Abstract

We present an efficient approach for calculating the electromagnetic scattered fields (light) from a single dielectric body situated above a perfectly conducting (or reflecting) half-space. This approach employs the boundary integral equation method and is applicable to arbitrarily shaped scatterers located anywhere above the conducting half-space surface, impinged upon by arbitrary incident fields. Numerical results for spherical scatterers are presented and are compared with published results obtained with an analytical approach.

© 1996 Optical Society of America

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References

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  1. R. P. Young, “Low scatter mirror degradation by particle contamination,” Opt. Eng. 15, 516–520 (1976).
    [CrossRef]
  2. B. R. Johnson, “Light scattering from a spherical particle on a conducting plane: I. Normal incidence,” J. Opt. Soc. Am. A 9, 1341–1351 (1992).
    [CrossRef]
  3. G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991).
    [CrossRef]
  4. P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
    [CrossRef]
  5. I. V. Lindell, A. Sihvola, K. Muinonen, P. Barber, “Scattering by small object close to an interface: I. Exact image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
    [CrossRef]
  6. K. B. Nahm, W. L. Wolfe, “Light scattering models for sphere on a conducting plane: comparison with experiments,” Appl. Opt. 26, 2995–2999 (1987).
    [CrossRef] [PubMed]
  7. D. C. Weber, E. D. Hirleman, “Light scattering signatures of individual spheres on optically smooth conducting surfaces,” J. Opt. Soc. Am. A 19, 4019–4026 (1988).
  8. W. S. Hall, X. Mao, W. Robertson, “Quadratic, isoparametric BEM formulation for electromagnetic scattering from arbitrarily shaped three-dimensional homogeneous dielectric objects,” in Boundary Elements XIV, C. A. Brebbia, J. Dominguez, F. Parvis, eds. (Computational Mechanics Publications, Southampton, UK, 1992).
  9. J. C. Chao, Y. J. Liu, F. J. Rizzo, P. A. Martin, L. Udpa, “Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions,” IEEE Trans. Antennas Propag. (to be published).
  10. J. R. Mautz, “A stable integral equation for electromagnetic scattering from homogeneous dielectric bodies,” IEEE Trans. Antennas Propag. AP-37, 1070–1071 (1987).
  11. E. Marx, “Integral equation for scattering by a dielectric,” IEEE Trans. Antennas Propag. AP-32, 166–172 (1984).
    [CrossRef]
  12. W. C. Chew, Waves and Fields in Inhomogeneous Media, 1st ed. (Van Nostrand Reinhold, New York, 1990), Chap. 2, pp. 68–72.
  13. C. A. Balanis, Advanced Engineering Electromagnetics, 1st ed. (Wiley, New York, 1989), Chap. 7, p. 317.
  14. P. A. Martin, P. Ola, “Boundary integral equations for the scattering of electromagnetic waves by homogeneous dielectric obstacles,” Proc. R. Soc. Edinburgh A 123, 185–208 (1993).
    [CrossRef]
  15. J. R. Mautz, R. F. Harrington, “Electromagnetic scattering from homogeneous body of revolution,” Archiv. Elektronik Übertagungstechnik, 33, 71–80 (1979).
  16. J. C. Chao, “A boundary integral equation approach to three dimensional electromagnetic wave scattering problems,” Ph.D. dissertation (Iowa State University, Ames, Ia., 1994).

1993 (1)

P. A. Martin, P. Ola, “Boundary integral equations for the scattering of electromagnetic waves by homogeneous dielectric obstacles,” Proc. R. Soc. Edinburgh A 123, 185–208 (1993).
[CrossRef]

1992 (1)

1991 (2)

1988 (1)

D. C. Weber, E. D. Hirleman, “Light scattering signatures of individual spheres on optically smooth conducting surfaces,” J. Opt. Soc. Am. A 19, 4019–4026 (1988).

