Abstract

The newly developed iterative extended boundary condition method (IEBCM) is extended to calculate the scattering by low-loss or lossless elongated dielectric objects. Specifically the iterative procedure is modified so as to utilize an initial assumption of the surface fields obtained from the Mie solution of a spherical object of the same dielectric properties. The solution for the elongated object is obtained by iteratively utilizing the regular EBCM technique to solve for objects of intermediate geometries between the substitute sphere and the object of interest. The other feature of the IEBCM which is related to subdividing the internal volume of the object into several overlapping subregions in each of which a separate field expansion is used is also utilized in the present extension. Results illustrating the adequacy of the IEBCM procedure to calculate the scattering by spheroids of an aspect ratio of more than 7:1 are presented.

© 1984 Optical Society of America

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References

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  1. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  3. T. Oguchi, Radio Sci. 8, 31 (1973).
    [CrossRef]
  4. J. A. Morrison, M. J. Cross, Bell Syst. Tech. J. 53, 955 (1974).
  5. P. W. Barber, C. Yeh, Appl. Opt. 14, 2864 (1975).
    [CrossRef] [PubMed]
  6. A. R. Holt, “The Fredholm Integral Equation Method and Comparison with the T-Matrix Approach,” in Acoustic, Electromagnetic and Elastic Wave Scattering, V. K. Varadan, V. V. Varadan, Eds. (Pergamon, New York, 1980).
  7. R. H. T. Bates, D. J. N. Wall, Philos. Trans. R. Soc. London Sec. A 287, 45 (1977).
    [CrossRef]
  8. D. J. N. Wall, “The Null Field Approach to the Antenna Boundary Value Problem,” at IEEE International Conference on Antennas and Propagation, Part 1 (1979), p. 174.
  9. R. F. Harrington, J. R. Mautz, “Surface Integral Equations for Conducting and Dielectric Bodies,” in Theoretical Methods for Determining the Interaction of Electromagnetic Waves with Structures, J. K. Skwirzynski, Ed. (Sijthoff and Noordhoff, Rockville, Md., 1981).
    [CrossRef]
  10. S. Asano, G. Yamamoto, Appl. Opt. 14, 29 (1975); see also S. Asano, M. Sato, Appl. Opt. 19, 962 (1980).
    [CrossRef] [PubMed]
  11. M. F. Iskander, A. Lakhtakia, C. H. Durney, Proc. IEEE 70, 1361 (1982).
    [CrossRef]
  12. M. F. Iskander, A. Lakhtakia, C. H. Durney, IEEE Trans. Antennas Propag. AP-31, 317 (1983).
    [CrossRef]
  13. A. Lakhtakia, M. F. Iskander, C. H. Durney, IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
    [CrossRef]
  14. A. Lakhtakia, M. F. Iskander, “Theoretical and Experimental Evaluation of Power Absorption in Elongated Biological Objects at and Beyond Resonance,” IEEE Trans. Electromagn. Compat. EMC-25, 448 (1983).
    [CrossRef]
  15. M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
    [CrossRef]
  16. P. W. Barber, IEEE Trans. Biomed. Eng. BME-24, 513 (1977); see also IEEE Trans. Biomed. Eng. BME-25, 155 (1978).
    [CrossRef]
  17. P. C. Waterman, “Survey of T-Matrix Methods and Surface Field Representations,” in Acoustic, Electromagnetic and Elastic Wave Scattering—Focus on the T-Matrix Approach, V. K. Varadan, V. V. Varadan, Eds. (Pergamon, New York, 1980).
  18. D. J. N. Wall, “Methods of Overcoming Numerical Instabilities Associated with the T-Matrix Method,” in Acoustic, Electromagnetic and Elastic Wave Scattering, V. K. Varadan, V. V. Varadan, Eds. (Pergamon, New York, 1980).
  19. R. Bansal, “A Theoretical and Experimental Study of Electromagnetic Fields in Finite Dielectric Cylinders,” Ph.D. Thesis, Harvard U., Cambridge, Mass. (1981).
  20. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

1983 (3)

