Abstract

A computer method for determining the scattering, absorption, and internal field structure of thin flat disks of arbitrary refractive index is described. The code is shown to be accurate for all angles of incidence for radii up to at least two free space wavelengths and for media ranging from pure dielectric to highly conductive ones. The accuracy of the method is assessed by comparison with published experimental data and with results computed by other methods. The applicability of this technique for analyzing clouds of disk-shaped aerosols is also discussed.

© 1987 Optical Society of America

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References

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  1. H. Weil, C. M. Chu, “Scattering and Absorption by Thin Flat Aerosols,” Appl. Opt. 19, 2066 (1980).
    [CrossRef] [PubMed]
  2. P. C. Waterman, “Scattering by Dielectric Obstacles,” Alta Freq. 38 (Speciale), 348 (1969).
  3. P. Barber, C. Yeh, “Scattering of Electromagnetic Waves by Arbitrarily Shaped Dielectric Bodies,” Appl. Opt. 14, 2864 (1975).
    [CrossRef] [PubMed]
  4. M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of EBCM,” IEEE Trans. Antennas Propag. AP-31, 317 (1983).
    [CrossRef]
  5. A. Lakhtakia, M. F. Iskander, C. H. Durney, “An Iterative Extended Boundary Condition Method for Solving the Absorption Characteristics of Lossy Dielectric Objects of Large Aspect Ratios,” IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
    [CrossRef]
  6. K. Umashankar, A. Taflove, S. M. Rao, “Electromagnetic Scattering by Arbitrary Shaped Three-Dimensional Homogeneous Lossy Dielectric Objects,” IEEE Trans. Antennas Propag. AP-34, 758 (1986).
    [CrossRef]
  7. D. H. Schaubert, D. R. Wilton, A. W. Glisson, “A Tetrahedral Modeling Method for Electromagnetic Scattering by Arbitrarily Shaped Inhomogeneous Dielectric Bodies,” IEEE Trans. Antennas Propag. AP-32, 72 (1984).
  8. C-T. Tsai, H. Massoudi, C. H. Durney, M. F. Iskander, “A Procedure for Calculating Fields Inside Arbitrarily Shaped, In-homogeneous Dielectric Bodies Using Linear Basis Functions with the Moment Method,” IEEE Trans., MTT-34, 1131 (1986).
  9. A. Taflove, K. Umashankar, “Radar Cross Section of General Three-Dimensional Scatterers,” IEEE Trans. Electromagn. Compat. EMC-25, 433 (1983).
    [CrossRef]
  10. A. R. Holt, “The Fredholm Integral Equation Method and Comparison with the T-matrix Approach,” in Acoustic, Electromagnetic and Elastic Wave Scattering: Focus on the T-matrix Approach,V. V. Varadan, V. K. Varadan, Eds. (Pergamon, London, 1980), p. 255.
  11. J. W. Shepherd, A. R. Holt, “The Scattering of Electromagnetic Radiation from Finite Dielectric Circular Cylinders,” J. Phys A 16, 651 (1983).
    [CrossRef]
  12. M. F. Iskandar, S. C. Olson, R. E. Benner, D. Yoshida, “Optical Scattering by Metallic and Carbon Aerosols of High Aspect Ratio,” Appl. Opt. 25, 2514 (1986).
    [CrossRef]
  13. T. M. Willis, “Low Frequency Scattering by a Thin Dielectric Plate,” Radiation Lab. Memo 019955-502-M; EECS Dept., U. Michigan, Ann Arbor 48109-2122 (1982).
  14. L. E. Allen, G. C. McCormick, “Measurement of the Backscatter Matrix of Dielectric Bodies,” IEEE Trans. Antennas Propag. AP-28, 166 (1980).
    [CrossRef]
  15. R. DeVore, D. B. Hodge, R. G. Kouyoumjian, “Backscattering Cross Sections of Circular Disks,” J. Appl. Phys. 42, 3075 (1971).
    [CrossRef]
  16. D. M. Le Vine, A. Schneider, R. H. Lang, H. G. Carter, “Scattering from Thin Dielectric Disks,” IEEE Trans. Antennas Propag. AP-33, 1410 (1985).
    [CrossRef]
  17. T. M. Willis, H. Weil, “Internal Induced Fields, Scattering and Absorption of Electromagnetic Radiation by Disc Shaped Aerosols; an Improved Computational Formulation and Computer Code,” Radiation Lab. Report RL023618-1-T; EECS Dept., U. Michigan, Ann Arbor 48109-2122 (1986).
  18. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959, 1975), Sec. 13.5.
  19. H. Weil, T. Willis, “A Model for Polarization Effects in Remote Probing of Clouds,” Radio Sci. 17, 1018 (1982).
    [CrossRef]
  20. T. B. A. Senior, H. Weil, “On the Validity of Modeling Rayleigh Scatterers by Spheroids,” Appl. Phys. B 29, 117 (1982).
    [CrossRef]
  21. H. Weil, T. B. A. Senior, T. M. Willis, “Internal and Near Fields of Small Particles Irradiated in Spectral Absorption Bands,” J. Opt. Soc. Am. 2, 989 (1985).
    [CrossRef]
  22. R. Ruppin, R. Englman, “Optical Lattice Vibrations in Finite Ionic Crystals II,” J. Phys. C (Proc. Phys. Soc.) 1, 630 (1968).

