Abstract

The potency and versatility of a numerical procedure based on the generalized multipole technique (GMT) are demonstrated in the context of full-vector electromagnetic interactions for general incidence on arbitrarily shaped, geometrically composite, highly elongated, axisymmetric perfectly conducting or dielectric objects of large size parameters and arbitrary constitutive parameters. Representative computations that verify the accuracy of the technique are given for a large category of problems that have not been considered previously by the use of the GMT, to our knowledge. These problems involve spheroids of axial ratios as high as 20 and with the largest dimension of the dielectric object along the symmetry axis equal to 75 wavelengths; sphere–cone–sphere geometries; peanut-shaped scatterers; and finite-length cylinders with hemispherical, spherical, and flat end caps. Whenever possible, the extended boundary-condition method has been used in the process of examining the applicability of the suggested solution, with excellent agreement being achieved in all cases considered. It is believed that the numerical-scattering results presented here represent the largest detailed three-dimensional precise modeling ever verified as far as expansion functions that fulfill Maxwell’s equations throughout the relevant domain of interest are concerned.

© 1995 Optical Society of America

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References

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  1. H. M. Al-Rizzo, “Electromagnetic wave scattering from 3-D coated and homogeneous objects using the GPMT and GMT, numerical modelling and applications,” Ph.D. dissertation (University of New Brunswick, Fredericton, Canada, 1992).
  2. A. C. Ludwig, ed., “The generalized multipole technique,” in 1989 Antennas and Propagation Society International Symposium Proceedings (Antennas and Propagation Society, San Jose, Calif., 1989), Vol. 1, pp. 160–163.
  3. A. C. Ludwig, “The generalized multipole technique,” Comput. Phys. Commun. 68, 306–314 (1991).
    [CrossRef]
  4. C. Hafner, “Beitrage zur Berechnung der Ausbreitung electro-magneitscher Wellen in Zylindrischen Struckturen mit Hilfe des point-matching—Ver fahrens,” Ph.D. dissertation (Swiss Polytechnical Institute of Technology, Zurich, Switzerland, 1980).
  5. C. Hafner, R. Ballisti, “Electromagnetic field calculations on PC’s and workstations using the MMP method,” IEEE Trans. Magn. 25, 2828–2830 (1989).
    [CrossRef]
  6. N. Kuster, R. Ballisti, “MMP method simulation of antenna with scattering objects in the closer-near-field,” IEEE Trans. Magn. 25, 2881–2883 (1989).
    [CrossRef]
  7. J. Sroka, H. Baggenstos, R. Ballisti, “On the coupling of the generalized multipole technique with the finite element method,” IEEE Trans. Magn. 26, 658–661 (1990).
    [CrossRef]
  8. S. Kiener, “Eddy currents in bodies with sharp edges by the MMP-method,” IEEE Trans. Magn. 26, 482–485 (1990).
    [CrossRef]
  9. C. Hafner, “On the relationship between the MoM and the GMT,” IEEE Trans. Antennas Propag. Magn. 32, 12–19 (1990).
    [CrossRef]
  10. C. Hafner, N. Kuster, “Computation of electromagnetic fields by multiple multipole method (generalized multipole technique),” Radio Sci. 26, 291–297 (1991).
    [CrossRef]
  11. C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Boston, 1991).
  12. C. Hafner, “On the design of numerical methods,” IEEE Antennas Propag. Magn. 35, 13–21 (1993).
    [CrossRef]
  13. C. Hafner, L. Bomholt, The Electrodynamic Wave Simulator (Wiley, New York, 1993).
  14. P. Leuchtmann, F. Bomholt, “Field modeling with the MMP code,” IEEE Trans. Electromag. Compatabil. 35, 170–177 (1993).
    [CrossRef]
  15. A. C. Ludwig, “A comparison of spherical wave boundary value matching versus integral equation scattering solutions for a perfectly conducting body,” IEEE Trans. Antennas Propag. AP-34, 857–865 (1986).
    [CrossRef]
  16. A. C. Ludwig, “Cone-sphere scattering computed by the generalized multipole technique,” in Proceedings of the IEEE Antennas and Propagation International Symposium (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 48–51.
  17. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  18. K. Joo, M. F. Iskander, “A new procedure of point-matching method for calculating the absorption and scattering of lossy dielectric objects,” IEEE Trans. Antennas Propag. 38, 1483–1489 (1990).
    [CrossRef]
  19. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
  20. S. Ström, W. Zheng, “Basic features of the null field method for dielectric scatterers,” Radio Sci. 22, 1273–1281 (1987).
    [CrossRef]
  21. S. Asano, G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
    [PubMed]
  22. A. A. Sebak, L. Shafai, “Scattering by imperfectly conducting and impedance spheroids: a numerical approach,” Radio Sci. 19, 258–266 (1984).
    [CrossRef]
  23. P. Latimer, P. W. Barber, “Scattering by ellipsoids of revolution: a comparison of theoretical methods,” J. Colloid Interface Sci. 63, 310–316 (1978).
    [CrossRef]
  24. P. W. Barber, “Resonant scattering for characterization of axisymmetric dielectric objects,” IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
    [CrossRef]
  25. M. A. Morgan, C. H. Chen, S. C. Hill, P. W. Barber, “Finite element-boundary integral formulation for electromagnetic scattering,” Wave Motion 6, 91–103 (1984).
    [CrossRef]
  26. A. A. Sebak, L. Shafai, “Electromagnetic scattering by spheroidal objects with impedance boundary conditions at axial incidence,” Radio Sci. 23, 1048–1060 (1988).
    [CrossRef]
  27. 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, 317–324 (1983).
    [CrossRef]
  28. M. F. Iskander, H. Y. Chen, J. E. Penner, “Optical scattering and absorption by branched chains of aeorsols,” Appl. Opt. 28, 3083–3091 (1989).
    [CrossRef] [PubMed]
  29. S. C. Olson, “Extensions of the iterative extended boundary condition method,” M.S. thesis (University of Utah, Salt Lake City, Utah, 1987).