1987 (2)

J. R. Mautz, “A stable integral equation for electromagnetic scattering from homogeneous dielectric bodies,” IEEE Trans. Antennas Propag. AP-37, 1070–1071 (1987).

K. B. Nahm, W. L. Wolfe, “Light scattering models for sphere on a conducting plane: comparison with experiments,” Appl. Opt. 26, 2995–2999 (1987).
[CrossRef] [PubMed]

1986 (1)

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

1984 (1)

E. Marx, “Integral equation for scattering by a dielectric,” IEEE Trans. Antennas Propag. AP-32, 166–172 (1984).
[CrossRef]

1979 (1)

J. R. Mautz, R. F. Harrington, “Electromagnetic scattering from homogeneous body of revolution,” Archiv. Elektronik Übertagungstechnik, 33, 71–80 (1979).

1976 (1)

R. P. Young, “Low scatter mirror degradation by particle contamination,” Opt. Eng. 15, 516–520 (1976).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics, 1st ed. (Wiley, New York, 1989), Chap. 7, p. 317.

Barber, P.

Bobbert, P. A.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

Chao, J. C.

J. C. Chao, Y. J. Liu, F. J. Rizzo, P. A. Martin, L. Udpa, “Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions,” IEEE Trans. Antennas Propag. (to be published).

J. C. Chao, “A boundary integral equation approach to three dimensional electromagnetic wave scattering problems,” Ph.D. dissertation (Iowa State University, Ames, Ia., 1994).

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media, 1st ed. (Van Nostrand Reinhold, New York, 1990), Chap. 2, pp. 68–72.

Hall, W. S.

W. S. Hall, X. Mao, W. Robertson, “Quadratic, isoparametric BEM formulation for electromagnetic scattering from arbitrarily shaped three-dimensional homogeneous dielectric objects,” in Boundary Elements XIV, C. A. Brebbia, J. Dominguez, F. Parvis, eds. (Computational Mechanics Publications, Southampton, UK, 1992).

Harrington, R. F.

J. R. Mautz, R. F. Harrington, “Electromagnetic scattering from homogeneous body of revolution,” Archiv. Elektronik Übertagungstechnik, 33, 71–80 (1979).

Hirleman, E. D.

D. C. Weber, E. D. Hirleman, “Light scattering signatures of individual spheres on optically smooth conducting surfaces,” J. Opt. Soc. Am. A 19, 4019–4026 (1988).

Johnson, B. R.

Lindell, I. V.

Liu, Y. J.

J. C. Chao, Y. J. Liu, F. J. Rizzo, P. A. Martin, L. Udpa, “Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions,” IEEE Trans. Antennas Propag. (to be published).

Mao, X.

W. S. Hall, X. Mao, W. Robertson, “Quadratic, isoparametric BEM formulation for electromagnetic scattering from arbitrarily shaped three-dimensional homogeneous dielectric objects,” in Boundary Elements XIV, C. A. Brebbia, J. Dominguez, F. Parvis, eds. (Computational Mechanics Publications, Southampton, UK, 1992).

Martin, P. A.

P. A. Martin, P. Ola, “Boundary integral equations for the scattering of electromagnetic waves by homogeneous dielectric obstacles,” Proc. R. Soc. Edinburgh A 123, 185–208 (1993).
[CrossRef]

J. C. Chao, Y. J. Liu, F. J. Rizzo, P. A. Martin, L. Udpa, “Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions,” IEEE Trans. Antennas Propag. (to be published).

Marx, E.

E. Marx, “Integral equation for scattering by a dielectric,” IEEE Trans. Antennas Propag. AP-32, 166–172 (1984).
[CrossRef]

Mautz, J. R.

J. R. Mautz, “A stable integral equation for electromagnetic scattering from homogeneous dielectric bodies,” IEEE Trans. Antennas Propag. AP-37, 1070–1071 (1987).

J. R. Mautz, R. F. Harrington, “Electromagnetic scattering from homogeneous body of revolution,” Archiv. Elektronik Übertagungstechnik, 33, 71–80 (1979).

