Abstract

Treatment of the scattering of radiation by a spherical concentric core–shell system as a problem of multiple scattering by two spheres leads to a fuller understanding of the physical processes that produce the scattered fields of such a particle. The problem of scattering from a sphere containing multiple spherical inhomogeneities must, as a special case, be reducible to the problem considered here. Such a reduction leads to an expression of the scattering coefficients of coated spheres solely in terms of the scattering coefficients associated with a homogeneous host and with an isolated core, in agreement with the multiple scattering treatment.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. H. Bruning, Y. T. Lo, IEEE Trans. Antennas Propag. AP-19, 378 (1971).
    [CrossRef]
  2. K. A. Fuller, Appl. Opt. 30, 4716 (1991).
    [CrossRef] [PubMed]
  3. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  4. A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
    [CrossRef]
  5. S. Stein, Q. Appl. Math. 19, 15 (1961).
  6. O. R. Cruzan, Q. Appl. Math. 20, 33 (1962).
  7. F. Borghese, P. Denti, R. Saija, O. I. Sindoni, J. Opt. Soc. Am. A 9, 1327 (1992).
    [CrossRef]
  8. G. W. Kattawar, D. A. Hood, Appl. Opt. 15, 1996 (1976).
    [CrossRef] [PubMed]
  9. R. L. Hightower, C. B. Richardson, Appl. Opt. 27, 4850 (1988).
    [CrossRef] [PubMed]
  10. O. B. Toon, T. P. Ackerman, Appl. Opt. 20, 3657 (1981).
    [CrossRef] [PubMed]

1992 (1)

1991 (1)

1988 (1)

1981 (1)

1976 (1)

1971 (1)

J. H. Bruning, Y. T. Lo, IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

1962 (1)

O. R. Cruzan, Q. Appl. Math. 20, 33 (1962).

1961 (1)

S. Stein, Q. Appl. Math. 19, 15 (1961).

1951 (1)

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Ackerman, T. P.

Aden, A. L.

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Borghese, F.

Bruning, J. H.

J. H. Bruning, Y. T. Lo, IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

Cruzan, O. R.

O. R. Cruzan, Q. Appl. Math. 20, 33 (1962).

Denti, P.

Fuller, K. A.

Hightower, R. L.

Hood, D. A.

Kattawar, G. W.

Kerker, M.

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Lo, Y. T.

J. H. Bruning, Y. T. Lo, IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

Richardson, C. B.

Saija, R.

Sindoni, O. I.

Stein, S.

S. Stein, Q. Appl. Math. 19, 15 (1961).

Toon, O. B.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Appl. Opt. (4)

IEEE Trans. Antennas Propag. (1)

J. H. Bruning, Y. T. Lo, IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[CrossRef]

J. Appl. Phys. (1)

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

J. Opt. Soc. Am. A (1)

Q. Appl. Math. (2)

S. Stein, Q. Appl. Math. 19, 15 (1961).

O. R. Cruzan, Q. Appl. Math. 20, 33 (1962).

Other (1)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

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 (1)

Fig. 1
Fig. 1

Illustration of the multiple scattering calculation of the scattering coefficients of a coated sphere. Shown are the first three TM contributions. Note that the incident field is illustrated in its VSH representation.

Equations (16)

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

1 c ˇ n N m n ( 3 ) + 1 d ˇ n M m n ( 3 ) = 1 a ˇ n N m n ( 1 ) + 1 b ˇ n M m n ( 1 ) + N m n ( 3 ) + M m n ( 3 ) .
1 N 1 c ˇ n ξ n ( 1 ρ ) = ξ n ( 1 η ) + 1 a ˇ n ψ n ( 1 η ) ,
1 c ˇ n ξ n ( 1 ρ ) = ξ n ( 1 η ) + 1 a n ˇ ψ n ( 1 η ) .
1 c ˇ n = [ ψ n ( 1 ρ ) ξ n ( 1 ρ ) ξ n ( 1 ρ ) ψ n ( 1 ρ ) ] / [ 1 N ξ n ( 1 ρ ) ψ n ( 1 η ) ξ n ( 1 ρ ) ψ n ( 1 η ) ] .
1 a ˇ n = [ 1 N ξ n ( 1 ρ ) ξ n ( 1 η ) ξ n ( 1 ρ ) ξ n ( 1 η ) ] / 1 D n M ,
1 b ˇ n = [ 1 N ξ n ( 1 ρ ) ξ n ( 1 η ) ξ n ( 1 ρ ) ξ n ( 1 η ) ] / 1 D n E ,
1 d ˇ n = [ ξ n ( 1 η ) ψ n ( 1 η ) ψ n ( 1 η ) ξ n ( 1 η ) ] / 1 D n E = i / 1 D n E ,
A E ¯ m n = p m n [ 1 a n + 1 c n 2 a n 1 c n ˇ k = 0 ( 2 a n 1 a n ˇ ) k ] = p m n ( 1 a n + 2 a n 1 c n 1 c n ˇ 1 1 a ˇ n 2 a n ) ,
A H ¯ m n = q m n [ 1 b n + 1 d n 2 b n 1 d n ˇ k = 0 ( 2 b n 1 b n ˇ ) k ] = q m n ( 1 b n + 2 b n 1 d n 1 d n ˇ 1 1 b ˇ n 2 b n ) ,
E s = n = 1 m = n n l = 1 L [ l A E m n l N m n ( 3 ) + l A E m n l M m n ( 3 ) ] ,
l A E m n = l a n ν μ [ 1 C E μ ν A ˜ m n μ ν + 1 C H μ ν B ˜ m n μ ν + l l ( l A E μ ν A m n μ ν + l A H μ ν B m n μ ν ) ] ,
l A H m n = l b n ν μ [ 1 C H μ ν A ˜ m n μ ν + 1 C E μ ν B ˜ m n μ ν + l l ( l A H μ ν A m n μ ν + l A E μ ν B m n μ ν ) ] ,
1 C E m n = 1 c n p m n + 1 a ˇ n × l 1 ν μ ( l A E μ ν A ˜ m n μ ν + l A H μ ν B ˜ m n μ ν ) ,
1 C H m n = 1 d n q m n + 1 b ˇ n × l 1 ν μ ( l A H μ ν A ˜ m n μ ν + l A E μ ν B ˜ m n μ ν ) ,
1 A E m n = 1 a n p m n + ( 1 c ˇ n 1 ) × l l ν μ ( l A E μ ν A ˜ m n μ ν + l A H μ ν B ˜ m n μ ν ) ,
1 A H m n = 1 b n q m n + ( 1 d ˇ n 1 ) × l l ν μ ( l A H μ ν A ˜ m n μ ν + l A E μ ν B ˜ m n μ ν ) ,

Metrics