1986

K. Umashankar, A. Taflove, S. M. Rao, “Electromagnetic Scattering by Arbitrary Shaped Three-Dimensional Homogeneous Lossy Dielectric Objects,” IEEE Trans. Antennas Propag. AP-34, 758 (1986).
[CrossRef]

C-T. Tsai, H. Massoudi, C. H. Durney, M. F. Iskander, “A Procedure for Calculating Fields Inside Arbitrarily Shaped, In-homogeneous Dielectric Bodies Using Linear Basis Functions with the Moment Method,” IEEE Trans., MTT-34, 1131 (1986).

M. F. Iskandar, S. C. Olson, R. E. Benner, D. Yoshida, “Optical Scattering by Metallic and Carbon Aerosols of High Aspect Ratio,” Appl. Opt. 25, 2514 (1986).
[CrossRef]

1985

D. M. Le Vine, A. Schneider, R. H. Lang, H. G. Carter, “Scattering from Thin Dielectric Disks,” IEEE Trans. Antennas Propag. AP-33, 1410 (1985).
[CrossRef]

H. Weil, T. B. A. Senior, T. M. Willis, “Internal and Near Fields of Small Particles Irradiated in Spectral Absorption Bands,” J. Opt. Soc. Am. 2, 989 (1985).
[CrossRef]

1984

D. H. Schaubert, D. R. Wilton, A. W. Glisson, “A Tetrahedral Modeling Method for Electromagnetic Scattering by Arbitrarily Shaped Inhomogeneous Dielectric Bodies,” IEEE Trans. Antennas Propag. AP-32, 72 (1984).

1983

A. Taflove, K. Umashankar, “Radar Cross Section of General Three-Dimensional Scatterers,” IEEE Trans. Electromagn. Compat. EMC-25, 433 (1983).
[CrossRef]

J. W. Shepherd, A. R. Holt, “The Scattering of Electromagnetic Radiation from Finite Dielectric Circular Cylinders,” J. Phys A 16, 651 (1983).
[CrossRef]

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of EBCM,” IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

A. Lakhtakia, M. F. Iskander, C. H. Durney, “An Iterative Extended Boundary Condition Method for Solving the Absorption Characteristics of Lossy Dielectric Objects of Large Aspect Ratios,” IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
[CrossRef]

1982

H. Weil, T. Willis, “A Model for Polarization Effects in Remote Probing of Clouds,” Radio Sci. 17, 1018 (1982).
[CrossRef]

T. B. A. Senior, H. Weil, “On the Validity of Modeling Rayleigh Scatterers by Spheroids,” Appl. Phys. B 29, 117 (1982).
[CrossRef]

1980

L. E. Allen, G. C. McCormick, “Measurement of the Backscatter Matrix of Dielectric Bodies,” IEEE Trans. Antennas Propag. AP-28, 166 (1980).
[CrossRef]