Muinonen, K.

Nahm, K. B.

Ola, P.

P. A. Martin, P. Ola, “Boundary integral equations for the scattering of electromagnetic waves by homogeneous dielectric obstacles,” Proc. R. Soc. Edinburgh A 123, 185–208 (1993).
[CrossRef]

Rizzo, F. J.

J. C. Chao, Y. J. Liu, F. J. Rizzo, P. A. Martin, L. Udpa, “Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions,” IEEE Trans. Antennas Propag. (to be published).

Robertson, W.

W. S. Hall, X. Mao, W. Robertson, “Quadratic, isoparametric BEM formulation for electromagnetic scattering from arbitrarily shaped three-dimensional homogeneous dielectric objects,” in Boundary Elements XIV, C. A. Brebbia, J. Dominguez, F. Parvis, eds. (Computational Mechanics Publications, Southampton, UK, 1992).

Sihvola, A.

Udpa, L.

J. C. Chao, Y. J. Liu, F. J. Rizzo, P. A. Martin, L. Udpa, “Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions,” IEEE Trans. Antennas Propag. (to be published).

Videen, G.

Vlieger, J.

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

Weber, D. C.

D. C. Weber, E. D. Hirleman, “Light scattering signatures of individual spheres on optically smooth conducting surfaces,” J. Opt. Soc. Am. A 19, 4019–4026 (1988).

Wolfe, W. L.

Young, R. P.

R. P. Young, “Low scatter mirror degradation by particle contamination,” Opt. Eng. 15, 516–520 (1976).
[CrossRef]

Appl. Opt. (1)

Archiv. Elektronik Übertagungstechnik (1)

J. R. Mautz, R. F. Harrington, “Electromagnetic scattering from homogeneous body of revolution,” Archiv. Elektronik Übertagungstechnik, 33, 71–80 (1979).

IEEE Trans. Antennas Propag. (2)

J. R. Mautz, “A stable integral equation for electromagnetic scattering from homogeneous dielectric bodies,” IEEE Trans. Antennas Propag. AP-37, 1070–1071 (1987).

E. Marx, “Integral equation for scattering by a dielectric,” IEEE Trans. Antennas Propag. AP-32, 166–172 (1984).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Eng. (1)

R. P. Young, “Low scatter mirror degradation by particle contamination,” Opt. Eng. 15, 516–520 (1976).
[CrossRef]

Physica A (1)

P. A. Bobbert, J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–242 (1986).
[CrossRef]

Proc. R. Soc. Edinburgh A (1)

P. A. Martin, P. Ola, “Boundary integral equations for the scattering of electromagnetic waves by homogeneous dielectric obstacles,” Proc. R. Soc. Edinburgh A 123, 185–208 (1993).
[CrossRef]

Other (5)

J. C. Chao, “A boundary integral equation approach to three dimensional electromagnetic wave scattering problems,” Ph.D. dissertation (Iowa State University, Ames, Ia., 1994).

W. C. Chew, Waves and Fields in Inhomogeneous Media, 1st ed. (Van Nostrand Reinhold, New York, 1990), Chap. 2, pp. 68–72.

C. A. Balanis, Advanced Engineering Electromagnetics, 1st ed. (Wiley, New York, 1989), Chap. 7, p. 317.

W. S. Hall, X. Mao, W. Robertson, “Quadratic, isoparametric BEM formulation for electromagnetic scattering from arbitrarily shaped three-dimensional homogeneous dielectric objects,” in Boundary Elements XIV, C. A. Brebbia, J. Dominguez, F. Parvis, eds. (Computational Mechanics Publications, Southampton, UK, 1992).

J. C. Chao, Y. J. Liu, F. J. Rizzo, P. A. Martin, L. Udpa, “Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions,” IEEE Trans. Antennas Propag. (to be published).