1993

C. Hafner, “On the design of numerical methods,” IEEE Antennas Propag. Magn. 35, 13–21 (1993).
[CrossRef]

P. Leuchtmann, F. Bomholt, “Field modeling with the MMP code,” IEEE Trans. Electromag. Compatabil. 35, 170–177 (1993).
[CrossRef]

1991

C. Hafner, N. Kuster, “Computation of electromagnetic fields by multiple multipole method (generalized multipole technique),” Radio Sci. 26, 291–297 (1991).
[CrossRef]

A. C. Ludwig, “The generalized multipole technique,” Comput. Phys. Commun. 68, 306–314 (1991).
[CrossRef]

1990

J. Sroka, H. Baggenstos, R. Ballisti, “On the coupling of the generalized multipole technique with the finite element method,” IEEE Trans. Magn. 26, 658–661 (1990).
[CrossRef]

S. Kiener, “Eddy currents in bodies with sharp edges by the MMP-method,” IEEE Trans. Magn. 26, 482–485 (1990).
[CrossRef]

C. Hafner, “On the relationship between the MoM and the GMT,” IEEE Trans. Antennas Propag. Magn. 32, 12–19 (1990).
[CrossRef]

K. Joo, M. F. Iskander, “A new procedure of point-matching method for calculating the absorption and scattering of lossy dielectric objects,” IEEE Trans. Antennas Propag. 38, 1483–1489 (1990).
[CrossRef]

1989

C. Hafner, R. Ballisti, “Electromagnetic field calculations on PC’s and workstations using the MMP method,” IEEE Trans. Magn. 25, 2828–2830 (1989).
[CrossRef]

N. Kuster, R. Ballisti, “MMP method simulation of antenna with scattering objects in the closer-near-field,” IEEE Trans. Magn. 25, 2881–2883 (1989).
[CrossRef]

M. F. Iskander, H. Y. Chen, J. E. Penner, “Optical scattering and absorption by branched chains of aeorsols,” Appl. Opt. 28, 3083–3091 (1989).
[CrossRef] [PubMed]

1988

A. A. Sebak, L. Shafai, “Electromagnetic scattering by spheroidal objects with impedance boundary conditions at axial incidence,” Radio Sci. 23, 1048–1060 (1988).
[CrossRef]

1987

S. Ström, W. Zheng, “Basic features of the null field method for dielectric scatterers,” Radio Sci. 22, 1273–1281 (1987).
[CrossRef]

1986

A. C. Ludwig, “A comparison of spherical wave boundary value matching versus integral equation scattering solutions for a perfectly conducting body,” IEEE Trans. Antennas Propag. AP-34, 857–865 (1986).
[CrossRef]

1984

M. A. Morgan, C. H. Chen, S. C. Hill, P. W. Barber, “Finite element-boundary integral formulation for electromagnetic scattering,” Wave Motion 6, 91–103 (1984).
[CrossRef]

A. A. Sebak, L. Shafai, “Scattering by imperfectly conducting and impedance spheroids: a numerical approach,” Radio Sci. 19, 258–266 (1984).
[CrossRef]

1983

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, 317–324 (1983).
[CrossRef]

1982

P. W. Barber, “Resonant scattering for characterization of axisymmetric dielectric objects,” IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

1978

P. Latimer, P. W. Barber, “Scattering by ellipsoids of revolution: a comparison of theoretical methods,” J. Colloid Interface Sci. 63, 310–316 (1978).
[CrossRef]

1975

Al-Rizzo, H. M.

H. M. Al-Rizzo, “Electromagnetic wave scattering from 3-D coated and homogeneous objects using the GPMT and GMT, numerical modelling and applications,” Ph.D. dissertation (University of New Brunswick, Fredericton, Canada, 1992).

Asano, S.

Baggenstos, H.

J. Sroka, H. Baggenstos, R. Ballisti, “On the coupling of the generalized multipole technique with the finite element method,” IEEE Trans. Magn. 26, 658–661 (1990).
[CrossRef]

Ballisti, R.

J. Sroka, H. Baggenstos, R. Ballisti, “On the coupling of the generalized multipole technique with the finite element method,” IEEE Trans. Magn. 26, 658–661 (1990).
[CrossRef]

C. Hafner, R. Ballisti, “Electromagnetic field calculations on PC’s and workstations using the MMP method,” IEEE Trans. Magn. 25, 2828–2830 (1989).
[CrossRef]

N. Kuster, R. Ballisti, “MMP method simulation of antenna with scattering objects in the closer-near-field,” IEEE Trans. Magn. 25, 2881–2883 (1989).
[CrossRef]

Barber, P. W.

M. A. Morgan, C. H. Chen, S. C. Hill, P. W. Barber, “Finite element-boundary integral formulation for electromagnetic scattering,” Wave Motion 6, 91–103 (1984).
[CrossRef]

P. W. Barber, “Resonant scattering for characterization of axisymmetric dielectric objects,” IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

P. Latimer, P. W. Barber, “Scattering by ellipsoids of revolution: a comparison of theoretical methods,” J. Colloid Interface Sci. 63, 310–316 (1978).
[CrossRef]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Bomholt, F.

P. Leuchtmann, F. Bomholt, “Field modeling with the MMP code,” IEEE Trans. Electromag. Compatabil. 35, 170–177 (1993).
[CrossRef]

Bomholt, L.

C. Hafner, L. Bomholt, The Electrodynamic Wave Simulator (Wiley, New York, 1993).

Chen, C. H.

M. A. Morgan, C. H. Chen, S. C. Hill, P. W. Barber, “Finite element-boundary integral formulation for electromagnetic scattering,” Wave Motion 6, 91–103 (1984).
[CrossRef]

Chen, H. Y.

