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Scattering in an optical fiber
Specular reflection
Diffuse reflection

Scattering of light or other electromagnetic radiation is the deflection of rays in random directions by irregularities in the propagation medium, or in a surface or interface between two media. Scattering from a surface or interface can also be called diffuse reflection.

Most objects that one sees are visible due to light scattering from their surfaces. Moreover, this is our primary mechanism of physical observation.[1][2] Scattering of light depends on the wavelength or frequency of the light being scattered. Since visible light has wavelength on the order of a micron, objects much smaller than this cannot be seen, even with the aid of a microscope. Colloidal particles as small as 1 µm have been observed directly in aqueous suspension.[3][4]

The transmission of various frequencies of light is essential for applications ranging from window glass to fiber optic transmission cables and infrared (IR) heat-seeking missile detection systems. Light propagating through an optical system can be attenuated by absorption, reflection and scattering.[5][6]

Contents

Introduction

The interaction of light with matter can shed light on important information about the structure and dynamics of the material being examined. If the scattering centers are in motion, then the scattered radiation is doppler shifted. An analysis of the spectrum of scattered light can thus yield information regarding the motion of the scattering center. Periodicity or structural repetition in the scattering medium will cause interference in the spectrum of scattered light. Thus, a study of the scattered light intensity as a function of scattering angle gives information about the structure, spatial configuration, or morphology of the scattering medium. With regards to light scattering in liquids and solids, primary material considerations include:[7]

  • Crystalline structure: How close-packed its atoms or molecules are, and whether or not the atoms or molecules exhibit the long-range order evidenced in crystalline solids.
  • Glassy structure: Scattering centers include fluctuations in density and/or composition.
  • Microstructure: Scattering centers include internal surfaces in liquids due largely to density fluctuations, and microstructural defects in solids such as grains, grain boundaries, and microscopic pores.

In the process of light scattering, the most critical factor is the length scale of any or all of these structural features relative to the wavelength of the light being scattered.

An extensive review of light scattering in fluids has covered most of the mechanisms which contribute to the spectrum of scattered light in liquids, including density, anisotropy, and concentration fluctuations.[8] Thus, the study of light scattering by thermally driven density fluctuations (or Brillouin scattering) has been utilized successfully for the measurement of structural relaxation and viscoelasticity in liquids, as well as phase separation, vitrification and compressibility in glasses. In addition, the introduction of dynamic light scattering and photon correlation spectroscopy has made possible the measurement of the time dependence of spatial correlations in liquids and glasses in the relaxation time gap between 10−6 and 10−2 s in addition to even shorter time scales – or faster relaxation events. It has therefore become quite clear that light scattering is an extremely useful tool for monitoring the dynamics of structural relaxation in glasses on various temporal and spatial scales and therefore provides an ideal tool for quantifying the capacity of various glass compositions for guided light wave transmission well into the far infrared portions of the electromagnetic spectrum.[9]

Types of scattering

  • Rayleigh scattering is the elastic scattering of light or other electromagnetic radiation by objects or surfaces much smaller than the wavelength of the incoming light. It often can occur when light travels in transparent solids and liquids, but is more prevalent in gases. This type of scattering is responsible of the blue color of the sky during the day. Rayleigh scattering is inversely proportional to the fourth power of wavelength, which means that the shorter wavelength of blue light will be scattered more intensely than the longer wavelengths (e.g. green and red). This gives the sky a blue appearance.[11]
  • Mie scattering is scattering of light by spherical particles. Rayleigh scattering is Mie scattering in the special case where the diameter of the particles is much smaller than the wavelength of the light.
  • Brillouin scattering may result from the interaction of light photons with acoustic or vibrational quanta (phonons). The scattering is caused by the diffraction of incident planar monochromatic light waves by spontaneous, sinusoidal density fluctuations (i.e. standing thermal sound waves, or acoustic phonons). The light wave is considered to be scattered by the density maximum or amplitude of the acoustic phonon, in the same manner that X-rays are scattered by the crystal planes in a solid.[12] The role of the crystal planes in this process is analogous to the planes of the sound waves or density fluctuations. The interaction consists of an inelastic scattering process in which a phonon is either created or annihilated. The energy (and thus the frequency) of the scattered light is slightly increased or decreased.[13]
  • Raman scattering is similar to Brillouin scattering in that both phenomena represent inelastic scattering processes of light. The difference lies in the detected frequency shift range and type of information extracted from the sample. Raman scattering photons are scattered by interaction with vibrational and rotational transitions in molecules. Raman spectroscopy is therefore used to determine the chemical composition and molecular structure, while Brillouin scattering measures properties on a larger scale – such as the elastic behavior.[14]