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Figures (11)

Fig. 1
Fig. 1

Sample scattering problem of a dielectric object near a perfectly conducting half-space.

Fig. 2
Fig. 2

Recasting the original problem into a two-scatterer problem by application of the image theory.

Fig. 3
Fig. 3

Image theory illustrating the real and virtual sources for both electric and magnetic sources.

Fig. 4
Fig. 4

Test configuration for the problem of a spherical scatterer above a perfectly conducting half-space. The differential scattering cross section is calculated as a function of θ in the y− −z plane. The incident wave is a unit-amplitude plane wave polarized in the +y direction, traveling in the +z direction.

Fig. 5
Fig. 5

Differential scattering cross section of a sphere on a perfectly conducting half-space, with r = 0.2, d = 0.2, index of refraction N = 1.46.

Fig. 6
Fig. 6

Differential scattering cross section of a sphere on a perfectly conducting half-space, with r = 1.0, d = 1.0, index of refraction N = 1.46.

Fig. 7
Fig. 7

Differential scattering cross section of a sphere on a perfectly conducting half-space, with r = 1.0, d = 1.0, index of refraction N = 1.30.

Fig. 8
Fig. 8

Differential scattering cross section of a sphere on a perfectly conducting half space, with r = 1.0, d = 5.0, index of refraction N = 1.30.

Fig. 9
Fig. 9

Simulation of an ellipsoid above a perfectly conducting half-space. The differential scattering cross section is calculated as a function of θ in the y− −z plane. The incident wave is a unit-amplitude plane wave polarized in the +y direction, traveling in the +z direction.

Fig. 10
Fig. 10

Differential scattering cross section of an ellipsoid on a perfectly conducting half-space, with r = 0.5, d = 0.5, index of refraction N = 1.70.

Fig. 11
Fig. 11

Differential scattering cross section of an ellipsoid on a perfectly conducting half-space, with r = 1.0, d = 1.0, index of refraction N = 1.30.

Equations (27)

