Abstract

Since exact scattering solutions for particles of arbitrary shape are absent, we take advantage of the two cases involving particles of specific shape, for which solutions are known, and derive formulas for the electric and magnetic dipole contributions to the extinction and scattering cross sections by electric and magnetic lossy particles in the Rayleigh-scattering limit. The formulas involve a dimensionless shape factor β which reduces to 12 for the case of a sphere and zero for the case of an infinite cylinder. Thus, we conclude that for any intermediate particle with a long axis of symmetry, 0β12. The results further indicate that for very thin needle-shaped particles the magnetic-dipole contributions are negligible. This conclusion is to be expected since, with the magnetic vector vibrating parallel to the needle axis, the induced currents are azimuthal (rather than axial as in the corresponding electric case). The characteristic length associated with these currents, i.e., the circumference, is small compared to the wavelength so that the contribution of these currents to the scattered field is small.

© 1966 Optical Society of America

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Equations (36)

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