Durney, C. H.

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, 317–324 (1983).
[CrossRef]

Hafner, C.

C. Hafner, “On the design of numerical methods,” IEEE Antennas Propag. Magn. 35, 13–21 (1993).
[CrossRef]

C. Hafner, N. Kuster, “Computation of electromagnetic fields by multiple multipole method (generalized multipole technique),” Radio Sci. 26, 291–297 (1991).
[CrossRef]

C. Hafner, “On the relationship between the MoM and the GMT,” IEEE Trans. Antennas Propag. Magn. 32, 12–19 (1990).
[CrossRef]

C. Hafner, R. Ballisti, “Electromagnetic field calculations on PC’s and workstations using the MMP method,” IEEE Trans. Magn. 25, 2828–2830 (1989).
[CrossRef]

C. Hafner, “Beitrage zur Berechnung der Ausbreitung electro-magneitscher Wellen in Zylindrischen Struckturen mit Hilfe des point-matching—Ver fahrens,” Ph.D. dissertation (Swiss Polytechnical Institute of Technology, Zurich, Switzerland, 1980).

C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Boston, 1991).

C. Hafner, L. Bomholt, The Electrodynamic Wave Simulator (Wiley, New York, 1993).

Hill, S. C.

M. A. Morgan, C. H. Chen, S. C. Hill, P. W. Barber, “Finite element-boundary integral formulation for electromagnetic scattering,” Wave Motion 6, 91–103 (1984).
[CrossRef]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Iskander, M. F.

K. Joo, M. F. Iskander, “A new procedure of point-matching method for calculating the absorption and scattering of lossy dielectric objects,” IEEE Trans. Antennas Propag. 38, 1483–1489 (1990).
[CrossRef]

M. F. Iskander, H. Y. Chen, J. E. Penner, “Optical scattering and absorption by branched chains of aeorsols,” Appl. Opt. 28, 3083–3091 (1989).
[CrossRef] [PubMed]

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, 317–324 (1983).
[CrossRef]

Joo, K.

K. Joo, M. F. Iskander, “A new procedure of point-matching method for calculating the absorption and scattering of lossy dielectric objects,” IEEE Trans. Antennas Propag. 38, 1483–1489 (1990).
[CrossRef]

Kiener, S.

S. Kiener, “Eddy currents in bodies with sharp edges by the MMP-method,” IEEE Trans. Magn. 26, 482–485 (1990).
[CrossRef]

Kuster, N.

C. Hafner, N. Kuster, “Computation of electromagnetic fields by multiple multipole method (generalized multipole technique),” Radio Sci. 26, 291–297 (1991).
[CrossRef]

N. Kuster, R. Ballisti, “MMP method simulation of antenna with scattering objects in the closer-near-field,” IEEE Trans. Magn. 25, 2881–2883 (1989).
[CrossRef]

Lakhtakia, A.

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, 317–324 (1983).
[CrossRef]

Latimer, P.

P. Latimer, P. W. Barber, “Scattering by ellipsoids of revolution: a comparison of theoretical methods,” J. Colloid Interface Sci. 63, 310–316 (1978).
[CrossRef]

Leuchtmann, P.

P. Leuchtmann, F. Bomholt, “Field modeling with the MMP code,” IEEE Trans. Electromag. Compatabil. 35, 170–177 (1993).
[CrossRef]

Ludwig, A. C.

A. C. Ludwig, “The generalized multipole technique,” Comput. Phys. Commun. 68, 306–314 (1991).
[CrossRef]

A. C. Ludwig, “A comparison of spherical wave boundary value matching versus integral equation scattering solutions for a perfectly conducting body,” IEEE Trans. Antennas Propag. AP-34, 857–865 (1986).
[CrossRef]

A. C. Ludwig, “Cone-sphere scattering computed by the generalized multipole technique,” in Proceedings of the IEEE Antennas and Propagation International Symposium (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 48–51.

Morgan, M. A.

M. A. Morgan, C. H. Chen, S. C. Hill, P. W. Barber, “Finite element-boundary integral formulation for electromagnetic scattering,” Wave Motion 6, 91–103 (1984).
[CrossRef]

Olson, S. C.

S. C. Olson, “Extensions of the iterative extended boundary condition method,” M.S. thesis (University of Utah, Salt Lake City, Utah, 1987).

Penner, J. E.

Sebak, A. A.

A. A. Sebak, L. Shafai, “Electromagnetic scattering by spheroidal objects with impedance boundary conditions at axial incidence,” Radio Sci. 23, 1048–1060 (1988).
[CrossRef]

A. A. Sebak, L. Shafai, “Scattering by imperfectly conducting and impedance spheroids: a numerical approach,” Radio Sci. 19, 258–266 (1984).
[CrossRef]

Shafai, L.

A. A. Sebak, L. Shafai, “Electromagnetic scattering by spheroidal objects with impedance boundary conditions at axial incidence,” Radio Sci. 23, 1048–1060 (1988).
[CrossRef]

A. A. Sebak, L. Shafai, “Scattering by imperfectly conducting and impedance spheroids: a numerical approach,” Radio Sci. 19, 258–266 (1984).
[CrossRef]

Sroka, J.

J. Sroka, H. Baggenstos, R. Ballisti, “On the coupling of the generalized multipole technique with the finite element method,” IEEE Trans. Magn. 26, 658–661 (1990).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Ström, S.

S. Ström, W. Zheng, “Basic features of the null field method for dielectric scatterers,” Radio Sci. 22, 1273–1281 (1987).
[CrossRef]

Yamamoto, G.

Zheng, W.

S. Ström, W. Zheng, “Basic features of the null field method for dielectric scatterers,” Radio Sci. 22, 1273–1281 (1987).
[CrossRef]

Appl. Opt.

Comput. Phys. Commun.

