Abstract

Fictitious-current models have been applied extensively in recent years to a variety of time-harmonic electromagnetic-wave scattering problems. An extension of the current-model technique is introduced that facilitates the solution to problems subsuming scatterers that contain a variety of length scales. This extension is in tune with the current-model technique’s philosophy of using simple current sources whose fields are analytically derivable. The approach amounts to letting the coordinates of some of the source centers assume complex values. Positioned in complex space, the simple current sources radiate beam-type fields that are more localized and that are better approximations of the scattering from the smooth expanses of the object. The coordinates of the other source centers retain their conventional real values. These latter current sources are used, of course, to approximate the fields in the vicinity of the more rapidly varying expanses of the object. We use the new approach to analyze electromagnetic scattering by an object comprising two adjacent perfectly conducting spheres of different size. We find that it renders the solution computationally more effective at the expense of only a slight increase in its complexity.

© 1994 Optical Society of America

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References

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  1. Y. Leviatan, A. Boag, A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies. Theory and numerical solution,” IEEE Trans. Antennas Propag. 36, 1722–1734 (1988).
    [CrossRef]
  2. Y. Leviatan, A. Boag, A. Boag, “Analysis of electromagnetic scattering using a current model method,” Comput. Phys. Commun. 68, 331–345 (1991).
    [CrossRef]
  3. A. Ludwig, “A new technique for numerical electromagnetics,” IEEE Antennas Propag. Mag. 31 (1), 40–41 (1989).
  4. C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Norwood, Mass., 1990).
  5. A. Boag, Y. Leviatan, A. Boag, “Analysis of diffraction from doubly periodic arrays of perfectly conducting bodies by using a patch-current model,” J. Opt. Soc. Am. A 7, 1712–1718 (1990).
    [CrossRef]
  6. A. Boag, Y. Leviatan, A. Boag, “Analysis of electromagnetic scattering from linear periodic arrays of perfectly conducting bodies using a cylindrical current model,” IEEE Trans. Antennas Propag. 39, 1332–1337 (1991).
    [CrossRef]
  7. R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).
  8. G. A. Deschamps, “Gaussian beams as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
    [CrossRef]
  9. L. B. Felsen, “Geometrical theory of diffraction, evanescent waves, complex rays and Gaussian beams,” Geophys. J. R. Astron. Soc. 79, 77–88 (1984).
    [CrossRef]
  10. P. Regli, Swiss Federal Institute of Technology, Zurich (personal communication, 1993).

1991 (2)

Y. Leviatan, A. Boag, A. Boag, “Analysis of electromagnetic scattering using a current model method,” Comput. Phys. Commun. 68, 331–345 (1991).
[CrossRef]

A. Boag, Y. Leviatan, A. Boag, “Analysis of electromagnetic scattering from linear periodic arrays of perfectly conducting bodies using a cylindrical current model,” IEEE Trans. Antennas Propag. 39, 1332–1337 (1991).
[CrossRef]

1990 (1)

1989 (1)

A. Ludwig, “A new technique for numerical electromagnetics,” IEEE Antennas Propag. Mag. 31 (1), 40–41 (1989).

1988 (1)

Y. Leviatan, A. Boag, A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies. Theory and numerical solution,” IEEE Trans. Antennas Propag. 36, 1722–1734 (1988).
[CrossRef]

1984 (1)

L. B. Felsen, “Geometrical theory of diffraction, evanescent waves, complex rays and Gaussian beams,” Geophys. J. R. Astron. Soc. 79, 77–88 (1984).
[CrossRef]

1971 (1)

G. A. Deschamps, “Gaussian beams as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[CrossRef]

Boag, A.

Y. Leviatan, A. Boag, A. Boag, “Analysis of electromagnetic scattering using a current model method,” Comput. Phys. Commun. 68, 331–345 (1991).
[CrossRef]

Y. Leviatan, A. Boag, A. Boag, “Analysis of electromagnetic scattering using a current model method,” Comput. Phys. Commun. 68, 331–345 (1991).
[CrossRef]

A. Boag, Y. Leviatan, A. Boag, “Analysis of electromagnetic scattering from linear periodic arrays of perfectly conducting bodies using a cylindrical current model,” IEEE Trans. Antennas Propag. 39, 1332–1337 (1991).
[CrossRef]

A. Boag, Y. Leviatan, A. Boag, “Analysis of electromagnetic scattering from linear periodic arrays of perfectly conducting bodies using a cylindrical current model,” IEEE Trans. Antennas Propag. 39, 1332–1337 (1991).
[CrossRef]

A. Boag, Y. Leviatan, A. Boag, “Analysis of diffraction from doubly periodic arrays of perfectly conducting bodies by using a patch-current model,” J. Opt. Soc. Am. A 7, 1712–1718 (1990).
[CrossRef]

A. Boag, Y. Leviatan, A. Boag, “Analysis of diffraction from doubly periodic arrays of perfectly conducting bodies by using a patch-current model,” J. Opt. Soc. Am. A 7, 1712–1718 (1990).
[CrossRef]

Y. Leviatan, A. Boag, A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies. Theory and numerical solution,” IEEE Trans. Antennas Propag. 36, 1722–1734 (1988).
[CrossRef]

Y. Leviatan, A. Boag, A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies. Theory and numerical solution,” IEEE Trans. Antennas Propag. 36, 1722–1734 (1988).
[CrossRef]

Deschamps, G. A.

G. A. Deschamps, “Gaussian beams as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[CrossRef]

Felsen, L. B.

L. B. Felsen, “Geometrical theory of diffraction, evanescent waves, complex rays and Gaussian beams,” Geophys. J. R. Astron. Soc. 79, 77–88 (1984).
[CrossRef]

Hafner, C.

C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Norwood, Mass., 1990).

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

Leviatan, Y.

A. Boag, Y. Leviatan, A. Boag, “Analysis of electromagnetic scattering from linear periodic arrays of perfectly conducting bodies using a cylindrical current model,” IEEE Trans. Antennas Propag. 39, 1332–1337 (1991).
[CrossRef]

Y. Leviatan, A. Boag, A. Boag, “Analysis of electromagnetic scattering using a current model method,” Comput. Phys. Commun. 68, 331–345 (1991).
[CrossRef]

A. Boag, Y. Leviatan, A. Boag, “Analysis of diffraction from doubly periodic arrays of perfectly conducting bodies by using a patch-current model,” J. Opt. Soc. Am. A 7, 1712–1718 (1990).
[CrossRef]

Y. Leviatan, A. Boag, A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies. Theory and numerical solution,” IEEE Trans. Antennas Propag. 36, 1722–1734 (1988).
[CrossRef]

Ludwig, A.

A. Ludwig, “A new technique for numerical electromagnetics,” IEEE Antennas Propag. Mag. 31 (1), 40–41 (1989).

Regli, P.

P. Regli, Swiss Federal Institute of Technology, Zurich (personal communication, 1993).

Comput. Phys. Commun. (1)

Y. Leviatan, A. Boag, A. Boag, “Analysis of electromagnetic scattering using a current model method,” Comput. Phys. Commun. 68, 331–345 (1991).
[CrossRef]

Electron. Lett. (1)

G. A. Deschamps, “Gaussian beams as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[CrossRef]

Geophys. J. R. Astron. Soc. (1)

L. B. Felsen, “Geometrical theory of diffraction, evanescent waves, complex rays and Gaussian beams,” Geophys. J. R. Astron. Soc. 79, 77–88 (1984).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

A. Ludwig, “A new technique for numerical electromagnetics,” IEEE Antennas Propag. Mag. 31 (1), 40–41 (1989).

IEEE Trans. Antennas Propag. (2)

Y. Leviatan, A. Boag, A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies. Theory and numerical solution,” IEEE Trans. Antennas Propag. 36, 1722–1734 (1988).
[CrossRef]

A. Boag, Y. Leviatan, A. Boag, “Analysis of electromagnetic scattering from linear periodic arrays of perfectly conducting bodies using a cylindrical current model,” IEEE Trans. Antennas Propag. 39, 1332–1337 (1991).
[CrossRef]

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

Other (3)

C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Norwood, Mass., 1990).

R. F. Harrington, Field Computation by Moment Methods (Macmillan, New York, 1968).

P. Regli, Swiss Federal Institute of Technology, Zurich (personal communication, 1993).

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Figures (6)

Fig. 1
Fig. 1

Scatterer comprising two adjacent perfectly conducting spheres of different sizes excited by a plane wave.

Fig. 2
Fig. 2

Simulated equivalence for the unbounded region surrounding the two perfectly conducting spheres.

Fig. 3
Fig. 3

Plot of the boundary-condition error ΔEbc versus the z coordinate of points on SISII in the ϕ = 0 half-plane, with the number of pair of sources N2I as a parameter. N2I = 24, long-dashed curve; N2I = 42, short-dashed curve; N2I = 63 pairs, solid curve.

Fig. 4
Fig. 4

Plot of the scattering cross section σ versus θ in the ϕ = 0 half-plane, with the number of pairs of sources N2I as a parameter for the cases shown in Fig. 3. The asterisks indicate results obtained with the GMT reference solution.10

Fig. 5
Fig. 5

Plot of the boundary-condition error ΔEbc versus the z coordinate of points on SISII in the ϕ = 0 half-plane, calculated with a conventional source-model solution with NI = 72 pairs of sources placed at real coordinates (dashed curve) and with the new approach, with NI = N1I + N2I = 4 + 63 = 67 pairs of sources (solid curve).

Fig. 6
Fig. 6

Plot of the scattering cross section σ versus θ in the ϕ = 0 half-plane for the cases shown in Fig. 5.

Equations (13)

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E inc = û x exp ( j k 0 z ) ,
H inc = û y 1 η 0 exp ( j k 0 z ) ,
E s ( r ) = q = 1 2 i I l q i I E q i I ( r ) + q = 1 2 i I l q i II E q i II ( r ) ,
H s ( r ) = 1 j ω μ 0 × E s ( r ) .
E q i I = j ω μ 0 A q i I ( r ) + 1 j ω ɛ 0 A q i I ( r ) ,
A q i I ( r ) = exp { j k 0 [ ( r r i I ) ( r r i I ) ] 1 / 2 } 4 π [ ( r r i I ) ( r r i I ) ] 1 / 2 û q i I ,
E q i II = j ω μ 0 A q i II ( r ) + 1 j ω ɛ 0 A q i II ( r ) ,
A q i II ( r ) = exp ( j k 0 | r r i II | ) 4 π | r r i II | û q i II
n ˆ × E s = n ˆ × E inc on S I S II ,
[ Z ] I = V .
I = ( [ Z ] * [ Z ] ) 1 [ Z ] * V ,
Δ E bc = | n ˆ × ( E s + E inc ) | | E inc | on S I S II
σ = lim r 4 π r 2 | E S | 2 | E inc | 2 ,

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