Long-wavelength limit of scattering from a lossy dielectric sphere
JOSA, Vol. 72, Issue 8, pp. 1090-1091 (1982)
http://dx.doi.org/10.1364/JOSA.72.001090
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Abstract
It is shown that the cross section for scattering in the long-wavelength limit from a lossy dielectric sphere varies as λ^{-2} and not as λ^{-1}, as is suggested in standard treatments of the subject. The λ^{-1} variation is in conflict with the analytic properties of the scattering amplitudes as a function of k = 2πλ^{-1}, and this conflict is resolved when the wavelength dependence of the dielectric constant is taken into account.
© 1982 Optical Society of America
Citation
M. A. Box and Bruce H. J. McKellar, "Long-wavelength limit of scattering from a lossy dielectric sphere," J. Opt. Soc. Am. 72, 1090-1091 (1982)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-72-8-1090
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References
- H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1964), Secs. 6.13, 10.3, and 14.21.
- M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), Sec. 3.9.2.
- J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Sec. 9.14.
- Ref. 1, Sec. 4.21, gives the classical derivation. Ref. 3, Sec. 9.14, gives a derivation that parallels more closely the quantum-mechanical optical theorem.
- See, e.g., R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966), Sec. 4.2.2, especially Eq. (4.34), and the statement immediately following it. Note that Newton's A_{ii} and the S_{i}(0) of this Letter (and of Ref. 1) are related by A_{ii} = ik^{-1}S_{i}(0^{0}), so in relating Newton's result for A_{ii} to a statement about S(0) the terms real and imaginary and the terms even and odd must be interchanged.
- See, e.g., Ref. 3, Sec. 7.10. The fact that Im ∊(k) and Re S(0) are both odd functions of K is no accident. If we construct a material that is a dilute suspension of N of our scatterers per unit volume, the dielectric constant ∊¯ of that material is related to S(0) by ∊¯(k) = 1 + (4πNi/k^{2})S(0). That Im ∊¯ is odd in k implies that Re S(0) is odd and vice versa.
- See, e.g., Ref. 3, Sec. 7.10.
- Indeed, by using the dispersion relation for S(0) (e.g., Ref. 5), one can show by similar manipulations that [equation], where Im S¯(0, k′) = Im S(0, k′) - k′^{3} lim_{k′→0} [Im S(0, k′)/k′^{3}], exhibiting the λ^{-2} dependence of C_{tot} and identifying the coefficient in a different way. This and similar relations will be described in more detail elsewhere.^{9}
- B. H. J. McKellar, M. A. Box, and C. Bohren, J. Opt. Soc. Am. (to be published).
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