A. C. Ludwig, “The generalized multipole technique,” Comput. Phys. Commun. 68, 306–314 (1991).
[CrossRef]

IEEE Antennas Propag. Magn.

C. Hafner, “On the design of numerical methods,” IEEE Antennas Propag. Magn. 35, 13–21 (1993).
[CrossRef]

IEEE Trans. Antennas Propag.

A. C. Ludwig, “A comparison of spherical wave boundary value matching versus integral equation scattering solutions for a perfectly conducting body,” IEEE Trans. Antennas Propag. AP-34, 857–865 (1986).
[CrossRef]

K. Joo, M. F. Iskander, “A new procedure of point-matching method for calculating the absorption and scattering of lossy dielectric objects,” IEEE Trans. Antennas Propag. 38, 1483–1489 (1990).
[CrossRef]

P. W. Barber, “Resonant scattering for characterization of axisymmetric dielectric objects,” IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[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, 317–324 (1983).
[CrossRef]

IEEE Trans. Antennas Propag. Magn.

C. Hafner, “On the relationship between the MoM and the GMT,” IEEE Trans. Antennas Propag. Magn. 32, 12–19 (1990).
[CrossRef]

IEEE Trans. Electromag. Compatabil.

P. Leuchtmann, F. Bomholt, “Field modeling with the MMP code,” IEEE Trans. Electromag. Compatabil. 35, 170–177 (1993).
[CrossRef]

IEEE Trans. Magn.

C. Hafner, R. Ballisti, “Electromagnetic field calculations on PC’s and workstations using the MMP method,” IEEE Trans. Magn. 25, 2828–2830 (1989).
[CrossRef]

N. Kuster, R. Ballisti, “MMP method simulation of antenna with scattering objects in the closer-near-field,” IEEE Trans. Magn. 25, 2881–2883 (1989).
[CrossRef]

J. Sroka, H. Baggenstos, R. Ballisti, “On the coupling of the generalized multipole technique with the finite element method,” IEEE Trans. Magn. 26, 658–661 (1990).
[CrossRef]

S. Kiener, “Eddy currents in bodies with sharp edges by the MMP-method,” IEEE Trans. Magn. 26, 482–485 (1990).
[CrossRef]

J. Colloid Interface Sci.

P. Latimer, P. W. Barber, “Scattering by ellipsoids of revolution: a comparison of theoretical methods,” J. Colloid Interface Sci. 63, 310–316 (1978).
[CrossRef]

Radio Sci.

S. Ström, W. Zheng, “Basic features of the null field method for dielectric scatterers,” Radio Sci. 22, 1273–1281 (1987).
[CrossRef]

A. A. Sebak, L. Shafai, “Scattering by imperfectly conducting and impedance spheroids: a numerical approach,” Radio Sci. 19, 258–266 (1984).
[CrossRef]

A. A. Sebak, L. Shafai, “Electromagnetic scattering by spheroidal objects with impedance boundary conditions at axial incidence,” Radio Sci. 23, 1048–1060 (1988).
[CrossRef]

C. Hafner, N. Kuster, “Computation of electromagnetic fields by multiple multipole method (generalized multipole technique),” Radio Sci. 26, 291–297 (1991).
[CrossRef]

Wave Motion

M. A. Morgan, C. H. Chen, S. C. Hill, P. W. Barber, “Finite element-boundary integral formulation for electromagnetic scattering,” Wave Motion 6, 91–103 (1984).
[CrossRef]

Other

S. C. Olson, “Extensions of the iterative extended boundary condition method,” M.S. thesis (University of Utah, Salt Lake City, Utah, 1987).

C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Boston, 1991).

C. Hafner, L. Bomholt, The Electrodynamic Wave Simulator (Wiley, New York, 1993).

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

A. C. Ludwig, “Cone-sphere scattering computed by the generalized multipole technique,” in Proceedings of the IEEE Antennas and Propagation International Symposium (Institute of Electrical and Electronics Engineers, New York, 1990), pp. 48–51.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

C. Hafner, “Beitrage zur Berechnung der Ausbreitung electro-magneitscher Wellen in Zylindrischen Struckturen mit Hilfe des point-matching—Ver fahrens,” Ph.D. dissertation (Swiss Polytechnical Institute of Technology, Zurich, Switzerland, 1980).

H. M. Al-Rizzo, “Electromagnetic wave scattering from 3-D coated and homogeneous objects using the GPMT and GMT, numerical modelling and applications,” Ph.D. dissertation (University of New Brunswick, Fredericton, Canada, 1992).

A. C. Ludwig, ed., “The generalized multipole technique,” in 1989 Antennas and Propagation Society International Symposium Proceedings (Antennas and Propagation Society, San Jose, Calif., 1989), Vol. 1, pp. 160–163.

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Figures (13)

Fig. 1
Fig. 1

Geometry for the problem of scattering by a PC object, illustrating the N p origins of the spherical multiple multipole expansions for the scattered field, with the origin p = 1 located at the center of the scatterer.

Fig. 2
Fig. 2

Scattering geometry showing the local (x, y, z) and the principal (x′, y′, z′) frames. The direction of incidence is z′, and the symmetry axis of the object is z and is oriented at angles (θ0, ϕ0). The incident field makes an angle τ0 with respect to the positive x′ axis.

Fig. 3
Fig. 3

Plots of the normalized differential scattering cross-section (DSCS) patterns for a PC sphere–cone–sphere, k 0 a = 3.7699, for two incident directions: (a) an incident wave along the bigger sphere, and (b) an incident wave along the smaller sphere. Also shown are plots of the relative error in the BC match versus θ in the xz plane for the sphere–cone–sphere geometry, where the incident wave is along (c) and (d) the bigger sphere and (e) and (f) the smaller sphere.

Fig. 4
Fig. 4

Plots of the normalized DSCS patterns for PC prolate spheroidal scatterers of an axial ratio a/b = 5: (a) k 0 a = 7, (b) k 0 a = 10.