Elastic waves

Thermal motion in liquids can be decomposed into elementary longitudinal vibrations (or acoustic phonons) while transverse vibrations (or shear waves) were originally described only in elastic solids exhibiting the highly ordered crystalline state of matter. This is the fundamental reason why simple liquids cannot support a shearing stress, but rather yield via macroscopic plastic deformation (or viscous flow). Thus, the fact that a solid deforms while retaining its rigidity while a liquid yields to macroscopic viscous flow in response to the application of a shearing force is accepted by many as the mechanical distinction between the two.[15][16][17]

The inadequacies of this conclusion, however, were pointed out by Frenkel in his revision of the theory of elasticity in liquids. This revision follows directly from the continuous characteristic of the structural transition from the liquid state into the solid one when this transition is not accompanied by crystallization – ergo the supercooled liquid. Thus we see the intimate correlation between transverse acoustic phonons (or shear waves) and the onset of rigidity upon vitrification, as described by Bartenev in his mechanical description of the vitrification process.[18]

The relationship between these transverse waves and the mechanism of vitrification has been described by one author who proposed that the onset of correlations between such phonons results in an orientational ordering or "freezing" of local shear stresses in glass-forming liquids, thus yielding the glass transition. Molecular motion in condensed matter can therefore be represented by a Fourier series whose physical interpretation consists of a superposition of supersonic longitudinal and transverse waves of atomic displacement with varying directions and wavelengths. In monatomic systems, we call these waves: density fluctuations. (In polyatomic systems, they may also include compositional fluctuations.)

The velocities of longitudinal acoustic phonons in condensed matter are directly responsible for the thermal conductivity which levels out temperature differentials between compressed and expanded volume elements. Kittel proposed that the behavior of glasses is interpreted in terms of an approximately constant "mean free path" for lattice phonons, and that the value of the mean free path is of the order of magnitude of the scale of disorder in the molecular structure of a liquid or solid. Klemens subsequently emphasized that heat transport in dielectric solids occurs through elastic vibrations of the lattice, and that this transport is limited by elastic scattering of acoustic phonons by lattice defects (e.g. randomly spaced vacancies). These predictions were confirmed by experiments on commercial glasses and glass ceramics, where mean free paths were apparently limited by "internal boundary scattering" to length scales of 10 - 100 micrometers.[19][20][21][22]

Brillouin scattering

The first theoretical study of the light scattering by thermal phonons was published in 1918. Brillouin predicted independently the scattering of light from thermally excited acoustic waves. Gross provided experimental confirmation in liquids and crystals.[23][24][25][26]

With the development of laser technology, the original experiments using the technique of Brillouin scattering on fused silica glass confirmed the existence of structural interfaces and defects on spatial scales of 10 - 100 micrometers. The mechanism of the absorption of sound in solids – which is responsible for the damping of elastic waves of atomic and molecular displacement (or density and compositional fluctuations) – was considered by Akheiser, who regarded the absorption as arising partly from heat flow and partly from viscous damping. In this interpretation, modulated phonons "relax" towards local thermal equilibrium via anharmonic phonon-phonon collisions. This relaxation is an entropy producing process which removes energy from the sound wave driving it, and thus damps it. These conclusions would appear to be consistent with Zener's interpretation of internal friction in crystalline solids being due to intergranular thermal currents.[27][28][29]

