Abstract

Resonances in partial waves an and bn are directly responsible for a ripple structure in the normalized extinction cross section. The distance Δx in the size parameter between two neighboring resonances is equal to a basic period of a ripple structure.

© 1976 Optical Society of America

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References

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  1. H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 375.
  2. P. Chýlek, J. Opt. Soc. Am. 65, 1316 (1975).
    [Crossref]
  3. Reference 1, p. 373.
  4. H. M. Nussenzveig, J. Math. Phys. 10, 125 (1969).
    [Crossref]

1975 (1)

1969 (1)

H. M. Nussenzveig, J. Math. Phys. 10, 125 (1969).
[Crossref]

Chýlek, P.

Nussenzveig, H. M.

H. M. Nussenzveig, J. Math. Phys. 10, 125 (1969).
[Crossref]

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 375.

J. Math. Phys. (1)

H. M. Nussenzveig, J. Math. Phys. 10, 125 (1969).
[Crossref]

J. Opt. Soc. Am. (1)

Other (2)

Reference 1, p. 373.

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 375.

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Figures (4)

FIG. 1
FIG. 1

Normalized extinction cross section for refractive index m = 1.50 and the size parameter 0 ≤ x ≤ 20. The double-peaked structure of the ripple is clearly seen for all x > 10.

FIG. 2
FIG. 2

Real parts of a13(x) and b13(x) (solid lines) and imaginary parts of a13(x) and b13(x) (dotted lines) as a function of x. The first sharp peaks represent a13 and b13 partial-wave resonances. At the peak we have Re an = 1 and Iman = 0. The width of a resonance at half of maximum intensity is determined by the points Iman = 0.5 and −0.5. The same is valid for bn resonance. Broad secondary peaks contribute to the formation of smoothly varying background in Qext.

FIG. 3
FIG. 3

Normalized extinction cross section for m = 1.50 and 10 ≤ x ≤ 20. Each peak in the ripple structure corresponds to a resonance in a appropriate partial wave an or bn. The basic period of the ripple Δx is given by Eq. (4).

FIG. 4
FIG. 4

Same as Fig. 2, however, for complex refractive index m = 1.50 − 0.01i.

Equations (6)

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Q ext ( x , m ) = 2 x 2 n = 1 ( 2 n + 1 ) Re ( a n + b n ) ,
0 Re ( a n ( x , m ) ) 1 ,
0 Re ( b n ( x , m ) ) 1 ,
Re ( a n ( x , m ) ) = 1
Re ( b n ( x , m ) ) = 1.
Δ x = arctan ( m 2 - 1 ) 1 / 2 / ( m 2 - 1 ) 1 / 2 .