Abstract

The performance of most widespread surface integral equation (SIE) formulations with the method of moments (MoM) are studied in the context of plasmonic materials. Although not yet widespread in optics, SIE-MoM approaches bring important advantages for the rigorous analysis of penetrable plasmonic bodies. Criteria such as accuracy in near and far field calculations, iterative convergence and reliability are addressed to assess the suitability of these formulations in the field of plasmonics.

© 2012 OSA

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  1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  2. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
    [CrossRef] [PubMed]
  3. S. Kawata, ed., Near-Field Optis and Surface Plasmon Polaritons (Springer, 2010).
  4. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005).
    [CrossRef] [PubMed]
  5. L. Novotny and N. F. van Hulst, “Antennas for Light,” Nat. Photonics5(2), 83–90 (2011).
    [CrossRef]
  6. P. Biagioni, J. S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Physics Optics arXiv:1103.1568v1, (2011).
  7. J. Zhou, Y. Zhou, S. L. Ng, H. X. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, “Three-dimensional photonic band gap structure of a polymer-metal composite,” Appl. Phys. Lett.76, 3337–3339 (2000).
  8. B. T. Schwartz and R. Piestun, “Total external reflection from metamaterials with ultralow refractive index,” J. Opt. Soc. Am. B20(12), 2448–2453 (2003).
    [CrossRef]
  9. M. Salaün, B. Corbett, S. B. Newcomb, and M. E. Pemble, “Fabrication and characterization of three-dimensional silver/air inverted opal photonic crystals,” J. Mater. Chem.20(36), 7870–7874 (2010).
    [CrossRef]
  10. A. Taflove and M. E. Brodwin, “Numerical solution of steadystate electromagnetic scattering problems using the timedependent Maxwell’s equations,” IEEE Trans. Microw. Theory Tech.23(8), 623–630 (1975).
    [CrossRef]
  11. T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Arch. Elektron. Übertragungstech.31, 116–120 (1977).
  12. R. F. Harrington, Field Computation by Moment Method (IEEE Press, 1993).
  13. A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A26(4), 732–740 (2009).
    [CrossRef] [PubMed]
  14. B. Gallinet, A. M. Kern, and O. J. F. Martin, “Accurate and versatile modeling of electromagnetic scattering on periodic nanostructures with a surface integral approach,” J. Opt. Soc. Am. A27(10), 2261–2271 (2010).
    [CrossRef] [PubMed]
  15. J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, “Method-of-moments formulation for the analysis of plasmonic nano-optical antennas,” J. Opt. Soc. Am. A28(7), 1341–1348 (2011).
    [CrossRef] [PubMed]
  16. P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci.40(6), RS6002 (2005).
    [CrossRef]
  17. Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antenn. Propag.57(1), 176–187 (2009).
    [CrossRef]
  18. M. G. Araújo, J. M. Taboada, J. Rivero, and F. Obelleiro, “Comparison of Surface Integral Equations for Left-Handed Materials,” Prog. Electromagn. Res.118, 425–440 (2011).
    [CrossRef]
  19. Ö. Ergül, “Fast and Accurate Analysis of Homogenized Metamaterials With the Surface Integral Equations and the Multilevel Fast Multipole Algorithm,” IEEE Antennas Wirel. Propag. Lett.10, 1286–1289 (2011).
    [CrossRef]
  20. J. R. Mautz and R. F. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag.33, 71–80 (1979).
  21. C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer, 1969).
  22. P. Ylä-Oijala and M. Taskinen, “Well-conditioned Müller formulation for electromagnetic scattering by dielectric objects,” IEEE Trans. Antenn. Propag.53(10), 3316–3323 (2005).
    [CrossRef]
  23. P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antenn. Propag.53(3), 1168–1173 (2005).
    [CrossRef]
  24. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley, 1983).
  25. S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag.30(3), 409–418 (1982).
    [CrossRef]
  26. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
    [CrossRef]
  27. G. Hass and J. E. Waylonis, “Optical Constants and Reflectance and Transmittance of Evaporated Aluminum in the Visible and Ultraviolet,” J. Opt. Soc. Am.51(7), 719–722 (1961).
    [CrossRef]
  28. D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag.32(3), 276–281 (1984).
    [CrossRef]
  29. R. E. Hodges and Y. Rahmat-Samii, “The evaluation of MFIE integrals with the use of vector triangle basis functions,” Microw. Opt. Technol. Lett.14(1), 9–14 (1997).
    [CrossRef]
  30. R. D. Graglia, “On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,” IEEE Trans. Antenn. Propag.41(10), 1448–1455 (1993).
    [CrossRef]
  31. P. Ylä-Oijala and M. Taskinen, “Calculation of CFIE impedance matrix elements with RWG andn^× RWG functions,” IEEE Trans. Antenn. Propag.51(8), 1837–1846 (2003).
    [CrossRef]
  32. A. Ishimaru, Electromagnetic Wave Propagation, Radiation and Scattering (Prentice-Hall, 1991).
  33. Y. Saad and M. Schultz, “Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAMJ. Sci. Statist. Comput.7(3), 856–869 (1986).
    [CrossRef]
  34. T. W. Lloyd, J. M. Song, and M. Yang, “Numerical study of surface integral formulations for low-contrast objects,” IEEE Antennas Wirel. Propag. Lett.4(1), 482–485 (2005).
    [CrossRef]
  35. P. Ylä-Oijala and M. Taskinen, “Improving conditioning of electromagnetic surface integral equations using normalized field quantities,” IEEE Trans. Antenn. Propag.55(1), 178–185 (2007).
    [CrossRef]
  36. Y. A. Liu and W. C. Chew, “Stability of surface integral equation for left-handed materials,” IEEE Trans. Microw. Antennas Propag.1(1), 84–89 (2007).
    [CrossRef]

