Abstract

The iterative extended boundary condition method (IEBCM) is utilized to calculate scattering and absorption by metallic colloids and carbon aerosols in the 0.4-μm < λ < 10-μm optical wavelength range. The colloids and aerosols were modeled by dielectric spheroids of high aspect ratio. The new IEBCM method is found to be suitable for making calculations for particles with aspect ratios as high as 12. Results are presented for silver and aluminum metallic aerosols as well as for atmospheric aerosols such as soot and iron oxides (magnetite). The various parameters used to examine the convergence of the IEBCM solution, such as the number of subdomain expansions and the size of the incremental change in intermediate object sizes used in the iterative process, are discussed. Using the internal field distribution to test the convergence of the results is also found to be more accurate than the traditional procedure which utilizes extinction and scattering cross-section data.

© 1986 Optical Society of America

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References

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  1. R. K. Chang, T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, New York, 1982).
    [CrossRef]
  2. R. H. Kohl, D. Stroud, Eds., Proceedings, Chemical Research and Development Center’s 1984 Scientific Conference on Obscuration and Aerosol Research, CRDC-SP-85007 (June1985).
  3. T. P. Ackerman, O. B. Toon, “Absorption of Visible Radiation in Atmosphere Containing Mixtures of Absorbing and Nonabsorbing Particles,” Appl. Opt. 20, 3661 (1981).
    [CrossRef] [PubMed]
  4. P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
    [CrossRef]
  5. V. K. Varadan, V. V. Varadan, Eds., Acoustic, Electromagnetic, and Elastic Wave Scattering, Focus on the T-Matrix Approach (Pergamon, New York, 1980).
  6. M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, “Irradiation of Prolate Spheroidal Models of Humans in the Near Field of a Short Electric Dipole,” IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
    [CrossRef]
  7. M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317 (1983).
    [CrossRef]
  8. M. F. Iskander, A. Lakhtakia, “Extension of the Iterative EBCM to Calculate Scattering by Low-Loss or Lossless Elongated Dielectric Objects,” Appl. Opt. 23, 948 (1984).
    [CrossRef] [PubMed]
  9. 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]
  10. A. Lakhtakia, M. F. Iskander, “Theoretical and Experimental Evaluation of Power Absorption in Elongated Objects At and Beyond Resonance,” IEEE Trans. Electromag. Compat. EMC-25, 448 (1983).
    [CrossRef]
  11. M. F. Iskander, S. C. Olson, C. H. Durney, “Extension of the Iterative EBCM to Calculate Scattering by Low-Loss Elongated Dielectric Objects and its Hybridization with the Geometrical Optics Approximation,” in International IEEE/APS Symposium and National Radio Science Meeting, Boston, (2 June 1984), pp. 948–953.
  12. B. P. Sinha, M. F. R. Cooray, “Electromagnetic Scattering by Dielectric Prolate Spheroids,” presented at the National Radio Science Meeting, U. Colorado, Boulder, 13–16, Jan. 1986.

1984 (1)

1983 (3)

M. F. Iskander, A. Lakhtakia, C. H. Durney, “A New Procedure for Improving the Solution Stability and Extending the Frequency Range of the 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]

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

1982 (1)

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[CrossRef]

1981 (1)

1980 (1)

M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, “Irradiation of Prolate Spheroidal Models of Humans in the Near Field of a Short Electric Dipole,” IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

Ackerman, T. P.

Barber, P. W.

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[CrossRef]

M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, “Irradiation of Prolate Spheroidal Models of Humans in the Near Field of a Short Electric Dipole,” IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

Chang, R. K.

R. K. Chang, T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, New York, 1982).
[CrossRef]

Cooray, M. F. R.

B. P. Sinha, M. F. R. Cooray, “Electromagnetic Scattering by Dielectric Prolate Spheroids,” presented at the National Radio Science Meeting, U. Colorado, Boulder, 13–16, Jan. 1986.

Durney, C. H.

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 the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, “Irradiation of Prolate Spheroidal Models of Humans in the Near Field of a Short Electric Dipole,” IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

M. F. Iskander, S. C. Olson, C. H. Durney, “Extension of the Iterative EBCM to Calculate Scattering by Low-Loss Elongated Dielectric Objects and its Hybridization with the Geometrical Optics Approximation,” in International IEEE/APS Symposium and National Radio Science Meeting, Boston, (2 June 1984), pp. 948–953.