H. Weil, C. M. Chu, “Scattering and Absorption by Thin Flat Aerosols,” Appl. Opt. 19, 2066 (1980).
[CrossRef] [PubMed]

1975

1971

R. DeVore, D. B. Hodge, R. G. Kouyoumjian, “Backscattering Cross Sections of Circular Disks,” J. Appl. Phys. 42, 3075 (1971).
[CrossRef]

1969

P. C. Waterman, “Scattering by Dielectric Obstacles,” Alta Freq. 38 (Speciale), 348 (1969).

1968

R. Ruppin, R. Englman, “Optical Lattice Vibrations in Finite Ionic Crystals II,” J. Phys. C (Proc. Phys. Soc.) 1, 630 (1968).

Allen, L. E.

L. E. Allen, G. C. McCormick, “Measurement of the Backscatter Matrix of Dielectric Bodies,” IEEE Trans. Antennas Propag. AP-28, 166 (1980).
[CrossRef]

Barber, P.

Benner, R. E.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959, 1975), Sec. 13.5.

Carter, H. G.

D. M. Le Vine, A. Schneider, R. H. Lang, H. G. Carter, “Scattering from Thin Dielectric Disks,” IEEE Trans. Antennas Propag. AP-33, 1410 (1985).
[CrossRef]

Chu, C. M.

DeVore, R.

R. DeVore, D. B. Hodge, R. G. Kouyoumjian, “Backscattering Cross Sections of Circular Disks,” J. Appl. Phys. 42, 3075 (1971).
[CrossRef]

Durney, C. H.

C-T. Tsai, H. Massoudi, C. H. Durney, M. F. Iskander, “A Procedure for Calculating Fields Inside Arbitrarily Shaped, In-homogeneous Dielectric Bodies Using Linear Basis Functions with the Moment Method,” IEEE Trans., MTT-34, 1131 (1986).

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of EBCM,” IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

A. Lakhtakia, M. F. Iskander, C. H. Durney, “An Iterative Extended Boundary Condition Method for Solving the Absorption Characteristics of Lossy Dielectric Objects of Large Aspect Ratios,” IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
[CrossRef]

Englman, R.

R. Ruppin, R. Englman, “Optical Lattice Vibrations in Finite Ionic Crystals II,” J. Phys. C (Proc. Phys. Soc.) 1, 630 (1968).

Glisson, A. W.

D. H. Schaubert, D. R. Wilton, A. W. Glisson, “A Tetrahedral Modeling Method for Electromagnetic Scattering by Arbitrarily Shaped Inhomogeneous Dielectric Bodies,” IEEE Trans. Antennas Propag. AP-32, 72 (1984).

Hodge, D. B.

R. DeVore, D. B. Hodge, R. G. Kouyoumjian, “Backscattering Cross Sections of Circular Disks,” J. Appl. Phys. 42, 3075 (1971).
[CrossRef]

Holt, A. R.

J. W. Shepherd, A. R. Holt, “The Scattering of Electromagnetic Radiation from Finite Dielectric Circular Cylinders,” J. Phys A 16, 651 (1983).
[CrossRef]

A. R. Holt, “The Fredholm Integral Equation Method and Comparison with the T-matrix Approach,” in Acoustic, Electromagnetic and Elastic Wave Scattering: Focus on the T-matrix Approach,V. V. Varadan, V. K. Varadan, Eds. (Pergamon, London, 1980), p. 255.

Iskandar, M. F.

Iskander, M. F.

C-T. Tsai, H. Massoudi, C. H. Durney, M. F. Iskander, “A Procedure for Calculating Fields Inside Arbitrarily Shaped, In-homogeneous Dielectric Bodies Using Linear Basis Functions with the Moment Method,” IEEE Trans., MTT-34, 1131 (1986).

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of EBCM,” IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

A. Lakhtakia, M. F. Iskander, C. H. Durney, “An Iterative Extended Boundary Condition Method for Solving the Absorption Characteristics of Lossy Dielectric Objects of Large Aspect Ratios,” IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
[CrossRef]

Kouyoumjian, R. G.