2011

L. Novotny and N. F. van Hulst, “Antennas for Light,” Nat. Photonics5(2), 83–90 (2011).
[CrossRef]

M. G. Araújo, J. M. Taboada, J. Rivero, and F. Obelleiro, “Comparison of Surface Integral Equations for Left-Handed Materials,” Prog. Electromagn. Res.118, 425–440 (2011).
[CrossRef]

Ö. Ergül, “Fast and Accurate Analysis of Homogenized Metamaterials With the Surface Integral Equations and the Multilevel Fast Multipole Algorithm,” IEEE Antennas Wirel. Propag. Lett.10, 1286–1289 (2011).
[CrossRef]

J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, “Method-of-moments formulation for the analysis of plasmonic nano-optical antennas,” J. Opt. Soc. Am. A28(7), 1341–1348 (2011).
[CrossRef] [PubMed]

2010

B. Gallinet, A. M. Kern, and O. J. F. Martin, “Accurate and versatile modeling of electromagnetic scattering on periodic nanostructures with a surface integral approach,” J. Opt. Soc. Am. A27(10), 2261–2271 (2010).
[CrossRef] [PubMed]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

M. Salaün, B. Corbett, S. B. Newcomb, and M. E. Pemble, “Fabrication and characterization of three-dimensional silver/air inverted opal photonic crystals,” J. Mater. Chem.20(36), 7870–7874 (2010).
[CrossRef]

2009

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antenn. Propag.57(1), 176–187 (2009).
[CrossRef]

A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A26(4), 732–740 (2009).
[CrossRef] [PubMed]

2007

P. Ylä-Oijala and M. Taskinen, “Improving conditioning of electromagnetic surface integral equations using normalized field quantities,” IEEE Trans. Antenn. Propag.55(1), 178–185 (2007).
[CrossRef]

Y. A. Liu and W. C. Chew, “Stability of surface integral equation for left-handed materials,” IEEE Trans. Microw. Antennas Propag.1(1), 84–89 (2007).
[CrossRef]

2005

T. W. Lloyd, J. M. Song, and M. Yang, “Numerical study of surface integral formulations for low-contrast objects,” IEEE Antennas Wirel. Propag. Lett.4(1), 482–485 (2005).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Well-conditioned Müller formulation for electromagnetic scattering by dielectric objects,” IEEE Trans. Antenn. Propag.53(10), 3316–3323 (2005).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antenn. Propag.53(3), 1168–1173 (2005).
[CrossRef]

P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci.40(6), RS6002 (2005).
[CrossRef]

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

2003

B. T. Schwartz and R. Piestun, “Total external reflection from metamaterials with ultralow refractive index,” J. Opt. Soc. Am. B20(12), 2448–2453 (2003).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Calculation of CFIE impedance matrix elements with RWG andn^× RWG functions,” IEEE Trans. Antenn. Propag.51(8), 1837–1846 (2003).
[CrossRef]

2000

J. Zhou, Y. Zhou, S. L. Ng, H. X. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, “Three-dimensional photonic band gap structure of a polymer-metal composite,” Appl. Phys. Lett.76, 3337–3339 (2000).