Fig. 5
Fig. 5

Plots of the normalized DSCS patterns for PC prolate spheroidal scatterers of an axial ratio a/b = 10: (a) k 0 a = 7, (b) k 0 a = 10.

Fig. 6
Fig. 6

Plots of the normalized DSCS patterns for a 2:1 peanut-shaped dielectric scatterer, ɛ r = 4: (a) k 0 a = 1/3, (b) k 0 a = 2. Also shown are plots of the relative error in the BC match versus θ in the xz plane for a 2:1 peanut-shaped dielectric scatterer, with (c) and (d) k 0 a = 1/3, ɛ r = 4 and (e) and (f) k 0 a = 2, ɛ r = 4.

Fig. 7
Fig. 7

Plots of the normalized DSCS patterns for a 10/3 peanut-shaped dielectric scatterer, ɛ r = 4: (a) k 0 a = 1, (b) k 0 a = 10/3.

Fig. 8
Fig. 8

Plots of the normalized DSCS patterns for two hemispherical-capped dielectric cylinders, ɛ r = 2.28: (a) a/b = 1, k 0 a = 4.765, (b) a/b = 1/2, k 0 a = 2.382. Also shown are plots of the relative error in the BC match versus θ in the xz plane for a hemispherical-capped dielectric cylinder, with (c) and (d) a/b = 1, k 0 a = 4.765, ɛ r = 2.28, (e) and (f) a/b = 1/2, k 0 a = 2.382, ɛ r = 2.28.

Fig. 9
Fig. 9

Plots of the normalized DSCS patterns for a lossless prolate spheroidal scatterer of axial ratio (a) a/b = 1.75, with ɛ r = 2.25, k 0 a = 113.0973, and (b) a/b = 1.25, with ɛ r = 2.25, k 0 a = 125.6637. (c)–(f) Plots of the normalized DSCS patterns for prolate spheroidal dielectric scatterers, ɛ r = 2.25: (c) a/b = 6, k 0 a = 8, (d) a/b = 5, k 0 a = 8. (e) a/b = 10, k 0 a = 3, (f) a/b = 10, k 0 a = 5. (g) and (h) Plots of the normalized DSCS patterns for oblate spheroidal scatterers, ɛ r = 2.25: (g) a/b = 0.60, k 0 a = 15, (h) a/b = 0.80, k 0 a = 20.

Fig. 10
Fig. 10

(a) and (b) Plots of the normalized DSCS pattern for a lossless homogeneous prolate scatterer of axial ratio, a/b = 1.2, k 0 a 1 = 30, and ɛ r = 2.25. (c) τ0 = 0°, where main (co-) polarization is parallel to the scattering (xz) plane. (d) τ0 = 90°, where main (co-) polarization is perpendicular to the scattering (xz) plane. Also shown are plots of the normalized DSCS patterns for a lossless prolate spheroidal scatterer of axial ratio (e) a/b = 1.25, with ɛ r = 2.25, k 0 a = 235.6194. (f) a/b = 1.5, with ɛ r = 2.25, k 0 a = 235.6194, (g) a/b = 4, with ɛ r = 2.25, k 0 a = 125.6637, (h) a/b = 5, with ɛ r = 2.25, k 0 a = 157.0796.

Fig. 11
Fig. 11

(a), (d), (e) Plots of the normalized DSCS patterns for 2:1 finite circular cylinders with spherical end caps, ɛ r = 1.96: (d) k 0 a = 5.288, (e) k 0 a = 10.576. (b), (c), (f), (g) Plots of the normalized DSCS patterns for 3:1 finite circular cylinders with spherical end caps, ɛ r = 1.96: (f) k 0 a = 2.780, (g) k 0 a = 3.336.

Fig. 12
Fig. 12

Plots of the normalized DSCS patterns for finite dielectric circular cylinders of radius b and height 2a, k 0 a = 1, ɛ r = 4, θ0 = ϕ0 = 0°. (a) a/b = 1, (b) a/b = 2, (c) a/b = 3, (d) a/b = 4.

Fig. 13
Fig. 13

Illustration of the geometric locations of points used in the evaluation of the internal fields induced along the axis of rotational symmetry of an irradiated prolate spheroidal object.

Tables (4)

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Table 1 Normalized Extinction and Backscattering Cross Sections of the PC Scattering Test Cases

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Table 2 Normalized Extinction and Backscattering Cross Sections of the Lossless Dielectric Test Cases

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Table 3 Comparison of the Magnitude of the Internal Electric-Field Distribution (V/m) at Selected Equidistant Points along the Major Axes of Highly Elongated Dielectric Objects with the GMT, Iterative Extended-Boundary-Condition Method (IEBCM), the Volume Integral-Equation Formula (VIEF), and the Improved PMT for an Incident Electric Field of 1 V/m

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Table 4 Comparison of the Magnitude of the Internal Electric-Field Distribution (V/m) at Selected Equidistant Points along the Major Axes of Highly Elongated Dielectric Objects with the GMT, IEBCM, and the VIEF for an Incident Electric Field of 1 V/m

Equations (23)