Improvements in the theory have made it possible to reasonably predict the acoustic loss of non-crystalline solids from the known thermal and elastic properties. Results indicate that infrared optical vibrational modes can contribute to such phenomena. This is not surprising in light of the notion that optic phonons can indeed carry heat in crystalline solids if the acousto-optic energy gap is small enough, and if the optic phonon group velocity is large enough.[30][31]

Mechanisms of attenuation of high-frequency shear modes and longitudinal waves were considered by Mason, et al. at Bell Labs with viscous liquids, polymers and glasses. The subsequent work in the Physics Department of the Catholic University of America led to an entirely new interpretation of the glass transition in viscous liquids in terms of a spectrum of structural relaxation phenomena occurring over a range of length and time scales. Experimentally, the use of light scattering experiments makes possible the study of molecular processes from time intervals as short as 10−11 sec. This is equivalent to extending the available frequency range from 109 Hz or greater than 109 Hz.[32][33][34][35][36][37]

Critical phenomena

Density fluctuations are responsible for the phenomenon of critical opalescence, which arises in the region of a continuous, or second-order, phase transition. The phenomenon is most commonly demonstrated in binary fluid mixtures, such as methanol and cyclohexane. As the critical point is approached the sizes of the gas and liquid region begin to fluctuate over increasingly large length scales. As the length scale of the density fluctuations approaches the wavelength of light, the light is scattered and causes the normally transparent fluid to appear cloudy.[38][39][40][41]