Furtak, T. E.

R. K. Chang, T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, New York, 1982).
[CrossRef]

Iskander, M. F.

M. F. Iskander, A. Lakhtakia, “Extension of the Iterative EBCM to Calculate Scattering by Low-Loss or Lossless Elongated Dielectric Objects,” Appl. Opt. 23, 948 (1984).
[CrossRef] [PubMed]

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 the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

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

M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, “Irradiation of Prolate Spheroidal Models of Humans in the Near Field of a Short Electric Dipole,” IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

M. F. Iskander, S. C. Olson, C. H. Durney, “Extension of the Iterative EBCM to Calculate Scattering by Low-Loss Elongated Dielectric Objects and its Hybridization with the Geometrical Optics Approximation,” in International IEEE/APS Symposium and National Radio Science Meeting, Boston, (2 June 1984), pp. 948–953.

Lakhtakia, A.

M. F. Iskander, A. Lakhtakia, “Extension of the Iterative EBCM to Calculate Scattering by Low-Loss or Lossless Elongated Dielectric Objects,” Appl. Opt. 23, 948 (1984).
[CrossRef] [PubMed]

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 the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317 (1983).
[CrossRef]

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

Massoudi, H.

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[CrossRef]

M. F. Iskander, P. W. Barber, C. H. Durney, H. Massoudi, “Irradiation of Prolate Spheroidal Models of Humans in the Near Field of a Short Electric Dipole,” IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

Olson, S. C.

M. F. Iskander, S. C. Olson, C. H. Durney, “Extension of the Iterative EBCM to Calculate Scattering by Low-Loss Elongated Dielectric Objects and its Hybridization with the Geometrical Optics Approximation,” in International IEEE/APS Symposium and National Radio Science Meeting, Boston, (2 June 1984), pp. 948–953.

Sinha, B. P.

B. P. Sinha, M. F. R. Cooray, “Electromagnetic Scattering by Dielectric Prolate Spheroids,” presented at the National Radio Science Meeting, U. Colorado, Boulder, 13–16, Jan. 1986.

Toon, O. B.

Aerosol Sci. Technol. (1)

P. W. Barber, H. Massoudi, “Recent Advances in Light Scattering Calculations for Nonspherical Particles,” Aerosol Sci. Technol. 1, 303 (1982).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (1)

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

IEEE Trans. Electromag. Compat. (1)

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

IEEE Trans. Microwave Theory Tech. (2)

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, P. W. Barber, C. H. Durney, H. Massoudi, “Irradiation of Prolate Spheroidal Models of Humans in the Near Field of a Short Electric Dipole,” IEEE Trans. Microwave Theory Tech. MTT-28, 801 (1980).
[CrossRef]

Other (5)

V. K. Varadan, V. V. Varadan, Eds., Acoustic, Electromagnetic, and Elastic Wave Scattering, Focus on the T-Matrix Approach (Pergamon, New York, 1980).

M. F. Iskander, S. C. Olson, C. H. Durney, “Extension of the Iterative EBCM to Calculate Scattering by Low-Loss Elongated Dielectric Objects and its Hybridization with the Geometrical Optics Approximation,” in International IEEE/APS Symposium and National Radio Science Meeting, Boston, (2 June 1984), pp. 948–953.

B. P. Sinha, M. F. R. Cooray, “Electromagnetic Scattering by Dielectric Prolate Spheroids,” presented at the National Radio Science Meeting, U. Colorado, Boulder, 13–16, Jan. 1986.

R. K. Chang, T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, New York, 1982).
[CrossRef]

R. H. Kohl, D. Stroud, Eds., Proceedings, Chemical Research and Development Center’s 1984 Scientific Conference on Obscuration and Aerosol Research, CRDC-SP-85007 (June1985).

