Abstract

Electromagnetic scattering from absorbing spheres near resonances is illustrated through calculations of the dependence of the efficiency factor for extinction Qext and of the angular scattering functions on n1 and n2 (the real and imaginary parts of the index of refraction). Among the interesting features discussed are the following: (1) the maximum value of Qext at the first resonance decreases rapidly when a small amount of absorption is introduced; (2) over a considerable range of the parameters the width of the first resonance of Qext is proportional to n1−4 when there is no absorption and to n2n1−2 when there is absorption; (3) when n1 ≫ 1, the scattered intensity near the first resonance is predominately forward, symmetrical, or predominately backward when x is respectively somewhat smaller than, equal to, or larger than the resonance value; (4) as n2 increases, the forward scattered intensity first increases before it decreases, when x ≥ 1 and for most values of n1; (5) strong forward scattering occurs on one side of a resonance and strong backward scattering on the other side, although this effect may be obscured by other factors for high multipole resonances.

© 1967 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. W. Kattawar, G. N. Plass, Appl. Opt. 6, 1377 (1967).
    [CrossRef] [PubMed]
  2. H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).
  3. G. N. Plass, Appl. Opt. 5, 279 (1966).
    [CrossRef] [PubMed]
  4. W. M. Irvine, J. Opt. Soc. Am. 55, 16 (1965).
    [CrossRef]

1967 (1)

1966 (1)

1965 (1)

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Other (1)

H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Maximum value of Qext at the first resonance as a function of n1 for various values of n2.

Fig. 2
Fig. 2

Width at half maximum (in units of x) as a function of n1 for various values of n2.

Fig. 3
Fig. 3

Average value of the cosine of the scattering angle as a function of n2 for x = 0.1 and various values of n1.

Fig. 4
Fig. 4

Average value of the cosine of the scattering angle as a function of n2 for x = 1 and various values of n1.

Fig. 5
Fig. 5

Average value of the cosine of the scattering angle as a function of n2 for x = 10 and various values of n1.

Fig. 6
Fig. 6

Average value of the cosine of the scattering angle and Qext as a function of x for n1 = 10 and n2 = 0. The scales for the cosine and for Qext are on the left and right, respectively.

Fig. 7
Fig. 7

Average value of the cosine of the scattering angle and Qext as a function of x for n1 = 10 and n2 = 0 in the vicinity of the second to the fifth resonances. The scales for the cosine and for Qext are the left and right, respectively.

Fig. 8
Fig. 8

Average value of the cosine of the scattering angle as a function of the size parameter x for n1 = 10 and 100. These values of x are in the immediate neighborhood of the first resonance in Qext.

Fig. 9
Fig. 9

The scattered intensity as a function of the scattering angle for x = 0.275, 0.31131, and 0.360 and n1 = 10, n2 = 0. The values of the intensity at 0° and 180° are indicated above the curves near each margin. The solid curve is the intensity i1 (as defined by Van de Hulst2) and the dashed curve is the intensity i2. The logarithm of the intensity is plotted; each division indicated on this scale represents a factor of ten.

Fig. 10
Fig. 10

The scattered intensity as a function of the scattering angle for x = 0.44404, 0.44775, 0.57330, and 0.57516 and n1 = 10, n2 = 0. These values correspond to the electric dipole, magnetic quadrupole, electric quadrupole, and magnetic octopole resonances, respectively. See legend for Fig. 9.

Tables (2)

Tables Icon

Table I Values of x at First Resonance

Tables Icon

Table II Value of X and Qext at Resonance for n1 = 10, n2 = 0

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

x max = π n 1 - 1
Q ext , max = 6 π - 2 n 1 2 ,

Metrics