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P × S k ( n ^ × E ) k ( q ) G e ( P , q ) d S q + j ω e P × P × S k ( n ^ × H ) k ( q ) G e ( P , q ) d S q + P × S j ( n ^ × E ) j ( q ) G e ( P , q ) d S q + j ω e P × P × S j ( n ^ × H ) j ( q ) G e ( P , q ) d S q = { E e ( P ) P exterior - E inc ( P ) P interior of S k ,
P × S k ( n ^ × H ) k ( q ) G e ( P , q ) d S q - j ω μ e P × P × S k ( n ^ × E ) k ( q ) G e ( P , q ) d S q + P × S j ( n ^ × H ) j ( q ) G e ( P , q ) d S q - j ω μ e P × P × S j ( n ^ × E ) j ( q ) G e ( P , q ) d S q = { H e ( P ) P exterior - H inc ( P ) P interior of S k ,
P × S k ( n ^ × E ) k ( q ) G i k ( P , q ) d S q + j ω i k P × P × S k ( n ^ × H ) k ( q ) G i k ( P , q ) d S q = { 0 P exterior - E i ( P ) P interior of S k ,
P × S k ( n ^ × H ) k ( q ) G i k ( P , q ) d S q - j ω μ i k P × P × S k ( n ^ × E ) k ( q ) G i k ( P , q ) d S q = { 0 P exterior - H i ( P ) P interior of S k .
G α ( p , q ) = exp ( k α p - q ) 4 π p - q ,
n ^ 1 × E = n ^ 1 × E 1 = - M 1 ,
n ^ 1 × H = n ^ 1 × H 1 = J 1 ,
n ^ 2 × E = n ^ 2 × E 1 = - M 2 ,
n ^ 2 × H = n ^ 2 × H 1 = J 2 .
½ M 1 ( p ) - n ^ 1 p × P × S 1 M 1 ( q ) G e ( p , q ) d S q + j ω e n ^ 1 p × P × P × S 1 J 1 ( q ) G e ( p , q ) d S q - n ^ 1 p × P × S 2 M 2 ( q ) G e ( p , q ) d S q + j ω e n ^ 1 p × P × P × S 2 J 2 ( q ) G e ( p , q ) d S q = - n ^ 1 p × [ E inc ( p ) + E ref ( p ) ] ,
½ J 1 ( p ) - n ^ 1 p × p × S 1 J 1 ( q ) G e ( p , q ) d S q - j ω μ e n ^ 1 p × p × p × S 1 M 1 ( q ) G e ( p , q ) d S q - n ^ 1 p × p × S 2 J 2 ( q ) G e ( p , q ) d S q - j ω μ e n ^ 1 p × p × p × S 2 M 2 ( q ) G e ( p , q ) d S q = n ^ 1 p × [ H inc ( p ) + H ref ( p ) ] ,
½ M 1 ( p ) + n ^ 1 p × p × S 1 M 1 ( q ) G i ( p , q ) d S q - j ω i n ^ 1 p × p × P × S 1 J 1 ( q ) G i ( p , q ) d S q = 0 ,
½ J 1 ( p ) + n ^ 1 p × p × S 1 J 1 ( q ) G i ( p , q ) d S q + j ω μ i n ^ 1 p × p × p × S 1 M 1 ( q ) G i ( p , q ) d S q = 0.
e [ ½ M 1 ( p ) - n ^ 1 p × p × S 1 M 1 ( q ) G e ( p , q ) d S q + j ω e n ^ 1 p × p × p × S 1 J 1 ( q ) G e ( p , q ) d S q - n ^ 1 p × p × S 2 M 2 ( q ) G e ( p , q ) d S q + j ω e n ^ 1 p × p × p × S 2 J 2 ( q ) G e ( p , q ) d S q ] - i [ ½ M 1 ( p ) + n ^ 1 p × p × S 1 M 1 ( q ) G i ( p , q ) d S q - j ω i 1 n ^ 1 p × p × p × S 1 J 1 ( q ) G i ( p , q ) d S q ] = e { - n ^ 1 p × [ E inc ( p ) + E ref ( p ) ] } ,
μ e [ ½ J 1 ( p ) - n ^ 1 p × p × S 1 J 1 ( q ) G e ( p , q ) d S q - j ω μ e n ^ 1 p × p × p × S 1 M 1 ( q ) G e ( p , q ) d S q - n ^ 1 p × p × S 2 J 2 ( q ) G e ( p , q ) d S q - j ω μ e n ^ 1 p × p × p × S 2 M 2 ( q ) G e ( p , q ) d S q ] - μ i [ ½ J 1 ( p ) + n ^ 1 p × p S 1 J 1 ( q ) G i ( p , q ) d S q + j ω μ i 1 n ^ 1 p × p × p × S 1 M 1 ( q ) G i ( p , q ) d S q ] = μ e { n ^ 1 p × [ H inc ( p ) + H ref ( p ) ] } .
x k = β = 1 m N β x k β ,
M k = β = 1 m N β M k β ,
J k = β = 1 m N β J k β .
[ A 11 A 12 A 13 A 14 A 21 A 22 A 23 A 24 ] [ M k a J k a M k i J k i ] = { e [ - n ^ 1 × ( E inc + E ref ) ] μ e [ n ^ 1 × ( H inc + H ref ) ] } .
J x a = - J x i ,
J y a = - J y i ,
J z a = J z i ,
M x a = M x i ,
M y a = M y i ,
M z a = - M z i ,
[ ( A 11 ± A 13 ) ( A 12 ± A 14 ) ( A 21 ± A 23 ) ( A 22 ± A 24 ) ] [ M k a J k a ] = { e [ - n ^ 1 × ( E inc + E ref ) ] μ e [ n ^ 1 × ( H inc + H ref ) ] } ,
C sca = R 2 E sca ( R ) 2 E inc 2 ,

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