R. DeVore, D. B. Hodge, R. G. Kouyoumjian, “Backscattering Cross Sections of Circular Disks,” J. Appl. Phys. 42, 3075 (1971).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia, M. F. Iskander, C. H. Durney, “An Iterative Extended Boundary Condition Method for Solving the Absorption Characteristics of Lossy Dielectric Objects of Large Aspect Ratios,” IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
[CrossRef]

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of EBCM,” IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

Lang, R. H.

D. M. Le Vine, A. Schneider, R. H. Lang, H. G. Carter, “Scattering from Thin Dielectric Disks,” IEEE Trans. Antennas Propag. AP-33, 1410 (1985).
[CrossRef]

Le Vine, D. M.

D. M. Le Vine, A. Schneider, R. H. Lang, H. G. Carter, “Scattering from Thin Dielectric Disks,” IEEE Trans. Antennas Propag. AP-33, 1410 (1985).
[CrossRef]

Massoudi, H.

C-T. Tsai, H. Massoudi, C. H. Durney, M. F. Iskander, “A Procedure for Calculating Fields Inside Arbitrarily Shaped, In-homogeneous Dielectric Bodies Using Linear Basis Functions with the Moment Method,” IEEE Trans., MTT-34, 1131 (1986).

McCormick, G. C.

L. E. Allen, G. C. McCormick, “Measurement of the Backscatter Matrix of Dielectric Bodies,” IEEE Trans. Antennas Propag. AP-28, 166 (1980).
[CrossRef]

Olson, S. C.

Rao, S. M.

K. Umashankar, A. Taflove, S. M. Rao, “Electromagnetic Scattering by Arbitrary Shaped Three-Dimensional Homogeneous Lossy Dielectric Objects,” IEEE Trans. Antennas Propag. AP-34, 758 (1986).
[CrossRef]

Ruppin, R.

R. Ruppin, R. Englman, “Optical Lattice Vibrations in Finite Ionic Crystals II,” J. Phys. C (Proc. Phys. Soc.) 1, 630 (1968).

Schaubert, D. H.

D. H. Schaubert, D. R. Wilton, A. W. Glisson, “A Tetrahedral Modeling Method for Electromagnetic Scattering by Arbitrarily Shaped Inhomogeneous Dielectric Bodies,” IEEE Trans. Antennas Propag. AP-32, 72 (1984).

Schneider, A.

D. M. Le Vine, A. Schneider, R. H. Lang, H. G. Carter, “Scattering from Thin Dielectric Disks,” IEEE Trans. Antennas Propag. AP-33, 1410 (1985).
[CrossRef]

Senior, T. B. A.

H. Weil, T. B. A. Senior, T. M. Willis, “Internal and Near Fields of Small Particles Irradiated in Spectral Absorption Bands,” J. Opt. Soc. Am. 2, 989 (1985).
[CrossRef]

T. B. A. Senior, H. Weil, “On the Validity of Modeling Rayleigh Scatterers by Spheroids,” Appl. Phys. B 29, 117 (1982).
[CrossRef]

Shepherd, J. W.

J. W. Shepherd, A. R. Holt, “The Scattering of Electromagnetic Radiation from Finite Dielectric Circular Cylinders,” J. Phys A 16, 651 (1983).
[CrossRef]

Taflove, A.

K. Umashankar, A. Taflove, S. M. Rao, “Electromagnetic Scattering by Arbitrary Shaped Three-Dimensional Homogeneous Lossy Dielectric Objects,” IEEE Trans. Antennas Propag. AP-34, 758 (1986).
[CrossRef]

A. Taflove, K. Umashankar, “Radar Cross Section of General Three-Dimensional Scatterers,” IEEE Trans. Electromagn. Compat. EMC-25, 433 (1983).
[CrossRef]

Tsai, C-T.

C-T. Tsai, H. Massoudi, C. H. Durney, M. F. Iskander, “A Procedure for Calculating Fields Inside Arbitrarily Shaped, In-homogeneous Dielectric Bodies Using Linear Basis Functions with the Moment Method,” IEEE Trans., MTT-34, 1131 (1986).

Umashankar, K.

