics 44(16), 3320–3341.CrossRefGoogle ScholarPubMed
Butcher, R. J., Willetts, D. V., and Jones, W. J.. (1971). On the use of a Fabry–Perot etalon for the determination of rotational constants of simple molecules – the pure rotational Raman spectra of oxygen and nitrogen. Proc. R. Soc. London Ser. A 324(1557), 231–245.Google Scholar
Bendtsen, J., and Rasmussen, F.. (2000). High-resolution incoherent Fourier transform Raman spectrum of the fundamental band of 14N2. J. Raman Spectroscopy 31(5), 433–438.3.0.CO;2-T>CrossRefGoogle Scholar
Loëte, M., and Berger, H.. (1977). High resolution Raman spectroscopy of the fundamental vibrational band of 16O2. J. Mol. Spectrosc. 68(2), 317.CrossRefGoogle Scholar
She, C. Y., Herring, G. C., Moosmüller, H., and Lee, S. A.. (1985). Stimulated Rayleigh-Brillouin gain spectroscopy. Phys. Rev. A, 31(6), 3733–3740.CrossRefGoogle ScholarPubMed
Rahn, L. A., and Palmer, R. E.. (1986). Studies of nitrogen self-broadening at high temperature with inverse Raman spectroscopy. Jour. Opt. Soc. Amer. B, 3(9), 1164–1169.CrossRefGoogle Scholar
Tam, R. C. H. and May, A. D.. (1983). Motional narrowing of the rotational Raman band of compressed CO, N2, and CO2. Can. J. Phys. 61, 1558–1566.CrossRefGoogle Scholar
Pan, X.-G. (2003). “Coherent Rayleigh-Brillouin scattering,” Ph.D. dissertation, Princeton University.Google Scholar
Papoulis, A. (1962). The Fourier Integral and Its Applications. McGraw-Hill.Google Scholar
Yip, S., and Nelkin, M.. (1964). Application of a kinetic model to time-dependent density correlations in fluids. Phys. Rev. A 135(5A), 1241.Google Scholar
Herman, R. M., and Gray, M. A.. (1967). Theoretical prediction of stimulated thermal Rayleigh scattering in liquids. Phys. Rev. Lett. 19(15), 825–827.Google Scholar
Tenti, G., Boley, C., and Desai, R.. (1974). On the kinetic model description of Rayleigh -Brillouin scattering from molecular gases. Can. J. Phys. 52(4), 285–290.Google Scholar
Tang, S. Y., She, C. Y., and Lee, S. A.. (1987). Continuous-wave Rayleigh–Brillouin-gain spectroscopy of SF6. Optics Letters 12(11), 870–872.CrossRefGoogle ScholarPubMed
Vieitez, M. O., van Duijn, E. J., Ubachs, W. et al. (2010). Coherent and spontaneous Rayleigh–Brillouin scattering in atomic and molecular gases and gas mixtures. Phys. Rev. A 82(4), 0438361–14.Google Scholar
Witschas, B., Vieitez, M. O., van Duijn, E.-J. et al. (2010). Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air. Appl. Opt. 49(22), 4217–4227.Google Scholar
Krueger, D. A., Caldwell, L. M., Alvarez, R. J. II, and She, C. Y.. (1993). Self-consistent method for determining vertical profiles of aerosol and atmospheric properties using high-spectral-resolution Rayleigh–Mie lidar. J. Atm. Oceanic Tech. 10(4), 533–545.2.0.CO;2>CrossRefGoogle Scholar
Yan, Z. A. (2007). “A study of iodine filtrated atmospheric temperature lidar,” M.S. thesis, Ocean University of China (in Chinese).Google Scholar
Shimizu, H., Lee, S. A., and She, C. Y.. (1983). High spectral resolution lidar system with atomic blocking filters for measuring atmospheric parameters. Appl. Opt. 22(9), 1373–1381.Google Scholar

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