M. F. Iskander, A. Lakhtakia, C. H. Durney, IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

A. Lakhtakia, M. F. Iskander, C. H. Durney, IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
[CrossRef]

A. Lakhtakia, M. F. Iskander, “Theoretical and Experimental Evaluation of Power Absorption in Elongated Biological Objects at and Beyond Resonance,” IEEE Trans. Electromagn. Compat. EMC-25, 448 (1983).
[CrossRef]

1982 (1)

M. F. Iskander, A. Lakhtakia, C. H. Durney, Proc. IEEE 70, 1361 (1982).
[CrossRef]

1980 (1)

M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

1977 (2)

P. W. Barber, IEEE Trans. Biomed. Eng. BME-24, 513 (1977); see also IEEE Trans. Biomed. Eng. BME-25, 155 (1978).
[CrossRef]

R. H. T. Bates, D. J. N. Wall, Philos. Trans. R. Soc. London Sec. A 287, 45 (1977).
[CrossRef]

1975 (2)

1974 (1)

J. A. Morrison, M. J. Cross, Bell Syst. Tech. J. 53, 955 (1974).

1973 (1)

T. Oguchi, Radio Sci. 8, 31 (1973).
[CrossRef]

Asano, S.

Bansal, R.

R. Bansal, “A Theoretical and Experimental Study of Electromagnetic Fields in Finite Dielectric Cylinders,” Ph.D. Thesis, Harvard U., Cambridge, Mass. (1981).

Barber, P. W.

M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

P. W. Barber, IEEE Trans. Biomed. Eng. BME-24, 513 (1977); see also IEEE Trans. Biomed. Eng. BME-25, 155 (1978).
[CrossRef]

P. W. Barber, C. Yeh, Appl. Opt. 14, 2864 (1975).
[CrossRef] [PubMed]

Bates, R. H. T.

R. H. T. Bates, D. J. N. Wall, Philos. Trans. R. Soc. London Sec. A 287, 45 (1977).
[CrossRef]

Cross, M. J.

J. A. Morrison, M. J. Cross, Bell Syst. Tech. J. 53, 955 (1974).

Durney, C. H.

M. F. Iskander, A. Lakhtakia, C. H. Durney, IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

A. Lakhtakia, M. F. Iskander, C. H. Durney, IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
[CrossRef]

M. F. Iskander, A. Lakhtakia, C. H. Durney, Proc. IEEE 70, 1361 (1982).
[CrossRef]

M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

Harrington, R. F.

R. F. Harrington, J. R. Mautz, “Surface Integral Equations for Conducting and Dielectric Bodies,” in Theoretical Methods for Determining the Interaction of Electromagnetic Waves with Structures, J. K. Skwirzynski, Ed. (Sijthoff and Noordhoff, Rockville, Md., 1981).
[CrossRef]

Holt, A. R.

A. R. Holt, “The Fredholm Integral Equation Method and Comparison with the T-Matrix Approach,” in Acoustic, Electromagnetic and Elastic Wave Scattering, V. K. Varadan, V. V. Varadan, Eds. (Pergamon, New York, 1980).

Iskander, M. F.

A. Lakhtakia, M. F. Iskander, C. H. Durney, IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
[CrossRef]

M. F. Iskander, A. Lakhtakia, C. H. Durney, IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

A. Lakhtakia, M. F. Iskander, “Theoretical and Experimental Evaluation of Power Absorption in Elongated Biological Objects at and Beyond Resonance,” IEEE Trans. Electromagn. Compat. EMC-25, 448 (1983).
[CrossRef]

M. F. Iskander, A. Lakhtakia, C. H. Durney, Proc. IEEE 70, 1361 (1982).
[CrossRef]

M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Lakhtakia, A.

A. Lakhtakia, M. F. Iskander, “Theoretical and Experimental Evaluation of Power Absorption in Elongated Biological Objects at and Beyond Resonance,” IEEE Trans. Electromagn. Compat. EMC-25, 448 (1983).
[CrossRef]

M. F. Iskander, A. Lakhtakia, C. H. Durney, IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

A. Lakhtakia, M. F. Iskander, C. H. Durney, IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
[CrossRef]

M. F. Iskander, A. Lakhtakia, C. H. Durney, Proc. IEEE 70, 1361 (1982).
[CrossRef]

Massoudi, H.