K. Umashankar, A. Taflove, S. M. Rao, “Electromagnetic Scattering by Arbitrary Shaped Three-Dimensional Homogeneous Lossy Dielectric Objects,” IEEE Trans. Antennas Propag. AP-34, 758 (1986).
[CrossRef]

A. Taflove, K. Umashankar, “Radar Cross Section of General Three-Dimensional Scatterers,” IEEE Trans. Electromagn. Compat. EMC-25, 433 (1983).
[CrossRef]

Waterman, P. C.

P. C. Waterman, “Scattering by Dielectric Obstacles,” Alta Freq. 38 (Speciale), 348 (1969).

Weil, H.

H. Weil, T. B. A. Senior, T. M. Willis, “Internal and Near Fields of Small Particles Irradiated in Spectral Absorption Bands,” J. Opt. Soc. Am. 2, 989 (1985).
[CrossRef]

H. Weil, T. Willis, “A Model for Polarization Effects in Remote Probing of Clouds,” Radio Sci. 17, 1018 (1982).
[CrossRef]

T. B. A. Senior, H. Weil, “On the Validity of Modeling Rayleigh Scatterers by Spheroids,” Appl. Phys. B 29, 117 (1982).
[CrossRef]

H. Weil, C. M. Chu, “Scattering and Absorption by Thin Flat Aerosols,” Appl. Opt. 19, 2066 (1980).
[CrossRef] [PubMed]

T. M. Willis, H. Weil, “Internal Induced Fields, Scattering and Absorption of Electromagnetic Radiation by Disc Shaped Aerosols; an Improved Computational Formulation and Computer Code,” Radiation Lab. Report RL023618-1-T; EECS Dept., U. Michigan, Ann Arbor 48109-2122 (1986).

Willis, T.

H. Weil, T. Willis, “A Model for Polarization Effects in Remote Probing of Clouds,” Radio Sci. 17, 1018 (1982).
[CrossRef]

Willis, T. M.

H. Weil, T. B. A. Senior, T. M. Willis, “Internal and Near Fields of Small Particles Irradiated in Spectral Absorption Bands,” J. Opt. Soc. Am. 2, 989 (1985).
[CrossRef]

T. M. Willis, H. Weil, “Internal Induced Fields, Scattering and Absorption of Electromagnetic Radiation by Disc Shaped Aerosols; an Improved Computational Formulation and Computer Code,” Radiation Lab. Report RL023618-1-T; EECS Dept., U. Michigan, Ann Arbor 48109-2122 (1986).

T. M. Willis, “Low Frequency Scattering by a Thin Dielectric Plate,” Radiation Lab. Memo 019955-502-M; EECS Dept., U. Michigan, Ann Arbor 48109-2122 (1982).

Wilton, D. R.

D. H. Schaubert, D. R. Wilton, A. W. Glisson, “A Tetrahedral Modeling Method for Electromagnetic Scattering by Arbitrarily Shaped Inhomogeneous Dielectric Bodies,” IEEE Trans. Antennas Propag. AP-32, 72 (1984).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959, 1975), Sec. 13.5.

Yeh, C.

Yoshida, D.

Alta Freq.

P. C. Waterman, “Scattering by Dielectric Obstacles,” Alta Freq. 38 (Speciale), 348 (1969).

Appl. Opt.

Appl. Phys. B

T. B. A. Senior, H. Weil, “On the Validity of Modeling Rayleigh Scatterers by Spheroids,” Appl. Phys. B 29, 117 (1982).
[CrossRef]

IEEE Trans.

C-T. Tsai, H. Massoudi, C. H. Durney, M. F. Iskander, “A Procedure for Calculating Fields Inside Arbitrarily Shaped, In-homogeneous Dielectric Bodies Using Linear Basis Functions with the Moment Method,” IEEE Trans., MTT-34, 1131 (1986).

IEEE Trans. Antennas Propag.

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of EBCM,” IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

K. Umashankar, A. Taflove, S. M. Rao, “Electromagnetic Scattering by Arbitrary Shaped Three-Dimensional Homogeneous Lossy Dielectric Objects,” IEEE Trans. Antennas Propag. AP-34, 758 (1986).
[CrossRef]

D. H. Schaubert, D. R. Wilton, A. W. Glisson, “A Tetrahedral Modeling Method for Electromagnetic Scattering by Arbitrarily Shaped Inhomogeneous Dielectric Bodies,” IEEE Trans. Antennas Propag. AP-32, 72 (1984).

