Abstract

The use of Gaussian elimination with backsubstitution for matrix inversion in scattering theories is discussed. Within the framework of the T-matrix method (the state-of-the-art code by Mishchenko is freely available at http://www.giss.nasa.gov/∼crmim), it is shown that the domain of applicability of Mishchenko’s fortran 77 (F77) code can be substantially expanded in the direction of strongly absorbing particles where the current code fails to converge. Such an extension is especially important if the code is to be used in nanoplasmonic or nanophotonic applications involving metallic particles. At the same time, convergence can also be achieved for large nonabsorbing particles, in which case the non–Numerical Algorithms Group option of Mishchenko’s code diverges. Computer F77 implementation of Mishchenko’s code supplemented with Gaussian elimination with backsubstitution is freely available at http://www.wave-scattering.com.

© 2005 Optical Society of America

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References

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  1. P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969).
    [CrossRef]
  2. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
    [CrossRef]
  3. L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).
  4. M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computation of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
    [CrossRef]
  5. M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).
  6. V. G. Farafonov, N. V. Voshchinnikov, V. V. Somsikov, “Light-scattering by a core-mantle spheroidal particle,” Appl. Opt. 35, 5412–5425 (1996).
    [CrossRef] [PubMed]
  7. J. B. Pendry, Low Energy Electron Diffraction (Academic, London, 1974).
  8. J. M. McLaren, S. Crampin, D. D. Vvedensky, R. C. Albers, J. B. Pendry, “Layer KKR electronic structure code for bulk and interface geometries,” Comput. Phys. Commun. 60, 365–389 (1990).
    [CrossRef]
  9. N. Stefanou, V. Yannopapas, A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
    [CrossRef]
  10. V. Poborchii, T. Tada, T. Kanayama, A. Moroz, “Silver-coated silicon-pillar photonic crystals: enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
    [CrossRef]
  11. A. Moroz, “Metallo-dielectric diamond and zinc-blende photonic crystals,” Phys. Rev. B 66, 115109 (2002).
    [CrossRef]
  12. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in 77 (Cambridge U. Press, Cambridge, UK, 2001); see also http://www.nr.com .
  13. I. Ederra, R. Gonzalo, C. Mann, A. Moroz, P. de Maagt, “(Sub)mm-wave components and subsystems based on EBG technology,” in Proceedings of International Conference on Electromagnetics in Advanced Applications (ICEAA2003), (n.p., 2003), pp. 643–646.
  14. J. T. Krug, E. J. Sánchez, X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys. 116, 10895–10901 (2002).
    [CrossRef]

2003 (1)

V. Poborchii, T. Tada, T. Kanayama, A. Moroz, “Silver-coated silicon-pillar photonic crystals: enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
[CrossRef]

2002 (2)

A. Moroz, “Metallo-dielectric diamond and zinc-blende photonic crystals,” Phys. Rev. B 66, 115109 (2002).
[CrossRef]

J. T. Krug, E. J. Sánchez, X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys. 116, 10895–10901 (2002).
[CrossRef]

1998 (1)

N. Stefanou, V. Yannopapas, A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

1996 (2)

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computation of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

V. G. Farafonov, N. V. Voshchinnikov, V. V. Somsikov, “Light-scattering by a core-mantle spheroidal particle,” Appl. Opt. 35, 5412–5425 (1996).
[CrossRef] [PubMed]

1990 (1)

J. M. McLaren, S. Crampin, D. D. Vvedensky, R. C. Albers, J. B. Pendry, “Layer KKR electronic structure code for bulk and interface geometries,” Comput. Phys. Commun. 60, 365–389 (1990).
[CrossRef]

1971 (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

1969 (1)

P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969).
[CrossRef]

Albers, R. C.

J. M. McLaren, S. Crampin, D. D. Vvedensky, R. C. Albers, J. B. Pendry, “Layer KKR electronic structure code for bulk and interface geometries,” Comput. Phys. Commun. 60, 365–389 (1990).
[CrossRef]

Crampin, S.