See also

References

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  2. ^ Mandelstam, L.I. (1926). "Light Scattering by Inhomogeneous Media". Zh. Russ. Fiz-Khim. Ova. 58: 381.  
  3. ^ van de Hulst, H.C. (1981). Light scattering by small particles. New York: Dover. ISBN 0486642283.  
  4. ^ Bohren, C.F. and Huffmann, D.R. (1983). Absorption and scattering of light by small particles. New York: Wiley-Interscience. ISBN 0471293407.  
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  6. ^ Smith, R.G. (1972). "Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering". Appl. Opt. 11: 2489. doi:10.1364/AO.11.002489.  
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  8. ^ Boon, J.P. and Fleury, P.A., The Spectrum of Light Scattered by Fluids, Adv. Chem Phys. XXIV, Eds. Prigogine and Rice (Academic Press, New York, 1973)
  9. ^ Measures, R.M. (2001). Structural Monitoring with Fiber Optic Technology. Academic Press, San Diego. ISBN 0-12-487430-4. http://books.google.com/books?id=lzIw9fQFVy0C&printsec=frontcover.  
  10. ^ Griffin, Allan (1968). "Brillouin Light Scattering from Crystals in the Hydrodynamic Region". Reviews of Modern Physics 40: 167. doi:10.1103/RevModPhys.40.167.  
  11. ^ Pecora, R (1972). "Quasi-Elastic Light Scattering from Macromolecules". Annual Review of Biophysics and Bioengineering 1: 257. doi:10.1146/annurev.bb.01.060172.001353.  
  12. ^ Fabelinskii, I.L. (1957). "Theory of Light Scattering in Liquids and Solids". Adv. Phys. Sci. (USSR) 63: 474.  
  13. ^ Mountain, Raymond D. (1966). "Spectral Distribution of Scattered Light in a Simple Fluid". Reviews of Modern Physics 38: 205. doi:10.1103/RevModPhys.38.205.  
  14. ^ Peticolas, W L (1972). "Inelastic Light Scattering and the Raman Effect". Annual Review of Physical Chemistry 23: 93. doi:10.1146/annurev.pc.23.100172.000521.  
  15. ^ Born, M. (1940). "The Stability of Crystal Lattices". Proc. Camb. Phil. Soc. 36: 160. doi:10.1017/S0305004100017138.  
  16. ^ Born, M. (1939). "Thermodynamics of Crystals and Melting". J. Chem. Phys. 7: 591. doi:10.1063/1.1750497.  
  17. ^ Born, M. (1949). A General Kinetic Theory of Liquids. University Press.  
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  22. ^ Chang, G.K. and Jones, R.E. (1962). "Low Temperature Thermal Conductivity of Amorphous Solids". Phys. Rev. 126: 2055. doi:10.1103/PhysRev.126.2055.  
  23. ^ Fabelinskii, I. L. (1968). Molecular Scattering of Light. PLenum Press, New York.  
  24. ^ Brillouin, L (1922). "Diffusion de la lumiere et des rayonnes X par un corps transparent homogene; influence del'agitation thermique". Ann. Phys. (Paris) 17: 88.  
  25. ^ Gross, E. (1930). "Über Änderun der Wellenlänge bei Lichtzerstreuung in Kriztallen". Z. Phys. 63: 685.  
  26. ^ Gross, E. (1930). "Change of wavelength of light due to elastic heat waves at scattering in liquids". Nature 126: 400. doi:10.1038/126201a0.  
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  28. ^ Maris, H.J. in Mason, W.P. and Thurston, R.N., Eds. (1971). Physical Acoustics. 5. Academic Press, New York.  
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  31. ^ Slack, G.A. (1979). Sol. State Phys. 24: 1.  
  32. ^ Montrose, C.J., et al. (1968). "Brillouin Scattering and Relaxation in Liquids". J. Acoust. Soc. Am. 43: 117. doi:10.1121/1.1910741.  
  33. ^ Mason, W.P., et al. (1948). "Mechanical Properties of Long Chain Molecule Liquids at Ultrasonic Frequencies". Phys. Rev. 73: 1074. doi:10.1103/PhysRev.73.1074.  
  34. ^ Litovits, T.A. (1959). "Ultrasonic Spectroscopy in Liquids". J. Acoust. Soc. Am. 31: 681. doi:10.1121/1.1907773.  
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  36. ^ Candau, S., et al. (1967). "Brillouin Scattering in Viscoelastic Liquids". J. Acoust. Soc. Am. 41: 1601. doi:10.1121/1.2143675.  
  37. ^ Pinnow, D. et al. (1967). "On the Relation of the Intensity of Scattered Light to the Viscoelastic Properties of Liquids and Glasses". J. Acoust. Soc. Am. 41: 1601. doi:10.1121/1.2143676.  
  38. ^ Ostrowski, N. in Cummins, H.Z. and Pike, E.R., Eds. (1973). Photon Correlation and Light Beating Spectroscopy. Plenum Press. ISBN 0306357038.  
  39. ^ Demoulin, C., Montrose, C.J. and Ostrowsky, N., (1974). "Structural Relaxation by Digital Correlation Spectroscopy". Phys. Rev. A 9: 1740. doi:10.1103/PhysRevA.9.1740.  
  40. ^ Lai, C.C., Macedo, P.B., and Montrose, C.J. (1975). "Light-Scattering Measurements of Structural Relaxation in Glass by Digital Correlation Spectroscopy". J. Am. Ceram. Soc. 58: 120. doi:10.1111/j.1151-2916.1975.tb19573.x.  
  41. ^ Surovtsev, N.V.; Wiedersich, J.; Novikov, V.; Rössler, E.; Sokolov, A. (1998). "Light Scattering Spectra of Fast Relaxation in Glasses". Phys. Rev. B 58: 14888. doi:10.1103/PhysRevB.58.14888.  

Further reading

  • P. W. Barber, S. S. Hill: Light scattering by particles: Computational methods. Singapore, World Scientific, 1990.
  • G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Leipzig, Ann. Phys. 330, 377–445 (1908)[1]
  • M. Mishchenko, L. Travis, A. Lacis: Scattering, Absorption, and Emission of Light by Small Particles, Cambridge University Press, 2002.
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