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Figures (9)

Fig. 1
Fig. 1

Magnitude of the axial electric field distribution in magnetite, * = 2.4 − j0.83, semimajor axis = 100 nm, and aspect ratio a/b = 4 and 9. The direction of propagation of the incident plane electromagnetic wave is along the major axis of the spheroid. The incident wavelength is λ = 0.4 μm

Fig. 2
Fig. 2

Magnitude of the axial electric field distribution in soot spheroidal particles of * = 1.88 − j0.69, semimajor axis a = 100 nm, and aspect ratio a/b = 3 and 9. The direction of the incident plane wave is the same as Fig. 1, and the free space wavelength λ = 0.4 μm.

Fig. 3
Fig. 3

Extinction and scattering cross sections of magnetite and soot spheroidal particles (a = 100 nm) as a function of the aspect ratio a/b.2 The incident plane wave wavelength is λ = 0.4 μm.

Fig. 4
Fig. 4

Geometrical locations of the points ah along the axis z of the spheroid and utilized in the results given in Tables II and III.

Fig. 5
Fig. 5

Extinction and scattering efficiencies as well as axial field distribution (V/m) values are presented to show the importance of using the distribution as an indicator of the convergence of the solution instead of the efficiencies. The dielectric used was * = 3.058 + j0.0 with ka = 1.5707, a = 100 nm, and a/b = 8.0. Five and nine internal expansions were used for (a) and (b), respectively.

Fig. 6
Fig. 6

Origin locations and the number of internal expansionsused for three of the many possible numerical models used for the IEBCM: (a) three internal expansions close together; (b) three internal expansions spread far apart; (c) five internal expansions.

Fig. 7
Fig. 7

Numerical results obtained from the IEBCM for the three models shown in Fig. 6. The dielectric used is soot evaluated at ka = 1.5707, λ = 0.4 μm, a = 100 nm, a/b = 7, and * = 1.88–j0.69. It is to be emphasized that the modeling for (b) and (c) resulted in the same solution, whereas the model for (a) did not converge to the proper solution.

Fig. 8
Fig. 8

Results demonstrating the impact on the convergence of the solution by varying the total number of coefficients in each expansion used in the IEBCM solution procedure. Models (a)–(d) used seven internal expansions. The models used the following number of internal expansion coefficients: (a) 52; (b) 59; (c) 66; and (d) 73. The dielectric evaluated was magnetite with ka = 1.5707, λ = 0.4 μm, a = 100.0 nm, and a/b = 7.0, and * = 3.058 + j0.0.

Fig. 9
Fig. 9

IEBCM results demonstrating the effect on the convergence of the solution due to the size of the incremental change in geometry from one solution to the next. The same dielectric, geometrical, and electrical parameters used for Fig. 8 were used in this case also. Seven internal expansions were used in all cases. The change in the shape of the geometries in terms of aspect ratios is as follows: (a) 3:1–9:1; (b) 5:1–9:1; (c) 7:1–9:1; and (d) 8:1–9:1.

Tables (3)

Tables Icon

Table I Comparison between the Basic Features of the Regular (EBCM) and the New Advantages of the New Iterative Technique

Tables Icon

Table II Comparison Between the EBCM and IEBCM Results for Elongated Objectsa

Tables Icon

Table III Comparison Between the EBCM and IEBCM Results for a Spheroidal Soot Particle of Semimajor Axis a = 100 nm and as High an Aspect Ratio as ga

Equations (2)

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{ E ¯ i ( r ) + × s [ n ^ ( r ¯ ) × E ¯ int ( l - 1 ) ( r ¯ ) · G ¯ ( k r ¯ ) / k r ¯ ] d s - × × 1 j ω 0 [ n ^ ( r ¯ ) × H ¯ int ( l - 1 ) ( r ¯ ) · G ¯ ( k r ¯ ) / k r ¯ ) ] d s } = × × s 1 j ω 0 [ n ^ ( r ¯ ) × Δ H ¯ + ( l ) ( 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 - × × 1 j ω 0 [ n ^ ( r ¯ ) × H ¯ int ( - 1 ) ( r ¯ ) ] · G ¯ ( k r ¯ / k r ¯ ) ] d s - × s 1 j ω 0 r * [ n ^ ( r ¯ ) × × Δ H ¯ + ( 0 ) ( r ¯ ) ] · G ¯ ( k r ¯ / k r ¯ ) ] d s ,

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