M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

Mautz, J. R.

R. F. Harrington, J. R. Mautz, “Surface Integral Equations for Conducting and Dielectric Bodies,” in Theoretical Methods for Determining the Interaction of Electromagnetic Waves with Structures, J. K. Skwirzynski, Ed. (Sijthoff and Noordhoff, Rockville, Md., 1981).
[CrossRef]

Morrison, J. A.

J. A. Morrison, M. J. Cross, Bell Syst. Tech. J. 53, 955 (1974).

Oguchi, T.

T. Oguchi, Radio Sci. 8, 31 (1973).
[CrossRef]

Stratton, J. A.

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

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wall, D. J. N.

R. H. T. Bates, D. J. N. Wall, Philos. Trans. R. Soc. London Sec. A 287, 45 (1977).
[CrossRef]

D. J. N. Wall, “The Null Field Approach to the Antenna Boundary Value Problem,” at IEEE International Conference on Antennas and Propagation, Part 1 (1979), p. 174.

D. J. N. Wall, “Methods of Overcoming Numerical Instabilities Associated with the T-Matrix Method,” in Acoustic, Electromagnetic and Elastic Wave Scattering, V. K. Varadan, V. V. Varadan, Eds. (Pergamon, New York, 1980).

Waterman, P. C.

P. C. Waterman, “Survey of T-Matrix Methods and Surface Field Representations,” in Acoustic, Electromagnetic and Elastic Wave Scattering—Focus on the T-Matrix Approach, V. K. Varadan, V. V. Varadan, Eds. (Pergamon, New York, 1980).

Yamamoto, G.

Yeh, C.

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

J. A. Morrison, M. J. Cross, Bell Syst. Tech. J. 53, 955 (1974).

IEEE Trans. Antennas Propag. (1)

M. F. Iskander, A. Lakhtakia, C. H. Durney, IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

P. W. Barber, IEEE Trans. Biomed. Eng. BME-24, 513 (1977); see also IEEE Trans. Biomed. Eng. BME-25, 155 (1978).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

A. Lakhtakia, M. F. Iskander, “Theoretical and Experimental Evaluation of Power Absorption in Elongated Biological Objects at and Beyond Resonance,” IEEE Trans. Electromagn. Compat. EMC-25, 448 (1983).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

A. Lakhtakia, M. F. Iskander, C. H. Durney, IEEE Trans. Microwave Theory Tech. MTT-31, 640 (1983).
[CrossRef]

Philos. Trans. R. Soc. London Sec. A (1)

R. H. T. Bates, D. J. N. Wall, Philos. Trans. R. Soc. London Sec. A 287, 45 (1977).
[CrossRef]

Proc. IEEE (1)

M. F. Iskander, A. Lakhtakia, C. H. Durney, Proc. IEEE 70, 1361 (1982).
[CrossRef]

Radio Sci. (1)

T. Oguchi, Radio Sci. 8, 31 (1973).
[CrossRef]

Other (9)

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

D. J. N. Wall, “The Null Field Approach to the Antenna Boundary Value Problem,” at IEEE International Conference on Antennas and Propagation, Part 1 (1979), p. 174.

R. F. Harrington, J. R. Mautz, “Surface Integral Equations for Conducting and Dielectric Bodies,” in Theoretical Methods for Determining the Interaction of Electromagnetic Waves with Structures, J. K. Skwirzynski, Ed. (Sijthoff and Noordhoff, Rockville, Md., 1981).
[CrossRef]

A. R. Holt, “The Fredholm Integral Equation Method and Comparison with the T-Matrix Approach,” in Acoustic, Electromagnetic and Elastic Wave Scattering, V. K. Varadan, V. V. Varadan, Eds. (Pergamon, New York, 1980).

P. C. Waterman, “Survey of T-Matrix Methods and Surface Field Representations,” in Acoustic, Electromagnetic and Elastic Wave Scattering—Focus on the T-Matrix Approach, V. K. Varadan, V. V. Varadan, Eds. (Pergamon, New York, 1980).