L. E. Allen, G. C. McCormick, “Measurement of the Backscatter Matrix of Dielectric Bodies,” IEEE Trans. Antennas Propag. AP-28, 166 (1980).
[CrossRef]

D. M. Le Vine, A. Schneider, R. H. Lang, H. G. Carter, “Scattering from Thin Dielectric Disks,” IEEE Trans. Antennas Propag. AP-33, 1410 (1985).
[CrossRef]

IEEE Trans. Electromagn. Compat.

A. Taflove, K. Umashankar, “Radar Cross Section of General Three-Dimensional Scatterers,” IEEE Trans. Electromagn. Compat. EMC-25, 433 (1983).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

A. Lakhtakia, M. F. Iskander, C. H. Durney, “An Iterative Extended Boundary Condition Method for Solving the Absorption Characteristics of Lossy Dielectric Objects of Large Aspect Ratios,” IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
[CrossRef]

J. Appl. Phys.

R. DeVore, D. B. Hodge, R. G. Kouyoumjian, “Backscattering Cross Sections of Circular Disks,” J. Appl. Phys. 42, 3075 (1971).
[CrossRef]

J. Opt. Soc. Am.

H. Weil, T. B. A. Senior, T. M. Willis, “Internal and Near Fields of Small Particles Irradiated in Spectral Absorption Bands,” J. Opt. Soc. Am. 2, 989 (1985).
[CrossRef]

J. Phys A

J. W. Shepherd, A. R. Holt, “The Scattering of Electromagnetic Radiation from Finite Dielectric Circular Cylinders,” J. Phys A 16, 651 (1983).
[CrossRef]

J. Phys. C (Proc. Phys. Soc.)

R. Ruppin, R. Englman, “Optical Lattice Vibrations in Finite Ionic Crystals II,” J. Phys. C (Proc. Phys. Soc.) 1, 630 (1968).

Radio Sci.

H. Weil, T. Willis, “A Model for Polarization Effects in Remote Probing of Clouds,” Radio Sci. 17, 1018 (1982).
[CrossRef]

Other

T. M. Willis, “Low Frequency Scattering by a Thin Dielectric Plate,” Radiation Lab. Memo 019955-502-M; EECS Dept., U. Michigan, Ann Arbor 48109-2122 (1982).

A. R. Holt, “The Fredholm Integral Equation Method and Comparison with the T-matrix Approach,” in Acoustic, Electromagnetic and Elastic Wave Scattering: Focus on the T-matrix Approach,V. V. Varadan, V. K. Varadan, Eds. (Pergamon, London, 1980), p. 255.

T. M. Willis, H. Weil, “Internal Induced Fields, Scattering and Absorption of Electromagnetic Radiation by Disc Shaped Aerosols; an Improved Computational Formulation and Computer Code,” Radiation Lab. Report RL023618-1-T; EECS Dept., U. Michigan, Ann Arbor 48109-2122 (1986).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959, 1975), Sec. 13.5.

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Figures (6)

Fig. 1
Fig. 1

Spline functions used for the radial dependence of the basis functions W ̅ i.

Fig. 2
Fig. 2

Comparisons of CWW (solid lines) with computational (Ref. 11; long dashes) and experimental (Ref. 14; short dashes) backscatter results vs angle of incidence for a sample disk of ka = 2.283, kt = 0.460, = 3.13−j0.036. The quantities plotted are (a) σ2, (b) |v|2, and (c) Δ as defined in Eqs. (14) and (15).

