Light scattering

Light scattering is a form of scattering in which light in the form of propagating energy is scattered. Light scattering can be thought of as the deflection of a ray from a straight path, for example by irregularities in the propagation medium, particles, or in the interface between two media. Deviations from the law of reflection due to irregularities on a surface are also usually considered to be a form of scattering. When these irregularities are considered to be random and dense enough that their individual effects average out, this kind of scattered reflection is commonly referred to as diffuse reflection.

Most objects that one sees are visible due to light scattering from their surfaces. Indeed, 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 wavelengths on the order of hundreds of nanometers, 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]

Mechanisms of diffuse reflection include surface scattering from roughness and subsurface scattering from internal irregularities such as grain boundaries in polycrystalline solids.

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]

Introduction

The interaction of light with matter can reveal 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 regard 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]

• Note: Light scattering in an ideal defect-free crystalline (non-metallic) solid which provides no scattering centers for incoming lightwaves will be due primarily to any effects of anharmonicity within the ordered lattice. Lightwave transmission will be highly directional due to the typical anisotropy of crystalline substances, which includes their symmetry group and Bravais lattice. For example, the seven different crystalline forms of quartz silica (silicon dioxide, SiO₂) are all clear, transparent materials.^[10]

Types of scattering

• Rayleigh scattering is the elastic scattering of light by molecules and particulate matter much smaller than the wavelength of the incident light. It occurs when light penetrates gaseous, liquid, or solid phases of matter. Rayleigh scattering intensity has a very strong dependence on the size of the particles (it is proportional to the third power of their diameter). It is inversely proportional to the fourth power of the wavelength of light, which means that the shorter wavelengths in visible white light (violet and blue) are scattered stronger than the longer wavelengths toward the red end of the visible spectrum. This type of scattering is therefore responsible for the blue color of the sky during the day.^[11] and the orange colors during sunrise and sunset. Rayleigh scattering is the main cause of signal loss in optical fibers.^[12]
• Mie scattering is a broad class of scattering of light by spherical particles of any diameter. The scattering intensity is generally not strongly dependent on the wavelength, but is sensitive to the particle size. Mie scattering coincides with Rayleigh scattering in the special case where the diameter of the particles is much smaller than the wavelength of the light; in this limit, however, the shape of the particles no longer matters. Mie scattering intensity for large particles is proportional to the square of the particle diameter.
• Tyndall scattering is similar to Mie scattering without the restriction to spherical geometry of the particles. It is particularly applicable to colloidal mixtures and suspensions.
• Brillouin scattering occurs from the interaction of photons with acoustic phonons in solids, which are vibrational quanta of lattice vibrations, or with elastic waves in liquids. The scattering is inelastic, meaning it is shifted in energy from the Rayleigh line frequency by an amount that corresponds to the energy of the elastic wave or phonon, and it occurs on the higher and lower energy side of the Rayleigh line, which may be associated with the creation and annihilation of a phonon.^[13] 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.^[14] In solids, the role of the crystal planes in this process is analogous to the planes of the sound waves or density fluctuations. Brillouin scattering measurements require the use of a high-contrast Fabry–Pérot interferometer to resolve the Brillouin lines from the elastic scattering, because the energy shifts are very small (< 100 cm⁻¹) and very weak in intensity. Brillouin scattering measurements yield the sound velocities in a material, which may be used to calculate the elastic constants of the sample.

• Raman scattering is another form of inelastic light scattering, but instead of scattering from acoustic phonons, as in Brillouin scattering, the light interacts with optical phonons, which are predominantly intra-molecular vibrations and rotations with energies larger than acoustic phonons. Raman scattering may therefore be used to determine chemical composition and molecular structure.^[15] Since most Raman lines are stronger than Brillouin lines, and have higher energies, standard spectrometers using scanning monochromators may be used to measure them. Raman spectrometers are standard equipment in many chemical laboratories.

Static and dynamic scattering

A common dichotomy in light scattering terminology is static light scattering versus dynamic light scattering. In static light scattering, the experimental variable is the time-average intensity of scattered light, whereas in dynamic light scattering it is the fluctuations in light intensity that are studied. Both techniques are typically encountered in the field of colloid and polymer characterization. They also have a broad range of other applications.

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.^{[16][17][18][19]}

See also

• Backscattering
• Diffuse sky radiation
• Extinction
• Inverse scattering
• Linewidth
• Molecular scattering
• Scattering from rough surfaces
• Scintillation (physics)

References

1. Kerker, M. (1969). "The Scattering of Light". New York: Academic. ISBN 0-12-404550-2.
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 0-486-64228-3.
4. Bohren, C.F. and Huffmann, D.R. (1983). Absorption and scattering of light by small particles. New York: Wiley-Interscience. ISBN 0-471-29340-7.
5. Fox, M. (2002). Optical Properties of Solids. Oxford University Press, USA. ISBN 0-19-850612-0.
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 (11): 2489–94. Bibcode:1972ApOpt..11.2489S. doi:10.1364/AO.11.002489. PMID 20119362.
7. Flygare, W H; Gierke, T D (1974). "Light Scattering in Noncrystalline Solids and Liquid Crystals". Annual Review of Materials Science 4: 255. Bibcode:1974AnRMS...4..255F. doi:10.1146/annurev.ms.04.080174.001351.
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.
10. Griffin, Allan (1968). "Brillouin Light Scattering from Crystals in the Hydrodynamic Region". Reviews of Modern Physics 40: 167. Bibcode:1968RvMP...40..167G. doi:10.1103/RevModPhys.40.167.
11. Nave, Rod. "Blue sky and Rayleigh Scattering". Hyperphysics. Georgia State University. Retrieved July 15, 2010.
12. I. P. Kaminow, T. Li (2002), Optical fiber telecommunications IV, Vol.1, p. 223
13. Mountain, Raymond D. (1966). "Spectral Distribution of Scattered Light in a Simple Fluid". Reviews of Modern Physics 38: 205. Bibcode:1966RvMP...38..205M. doi:10.1103/RevModPhys.38.205.
14. Fabelinskii, I.L. (1957). "Theory of Light Scattering in Liquids and Solids". Adv. Phys. Sci. (USSR) 63: 474.
15. Peticolas, W L (1972). "Inelastic Light Scattering and the Raman Effect". Annual Review of Physical Chemistry 23: 93. Bibcode:1972ARPC...23...93P. doi:10.1146/annurev.pc.23.100172.000521.
16. Ostrowski, N. in Cummins, H.Z. and Pike, E.R., Eds. (1973). "Photon Correlation and Light Beating Spectroscopy". Plenum Press. ISBN 0-306-35703-8.
17. Demoulin, C., Montrose, C.J. and Ostrowsky, N., (1974). "Structural Relaxation by Digital Correlation Spectroscopy". Phys. Rev. A 9 (4): 1740. Bibcode:1974PhRvA...9.1740D. doi:10.1103/PhysRevA.9.1740.
18. 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 (3–4): 120. doi:10.1111/j.1151-2916.1975.tb19573.x.
19. Surovtsev, N.V.; Wiedersich, J.; Novikov, V.; Rössler, E.; Sokolov, A. (1998). "Light Scattering Spectra of Fast Relaxation in Glasses". Phys. Rev. B 58 (22): 14888. Bibcode:1998PhRvB..5814888S. 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)
• M. Mishchenko, L. Travis, A. Lacis: Scattering, Absorption, and Emission of Light by Small Particles, Cambridge University Press, 2002.

External links

• Optics Classification and Indexing Scheme (OCIS), Optical Society of America, 1997