J. M. McLaren, S. Crampin, D. D. Vvedensky, R. C. Albers, J. B. Pendry, “Layer KKR electronic structure code for bulk and interface geometries,” Comput. Phys. Commun. 60, 365–389 (1990).
[CrossRef]

de Maagt, P.

I. Ederra, R. Gonzalo, C. Mann, A. Moroz, P. de Maagt, “(Sub)mm-wave components and subsystems based on EBG technology,” in Proceedings of International Conference on Electromagnetics in Advanced Applications (ICEAA2003), (n.p., 2003), pp. 643–646.

Ederra, I.

I. Ederra, R. Gonzalo, C. Mann, A. Moroz, P. de Maagt, “(Sub)mm-wave components and subsystems based on EBG technology,” in Proceedings of International Conference on Electromagnetics in Advanced Applications (ICEAA2003), (n.p., 2003), pp. 643–646.

Farafonov, V. G.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in 77 (Cambridge U. Press, Cambridge, UK, 2001); see also http://www.nr.com .

Gonzalo, R.

I. Ederra, R. Gonzalo, C. Mann, A. Moroz, P. de Maagt, “(Sub)mm-wave components and subsystems based on EBG technology,” in Proceedings of International Conference on Electromagnetics in Advanced Applications (ICEAA2003), (n.p., 2003), pp. 643–646.

Kanayama, T.

V. Poborchii, T. Tada, T. Kanayama, A. Moroz, “Silver-coated silicon-pillar photonic crystals: enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
[CrossRef]

Kong, J. A.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Krug, J. T.

J. T. Krug, E. J. Sánchez, X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys. 116, 10895–10901 (2002).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computation of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Mann, C.

I. Ederra, R. Gonzalo, C. Mann, A. Moroz, P. de Maagt, “(Sub)mm-wave components and subsystems based on EBG technology,” in Proceedings of International Conference on Electromagnetics in Advanced Applications (ICEAA2003), (n.p., 2003), pp. 643–646.

McLaren, J. M.

J. M. McLaren, S. Crampin, D. D. Vvedensky, R. C. Albers, J. B. Pendry, “Layer KKR electronic structure code for bulk and interface geometries,” Comput. Phys. Commun. 60, 365–389 (1990).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computation of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).

Modinos, A.

N. Stefanou, V. Yannopapas, A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

Moroz, A.

V. Poborchii, T. Tada, T. Kanayama, A. Moroz, “Silver-coated silicon-pillar photonic crystals: enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
[CrossRef]

A. Moroz, “Metallo-dielectric diamond and zinc-blende photonic crystals,” Phys. Rev. B 66, 115109 (2002).
[CrossRef]

I. Ederra, R. Gonzalo, C. Mann, A. Moroz, P. de Maagt, “(Sub)mm-wave components and subsystems based on EBG technology,” in Proceedings of International Conference on Electromagnetics in Advanced Applications (ICEAA2003), (n.p., 2003), pp. 643–646.

Pendry, J. B.

J. M. McLaren, S. Crampin, D. D. Vvedensky, R. C. Albers, J. B. Pendry, “Layer KKR electronic structure code for bulk and interface geometries,” Comput. Phys. Commun. 60, 365–389 (1990).
[CrossRef]

J. B. Pendry, Low Energy Electron Diffraction (Academic, London, 1974).

Poborchii, V.

V. Poborchii, T. Tada, T. Kanayama, A. Moroz, “Silver-coated silicon-pillar photonic crystals: enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in 77 (Cambridge U. Press, Cambridge, UK, 2001); see also http://www.nr.com .

Sánchez, E. J.

J. T. Krug, E. J. Sánchez, X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys. 116, 10895–10901 (2002).
[CrossRef]

Shin, R. T.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Somsikov, V. V.

Stefanou, N.

N. Stefanou, V. Yannopapas, A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

Tada, T.