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E s , = - p = 1 N p m = - n m n 0 [ a m n , p , M m n , p ( 3 ) ( k 0 r p , θ p , ϕ p ) + b m n , p , N m n , p ( 3 ) ( k 0 r p , θ p , ϕ p ) ] , H s , = j k 0 ω μ 0 p = 1 N p m = - n m n 0 [ b m n , p , M m n , p ( 3 ) ( k 0 r p , θ p , ϕ p ) + a m n , p , N m n , p ( 3 ) ( k 0 r p , θ p , ϕ p ) ] ,
r p = f p ( θ p ) ,             0 ° θ p 180 ° .
p = 1 N p m = - n m n 0 E s , ϕ , p , = E i , ϕ , p = 1 N p m = - n m n 0 E s , θ , p , + 1 r p d f p ( θ p ) d θ E s , r , p , { 1 + [ 1 r p d f p ( θ p ) d θ ] 2 } 1 / 2 = E i , θ , + 1 r d f ( θ ) d θ E i , r , { 1 + [ 1 r d f ( θ ) d θ ] 2 } 1 / 2 ,
p = 1 N p n m n 0 h n ( 1 ) ( k 0 r p ) d P n m ( cos θ p ) d θ a m n , p , - j m P n m ( cos θ p ) sin θ p f ^ n ( 1 ) ( k 0 r p ) b m n , p = { - j m E i cos θ i m J m ( k 0 r sin θ i sin θ ) k 0 r sin θ i sin θ exp ( j k 0 r cos θ i cos θ ) j m + 1 E i J m ( k 0 r sin θ i sin θ ) exp ( j k 0 r cos θ i cos θ ) , p = 1 N p g ( θ , θ p ) n m n 0 j m h n ( 1 ) ( k 0 r p ) P n m ( cos θ p ) sin θ p a m n , p , + [ f ^ n ( 3 ) ( k 0 r p ) d P n m ( cos θ p ) d θ + 1 r p d f p ( θ p ) d θ n ( n + 1 ) h n ( 1 ) ( k 0 r p ) k 0 r p P n m ( cos θ p ) ] b m n , p , = { - j m E i { J m ( k 0 r sin θ i sin θ ) sin θ i sin θ - j J m ( k 0 r sin θ i sin θ ) cos θ i cos θ - 1 r d f ( θ ) d θ [ J m ( k 0 r sin θ i sin θ ) sin θ i sin θ + j J m ( k 0 r sin θ i sin θ ) cos θ i cos θ ] } exp ( j k 0 r cos θ i cos θ ) j m E i m J m ( k 0 r sin θ i sin θ ) k 0 r sin θ i sin θ ( cos θ + 1 r d f ( θ ) d θ sin θ ) exp ( j k 0 r cos θ i cos θ ) ,
g ( θ , θ p ) = - { 1 + [ 1 r d f ( θ ) d θ ] 2 1 + [ 1 r p d f p ( θ p ) d θ ] 2 } 1 / 2
a - m n , p = - a m n , p , a - m n , p = a m n , p , b - m n , p = - b m n , p , b - m n , p = b m n , p .
p = 1 N p g ( θ , θ p ) n m n 0 [ 1 r p d f p ( θ p ) d θ f ^ n ( 3 ) ( k 0 r p ) d P n m ( cos θ p ) d θ - n ( n + 1 ) P n m ( cos θ p ) h n ( 1 ) ( k 0 r p ) ] a m n , p , + j m 1 r p d f p ( θ p ) d θ P n m ( cos θ p ) sin θ p h n ( 1 ) ( k 0 r p ) b m n , p , = { j m + 1 E i exp ( j k 0 r cos θ i cos θ ) cos θ i m J m ( k 0 r sin θ i sin θ ) k 0 r sin θ i sin θ [ sin θ - 1 r d f ( θ ) d θ cos θ ] j m E i exp ( j k 0 r cos θ i cos θ ) cos θ i m J m ( k 0 r sin θ i sin θ ) k 0 r sin θ i sin θ [ sin θ - 1 r d f ( θ ) d θ cos θ ] .
E t , = - j = 1 N j m = - n m n 0 c m n , j , M m n , j ( 1 ) ( k 1 r j , θ j , ϕ j ) + d m n , j , N m n , j ( 1 ) ( k 1 r j , θ j , θ j ) ] , H t , = j k 1 ω μ 0 j = 1 N j m = - n m n 0 d m n , j , M m n , j ( 1 ) ( k 1 r j , θ j , ϕ j ) + c m n , j , N m n , j ( 1 ) ( k 1 r j , θ j , θ j ) ] ,
p = 1 N p n m n 0 h n ( 1 ) ( k 0 r p ) d P n m ( cos θ p ) d θ a m n , p , - j m f ^ n ( 3 ) ( k 0 r p ) P n m ( cos θ p ) sin θ p b m n , p , + j = 1 N j n m n 0 - j n ( k 1 r j ) d P n m ( cos θ j ) d θ c m n , j , + j m f ^ n ( 1 ) ( k 1 r j ) P n m ( cos θ j ) sin θ j d m n , j , = { - j m E i cos θ i m J m ( k 0 r sin θ i sin θ ) k 0 r sin θ i sin θ exp ( k 0 r cos θ i cos θ ) j m + 1 E i J m ( k 0 r sin θ i sin θ ) exp ( k 0 r cos θ i cos θ ) , p = 1 N p n m n 0 - j m f ^ n ( 3 ) ( k 0 r p ) P n m ( cos θ p ) sin θ p a m n , p , + h n ( 1 ) ( k 0 r p ) d P n m ( cos θ p ) d θ b m n , p , + ɛ r j = 1 N j n m n 0 j m f ^ n ( 1 ) ( k 1 r j ) P n m ( cos θ j ) sin θ j c m n , j , - j n ( k 1 r j ) d P n m ( cos θ j ) d θ d m n , j , = { - j m E i J m ( k 0 r sin θ i sin θ ) exp ( k 0 r cos θ i cos θ ) j m + 1 E i cos θ i m J m ( k 0 r sin θ i sin θ ) k 0 r sin θ i sin θ exp ( j k 0 r cos θ i cos θ ) , p = 1 N p g ( θ , θ p ) n m n 0 - j m h n ( 1 ) ( k 0 r p ) P n m ( cos θ p ) sin θ p a m n , p , + f ^ n ( 3 ) ( k 0 r p ) d P n m ( cos θ p ) d θ + 1 r p d f p ( θ p ) d θ n ( n + 1 ) h n ( 1 ) ( k 0 r p ) k 0 r p P n m ( cos θ p ) b m n , p , + j = 1 N j g ( θ , θ j ) n m n 0 j m P n m ( cos θ j ) sin θ j j n ( k 1 r j ) c m n , j . + [ f ^ n ( 1 ) ( k 1 r j ) d P n m ( cos θ j ) d θ + 1 r j d f j ( θ j ) d θ n ( n + 1 ) j n ( k 1 r j ) k 1 r j P n m ( cos θ j ) ] d m n , j , = { - j m E i { J m ( k 0 r sin θ i sin θ ) sin θ i sin θ - j J m ( k 0 r sin θ i sin θ ) cos θ i cos θ - 1 r d f ( θ ) d θ [ J m ( k 0 r sin θ i sin θ ) sin θ i cos θ + j J m ( k 0 r sin θ i sin θ ) cos θ i sin θ ] } exp ( j k 0 r cos θ i cos θ ) j m E i m J m ( k 0 r sin θ i sin θ ) k 0 r sin θ i sin θ [ cos θ + 1 r d f ( θ ) d θ sin θ ] exp ( j k 0 r cos θ i cos θ ) , p = 1 N p g ( θ , θ p ) n m n 0 - [ f ^ n ( 3 ) ( k 0 r p ) d P n m ( cos θ p ) d θ + 1 r p d f p ( θ p ) d θ n ( n + 1 ) h n ( 1 ) ( k 0 r p ) k 0 r p P n m ( cos θ p ) ] a m n , p , + j m h n ( 1 ) ( k 0 r p ) P n m ( cos θ p ) sin θ p b m n , p , + ɛ r j = 1 N j g ( θ , θ j ) n m n 0 [ f ^ n ( 1 ) ( k 1 r j ) d P n m ( cos θ j ) d θ + 1 r j d f j ( θ j ) d θ n ( n + 1 ) × j n ( k 1 r j ) k 1 r j P n m ( cos θ j ) ] c m n , j , + j m P n m ( cos θ j ) sin θ j j n ( k 1 r j ) d m n , j , = { j m + 1 E i m J m ( k 0 r sin θ i sin θ ) k 0 r sin θ i sin θ [ cos θ + 1 r d f ( θ ) d θ sin θ ] exp ( j k 0 r cos θ i cos θ ) j m + 1 E i { J m ( k 0 r sin θ i sin θ ) sin θ i sin θ - j J m ( k 0 r sin θ i sin θ ) cos θ i cos θ - 1 r d f ( θ ) d θ [ J m ( k 0 r sin θ i sin θ ) sin θ i cos θ + j J m ( k 0 r sin θ i sin θ ) cos θ i sin θ ] } exp ( j k 0 r cos θ i cos θ ) .
a - m n , p = - a m n , p , a - m n , p = a m n , p , b - m n , p = - b m n , p , b - m n , p = b m n , p , c - m n , j = - c m n , j , c m n , j = c m n , j , d - m n , j = - d m n , j , d - m n , j = d m n , j .
p = 1 N p g ( θ , θ p ) n m n 0 j m 1 r p d f p ( θ p ) d θ P n m ( cos θ p ) sin θ p h n ( 1 ) ( k 0 r p ) a m n , p , - [ 1 r p d f p ( θ p ) d θ f ^ n ( 3 ) ( k 0 r p ) d P n m ( cos θ p ) d θ - n ( n + 1 ) P n m ( cos θ p ) h n ( 1 ) ( k 0 r p ) k 0 r p ] b m n , p , + j = 1 N j g ( θ , θ j ) n m n 0 - j m 1 r j d f j ( θ j ) d θ P n m ( cos θ j ) sin θ j j n ( k 1 r j ) c m n , j , + ɛ r n ( n + 1 ) P n m ( cos θ j ) j n ( k 1 r j ) k 1 r j - 1 r j d f j ( θ j ) d θ f ^ n ( 1 ) ( k 1 r j ) d P n m ( cos θ j ) d θ d m n , j , = { j m E i exp ( j k 0 r cos θ i cos θ ) { J m ( k 0 r sin θ i sin θ ) sin θ i [ cos θ + 1 r d f ( θ ) d θ sin θ ] + j J m ( k 0 r sin θ i sin θ ) cos θ i [ sin θ - 1 r d f ( θ ) d θ cos θ ] } j m E i exp ( j k 0 r cos θ i cos θ ) m J m ( k 0 r sin θ i sin θ ) k 0 r sin θ i sin θ [ sin θ - 1 r d f ( θ ) d θ cos θ ] , p = 1 N p g ( θ , θ p ) n m n 0 - [ 1 r p d f p ( θ p ) d θ f ^ n ( 3 ) ( k 0 r p ) d P m m ( cos θ p ) d θ - n ( n + 1 ) P n m ( cos θ p ) × h n ( 1 ) ( k 0 r p ) k 0 r p ] a m n , p , + j m 1 r p d f p ( θ p ) d θ P n m ( cos θ p ) sin θ p h n ( 1 ) ( k 0 r p ) b m n , p , + j = 1 N j g ( θ , θ p ) × n m n 0 ɛ r [ n ( n + 1 ) P n m ( cos θ j ) j n ( k 1 r j ) k 1 r j 1 r j d f j ( θ j ) d θ f ^ n ( 1 ) ( k 1 r j ) d P n m ( cos θ j ) d θ ] c m n , j , - j m ɛ r 1 r j d f j ( θ j ) d θ P n m ( cos θ j ) j n ( k 1 r j ) d m n , j , = { j m + 1 E i exp ( j k 0 r cos θ i cos θ ) m J m ( k 0 r sin θ i sin θ ) k 0 r sin θ i sin θ [ sin θ - 1 r d f ( θ ) d θ cos θ ] - j m + 1 E i exp ( k 0 r cos θ i cos θ ) { J m ( k 0 r sin θ i sin θ ) sin θ i [ cos θ + 1 r d f ( θ ) d θ sin θ ] + j J m ( k 0 r sin θ i sin θ ) cos θ i [ sin θ - 1 r d f ( θ ) d θ cos θ ] } .