Fig. 3
Fig. 3

Comparisons of CWW backscatter computational results (solid lines) with Ref. 14 experimental data (dashed lines) for four sample disks, each with a/t = 4.8 and J m ( ) = 0.036.

sample number1234
ka0.7621.5232.2833.042
kt0.1620.3050.4600.614
ℛe()3.123.113.133.10
For sample 1 the σ2 results obtained by applying Rayleigh theory are shown as a dotted curve.
Fig. 4
Fig. 4

Comparisons of principal plane cross sections vs angle of incidence as computed by CWW (dashed lines) and by physical optics specialized for thin disks (dotted lines). For each case n = 2.0−j0.0: (a) ka = 6.01, kt = 0.01; (b) ka = 9.45, kt = 0.01; (c) ka = 12.57; kt = 0.01; (d) ka = 12.57, kt = 0.001.

Fig. 5
Fig. 5

Comparisons of principal plane cross sections vs angle of incidence for highly conductive disks as computed by CWW (dashed lines), the limiting case spheroid solution of Ref. 15 (large dots), and the experimental results of Ref. 15 (dotted lines). For each case kt = 0.0001: (a) ka = 0.94; (b) ka = 3.00; (c) ka = 6.01; (d) ka = 9.45.

Fig. 6
Fig. 6

Forward and backscattering, absorption, and extinction cross sections vs angle of incidence for disks of a/t = 100, = 3.12−j0.036: (a) resonant region ka = 3.0; (b) near Rayleigh ka = 0.3.

Tables (1)

Tables Icon

Table I Comparison of Electrically Small Disks Scattered Fields Computed by Three Methods

Equations (19)

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Ē i = 1 j ω 0 { L ̿ J ̅ J ̅ n 2 1 } ,
L ̿ J ̅ = k 2 V d V J ̅ ( R ̅ ) G ( R ̅ , R ̅ ) S d S J ̅ ( R ̅ ) n ̂ G ( R ̅ , R ̅ ) , G ( R ̅ , R ̅ ) = exp ( jk | R ̅ R ̅ | ) 4 π | R ̅ R ̅ | .
J ̅ ( R ̅ ) = j ω 0 j α j W ̅ j ( R ̅ ) .
{ W ̅ Ei lm ( ρ , ϕ , z ) } = { × R i ( ρ ) z l sin m ϕ × R i ( ρ ) z l cos m ϕ } ,
{ W ̅ Mi lm ( ρ , ϕ , z ) } = { × W ̅ Ei lm ( ρ , ϕ , z ] } .
{ x ̂ = ρ ̂ cos ϕ ϕ ̂ sin ϕ , ŷ = ρ ̂ sin ϕ + ϕ ̂ cos ϕ } .
I j W ̅ j Ē i V dV W ̅ j Ē i , Z ij W ̅ i L ̿ W ̅ j , W ij W ̅ i W ̅ j ,
I i = j α j ( Z ij W ij n 2 1 ) j α j z ij .
[ E x ( k ̂ ) E y ( k ̂ ) ] = exp ( jkR ) R [ S xx ( k ̂ , θ D ) S xy ( k ̂ , θ D ) S yx ( k ̂ , θ D ) S yy ( k ̂ , θ D ) ] [ E x i E y i ] .
σ B ( k ̂ ) = | S xx ( k ̂ , θ D ) E x i + S xy ( k ̂ , θ D ) E y i | 2 + | S yx ( k ̂ , θ D ) E x i + S yy ( k ̂ , θ D ) E y i | 2 ,
σ B = | S xx ( k ̂ i , θ D ) | 2 or σ B = | S yy ( k ̂ i , θ D ) | 2 ,
σ A = J m ( n 2 ) k | n 2 1 | 2 Z 0 2 V dV J ̅ J ̅ * ,
σ T = 0 π 0 2 π σ B ( k ̂ ) sin θ d ϕ d θ ,
σ E = σ T + σ A .
σ = π | S xx ( k ̂ i , θ D ) + S yy ( k ̂ i , θ D ) | 2 ,
η = S xx ( k ̂ i , θ D ) S yy ( k ̂ i , θ D ) S xx ( k ̂ i , θ D ) + S yy ( k ̂ i , θ D ) = ν exp ( j Δ ) .
σ E = lim R R exp ( jkR ) 4 π k 2 J m [ Ē 0 * Ē ( k ̂ i ) ] .
k S xx ( ± k ̂ i , 90 ° )
k S yy ( ± k ̂ i , 90 ° )

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