V. Poborchii, T. Tada, T. Kanayama, A. Moroz, “Silver-coated silicon-pillar photonic crystals: enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in 77 (Cambridge U. Press, Cambridge, UK, 2001); see also http://www.nr.com .

Travis, L. D.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computation of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).

Tsang, L.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in 77 (Cambridge U. Press, Cambridge, UK, 2001); see also http://www.nr.com .

Voshchinnikov, N. V.

Vvedensky, D. D.

J. M. McLaren, S. Crampin, D. D. Vvedensky, R. C. Albers, J. B. Pendry, “Layer KKR electronic structure code for bulk and interface geometries,” Comput. Phys. Commun. 60, 365–389 (1990).
[CrossRef]

Waterman, P. C.

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969).
[CrossRef]

Xie, X. S.

J. T. Krug, E. J. Sánchez, X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys. 116, 10895–10901 (2002).
[CrossRef]

Yannopapas, V.

N. Stefanou, V. Yannopapas, A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

V. Poborchii, T. Tada, T. Kanayama, A. Moroz, “Silver-coated silicon-pillar photonic crystals: enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
[CrossRef]

Comput. Phys. Commun. (2)

J. M. McLaren, S. Crampin, D. D. Vvedensky, R. C. Albers, J. B. Pendry, “Layer KKR electronic structure code for bulk and interface geometries,” Comput. Phys. Commun. 60, 365–389 (1990).
[CrossRef]

N. Stefanou, V. Yannopapas, A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113, 49–77 (1998).
[CrossRef]

J. Acoust. Soc. Am. (1)

P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969).
[CrossRef]

J. Chem. Phys. (1)

J. T. Krug, E. J. Sánchez, X. S. Xie, “Design of near-field optical probes with optimal field enhancement by finite difference time domain electromagnetic simulation,” J. Chem. Phys. 116, 10895–10901 (2002).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computation of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Phys. Rev. B (1)

A. Moroz, “Metallo-dielectric diamond and zinc-blende photonic crystals,” Phys. Rev. B 66, 115109 (2002).
[CrossRef]

Phys. Rev. D (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Other (5)

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).

J. B. Pendry, Low Energy Electron Diffraction (Academic, London, 1974).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in 77 (Cambridge U. Press, Cambridge, UK, 2001); see also http://www.nr.com .

I. Ederra, R. Gonzalo, C. Mann, A. Moroz, P. de Maagt, “(Sub)mm-wave components and subsystems based on EBG technology,” in Proceedings of International Conference on Electromagnetics in Advanced Applications (ICEAA2003), (n.p., 2003), pp. 643–646.

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Tables (2)

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Table 1 Comparison of the Total Extinction Efficiency as Calculated by Mishchenko’s Code with Three Different Inversion Techniques for the Case of a Sphere in Vacuuma

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Table 2 Comparison of the Total Extinction Efficiency as Calculated by Mishchenko’s Code with Three Different Inversion Techniques for the Case of a Prolate Spheroid with an Aspect Ratio 2 in Vacuumaa

Equations (6)

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T = Rg ( Q ) Q 1 ,
Q I = Q 2 I [ 1 Q I I I Q 2 III ] 1 Q 1 I , Q I I = Q 2 I I + Q 2 I Q 1 I I [ 1 Q 2 III Q 1 I I ] 1 Q 2 I V , Q III = Q 2 III + Q 1 I V Q 2 III [ 1 Q 1 I I Q 2 III ] 1 Q 1 I , Q I V = Q 2 I V [ 1 Q 2 III Q 1 I I ] 1 Q 2 I V .
T Q = Rg ( Q ) ,
[ x 1 , x 2 , x 3 , x 4 ] [ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44 ] = [ b 1 , b 2 , b 3 , b 4 ] .
[ x 1 , x 2 , x 3 , x 4 ] [ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44 ] = [ b 1 , b 2 , b 3 , b 4 ] .
x j = 1 a j j [ b j k = j + 1 N x k a k j ] ,

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