D. J. N. Wall, “Methods of Overcoming Numerical Instabilities Associated with the T-Matrix Method,” in Acoustic, Electromagnetic and Elastic Wave Scattering, V. K. Varadan, V. V. Varadan, Eds. (Pergamon, New York, 1980).

R. Bansal, “A Theoretical and Experimental Study of Electromagnetic Fields in Finite Dielectric Cylinders,” Ph.D. Thesis, Harvard U., Cambridge, Mass. (1981).

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

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Figures (4)

Fig. 1
Fig. 1

Schematic illustrating the partitioning of the object of volume V into subvolumes V(i). The ith subregion has a subsurface S(i), and the shaded regions are the overlapping zones OV(i,i+1). A prolate spheroid is subdivided into spherical subregions in each of which a separate field expansion is used.

Fig. 2
Fig. 2

Geometry of a prolate spheroid dielectric object of aspect ratio 7:1 and ɛ r * = 5.0 + j 0.0. The incident plane wave has a wave vector along the z axis.

Fig. 3
Fig. 3

Calculated values of the electric field distribution (V/m) at selected equispaced points along the axis of a prolate spheroidal model of ka = 1.35, where a is the semimajor axis ɛ r * = 5.0 + j 0.0, and of an aspect ratio (x = a/b) equal (a) x = 7 and (b) x = 4. The results were obtained using the regular EBCM procedure. The electric field values for x = 7 failed to converge to the correct solution.

Fig. 4
Fig. 4

Calculated values of the electric field distribution (V/m) at selected equispaced points along the axis of a prolate spheroidal model of ka = 1.35, where a is the semimajor axis, ɛ r * = 5.0 + j 0.0, and of an aspect ratio (x = a/b) equal (a) x = 7 and (b) x = 4. These results were obtained using the IEBCM procedure with a signal spherical expansion for x = 4 and two spherical expansions in two overlapping subregions for x = 7.

Tables (1)

Tables Icon

Table I Scattering and Extinction Efficiencies for a Spheroidal Dielectric Object of ka = 1.35 and ɛ r * = 5.0 + j 0.0

Equations (5)

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- E ¯ i ( r ¯ ) = × S [ n ^ ( r ¯ ) × E ¯ + ( r ¯ ) ] · G ¯ ( k r ¯ / k r ¯ ) d s - × × S 1 j ω ɛ 0 [ n ^ ( r ¯ ) × H ¯ + ( r ¯ ) ] · G ¯ ( k r ¯ / k r ¯ ) d s ,
- E ¯ i ( r ¯ ) = × S [ n ^ ( r ) × E ¯ int ( r ¯ ) ] · G ¯ ( k r ¯ / k r ¯ ) d s - × × S 1 j ω ɛ 0 [ n ^ ( r ¯ ) × H ¯ int ( r ¯ ) ] · G ¯ ( k r ¯ / k r ¯ ) d s ,
E ¯ i ( r ¯ ) + × S [ n ^ ( r ¯ ) × E ¯ int ( - 1 ) ( r ¯ ) ] · G ¯ ( k r ¯ / k r ¯ ) d s - × × S 1 j ω ɛ 0 [ n ^ ( r ¯ ) × H ¯ int ( - 1 ) ( r ¯ ) · G ¯ ( k r ¯ / k r ¯ ) d s = × × S 1 j ω ɛ 0 [ n ^ ( r ¯ ) × Δ H ¯ + ( 0 ) ( r ¯ ) ] · G ¯ ( k r ¯ / k r ¯ ) d s × × S 1 j ω ɛ 0 ɛ r * [ n ^ ( r ¯ ) × × Δ H ¯ + ( 0 ) ( r ¯ ) ] · G ¯ ( k r ¯ / k r ¯ ) d s ,
E ¯ s ( r ¯ ) = × S [ n ^ ( r ¯ ) × E ¯ int ( 0 ) ( r ¯ ) ] · G ¯ ( k r ¯ / k r ¯ ) d s - × × S 1 j ω ɛ 0 [ n ^ ( r ¯ ) × H ¯ int ( 0 ) ( r ¯ ) ] · G ¯ ( k r ¯ / k r ¯ ) d s .
lim k r E ¯ s ( r ¯ ) = F ¯ s ( θ , ϕ ) exp ( j k r ) r ,

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