E s , exp ( j k 0 r ) k 0 r p = 1 N p exp ( - j k 0 l p cos θ s ) × m = - n m n 0 ( - j ) n + 1 × { [ d P n m ( cos θ s ) d θ a ^ ϕ - j m P n m ( cos θ s ) sin θ s a ^ θ ] × a m n , p , - j × [ d P n m ( cos θ s ) d θ a ^ θ + j m P n m ( cos θ s ) sin θ s a ^ ϕ ] × b m n , p , } exp ( j m ϕ s ) ,
a m n , = p = 1 N p a m n , p , exp ( - j k 0 l p cos θ s ) , b m n , = p = 1 N p b m n , p , exp ( - j k 0 l p cos θ s ) ,
E s , = exp ( j k 0 r ) k 0 r m = - n m n 0 ( - j ) n + 1 { [ d P n m ( cos θ s ) d θ a ^ ϕ - j m P n m ( cos θ s ) sin θ s a ^ θ ] a m n , - j [ d P n m ( cos θ s ) d θ a ^ θ + j m P n m ( cos θ s ) sin θ s a ^ ϕ ] b m n , } exp ( j m ϕ s ) .
E t , r = - j = 1 N j m = 0 M 0 ( j ) n m n 0 N 0 ( j ) ɛ m n ( n + 1 ) j n ( k 1 r j ) k 1 r j × P n m ( cos θ j ) d m n , j cos ( m ϕ j ) , E t , θ = - j = 1 N j m = 0 M 0 ( j ) n m n 0 N 0 ( j ) ɛ m [ j m j n ( k 1 r j ) P n m ( cos θ j ) sin θ j c m n , j + f ^ n ( 1 ) ( k 1 r j ) d P n m ( cos θ j ) d θ d m n , j cos ( m ϕ j ) , E t , ϕ = j = 1 N j m = 0 M 0 ( j ) n m n 0 N 0 ( j ) ɛ m [ j j n ( k 1 r j ) d P n m ( cos θ j ) d θ c m n , j + m f ^ n ( 1 ) ( k 1 r j ) P n m ( cos θ j ) sin θ j d m n , j sin ( m ϕ j ) ,
E t , r = j = 1 N j m = 0 M 0 ( j ) n m n 0 N 0 ( j ) j ɛ m n ( n + 1 ) j n ( k 1 r j ) k 1 r j × P n m ( cos θ j ) d m n , j sin ( m ϕ j ) , E t , θ = j = 1 N j m = 0 M 0 ( j ) n m n 0 N 0 ( j ) ɛ m [ m j n ( k 1 r j ) P n m ( cos θ j ) sin θ j c m n , j - j f ^ n ( 1 ) ( k 1 r j ) d P n m ( cos θ j ) d θ d m n , j ( sin m ϕ j ) , E t , ϕ = j = 1 N j m = 0 M 0 ( j ) n m n 0 N 0 ( j ) ɛ m [ j n ( k 1 r j ) d P n m ( cos θ j ) d θ c m n , j - j m f ^ n ( 1 ) ( k 1 r j ) P n m ( cos θ j ) sin θ j d m n , j ( cos m ϕ j ) ,
( E s E s ) = exp ( j k s · r ) r [ f , f , f , f , ] ( E i E i ) ,
f , = 1 k 0 m = 0 M 0 n m n 0 N 0 ( - j ) n + 2 ɛ m [ m sin θ s P n m ( cos θ s ) a m n + d P n m ( cos θ s ) d θ b m n ] cos ( m ϕ s ) , f , = 1 k 0 m = 0 M 0 n m n 0 N 0 ( - j ) n + 1 ɛ m [ m sin θ s P n m ( cos θ s ) a m n + d P n m ( cos θ s ) d θ b mn ] sin ( m ϕ s ) , f , = - 1 k 0 m = 0 M 0 n m n 0 N 0 ( - j ) n + 2 ɛ m [ d P n m ( cos θ s ) d θ a m n + m sin θ s P n m ( cos θ s ) b m n ] sin ( m ϕ s ) , f , = 1 k 0 m = 0 M 0 n m n 0 N 0 ( - j ) n + 1 ɛ m [ d P n m ( cos θ s ) d θ a m n + m sin θ s P n m ( cos θ s ) b m n ] cos ( m ϕ s ) .
( E s E s ) = [ cos γ sin γ - sin γ cos γ ] [ f , f , f , f . ] × [ - cos ϕ 0 - sin ϕ 0 sin ϕ 0 - cos ϕ 0 ] ( E i E i ) ,
cos γ = cos ϕ s sin ϕ s sin ϕ 0 cos ϕ 0 - cos ϕ s cos ϕ 0 cos ϕ s , sin γ = cos θ s cos ϕ s sin ϕ s cos θ 0 cos ϕ 0 + sin θ s sin ϕ s sin θ 0 + cos θ s cos ϕ s cos ϕ s sin ϕ 0 ,
r ( θ ) = ( a 2 cos 2 θ + b 2 sin 2 θ ) 1 / 2 .
r ( θ ) = 2 b             0 ° θ γ ,             180 ° - γ θ 180 ° = b / sin θ             γ θ 180 ° - γ , r ( θ ) = b cos θ + b ( 4 - sin 2 θ )             0 ° θ γ = b / sin θ             γ θ 180 ° - γ = - b cos θ + b ( 4 - sin 2 θ ) 1 / 2             180 ° - γ θ 180 ° , r ( θ ) = 3 b             0 ° θ γ ,             180 ° - γ θ 180 ° = b / sin θ             γ θ 180 ° - γ ,
r ( θ ) = a cos θ             0 ° θ γ = b sin θ             γ θ 180 ° - γ = - a cos θ             180 ° - γ γ 180 ° ,

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