1997

R. E. Hodges and Y. Rahmat-Samii, “The evaluation of MFIE integrals with the use of vector triangle basis functions,” Microw. Opt. Technol. Lett.14(1), 9–14 (1997).
[CrossRef]

1993

R. D. Graglia, “On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,” IEEE Trans. Antenn. Propag.41(10), 1448–1455 (1993).
[CrossRef]

1986

Y. Saad and M. Schultz, “Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAMJ. Sci. Statist. Comput.7(3), 856–869 (1986).
[CrossRef]

1984

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag.32(3), 276–281 (1984).
[CrossRef]

1982

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag.30(3), 409–418 (1982).
[CrossRef]

1979

J. R. Mautz and R. F. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag.33, 71–80 (1979).

1977

T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Arch. Elektron. Übertragungstech.31, 116–120 (1977).

1975

A. Taflove and M. E. Brodwin, “Numerical solution of steadystate electromagnetic scattering problems using the timedependent Maxwell’s equations,” IEEE Trans. Microw. Theory Tech.23(8), 623–630 (1975).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

1961

Al-Bundak, O. M.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag.32(3), 276–281 (1984).
[CrossRef]

Araújo, M. G.

M. G. Araújo, J. M. Taboada, J. Rivero, and F. Obelleiro, “Comparison of Surface Integral Equations for Left-Handed Materials,” Prog. Electromagn. Res.118, 425–440 (2011).
[CrossRef]

J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, “Method-of-moments formulation for the analysis of plasmonic nano-optical antennas,” J. Opt. Soc. Am. A28(7), 1341–1348 (2011).
[CrossRef] [PubMed]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Brodwin, M. E.

A. Taflove and M. E. Brodwin, “Numerical solution of steadystate electromagnetic scattering problems using the timedependent Maxwell’s equations,” IEEE Trans. Microw. Theory Tech.23(8), 623–630 (1975).
[CrossRef]

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Butler, C. M.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag.32(3), 276–281 (1984).
[CrossRef]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Chan, Y. C.

J. Zhou, Y. Zhou, S. L. Ng, H. X. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, “Three-dimensional photonic band gap structure of a polymer-metal composite,” Appl. Phys. Lett.76, 3337–3339 (2000).

Chew, W. C.

Y. A. Liu and W. C. Chew, “Stability of surface integral equation for left-handed materials,” IEEE Trans. Microw. Antennas Propag.1(1), 84–89 (2007).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Corbett, B.

M. Salaün, B. Corbett, S. B. Newcomb, and M. E. Pemble, “Fabrication and characterization of three-dimensional silver/air inverted opal photonic crystals,” J. Mater. Chem.20(36), 7870–7874 (2010).
[CrossRef]

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Ergül, Ö.

Ö. Ergül, “Fast and Accurate Analysis of Homogenized Metamaterials With the Surface Integral Equations and the Multilevel Fast Multipole Algorithm,” IEEE Antennas Wirel. Propag. Lett.10, 1286–1289 (2011).
[CrossRef]

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antenn. Propag.57(1), 176–187 (2009).
[CrossRef]

Gallinet, B.

Glisson, A. W.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag.32(3), 276–281 (1984).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag.30(3), 409–418 (1982).
[CrossRef]

Graglia, R. D.

R. D. Graglia, “On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,” IEEE Trans. Antenn. Propag.41(10), 1448–1455 (1993).
[CrossRef]

Gürel, L.

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antenn. Propag.57(1), 176–187 (2009).
[CrossRef]

Harrington, R. F.

J. R. Mautz and R. F. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag.33, 71–80 (1979).

Hass, G.

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Hodges, R. E.

R. E. Hodges and Y. Rahmat-Samii, “The evaluation of MFIE integrals with the use of vector triangle basis functions,” Microw. Opt. Technol. Lett.14(1), 9–14 (1997).
[CrossRef]

Järvenpää, S.

P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci.40(6), RS6002 (2005).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Kam, C. H.

J. Zhou, Y. Zhou, S. L. Ng, H. X. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, “Three-dimensional photonic band gap structure of a polymer-metal composite,” Appl. Phys. Lett.76, 3337–3339 (2000).

Kern, A. M.

Lam, Y. L.

J. Zhou, Y. Zhou, S. L. Ng, H. X. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, “Three-dimensional photonic band gap structure of a polymer-metal composite,” Appl. Phys. Lett.76, 3337–3339 (2000).

Landesa, L.

Liu, Y. A.

Y. A. Liu and W. C. Chew, “Stability of surface integral equation for left-handed materials,” IEEE Trans. Microw. Antennas Propag.1(1), 84–89 (2007).
[CrossRef]

Lloyd, T. W.

T. W. Lloyd, J. M. Song, and M. Yang, “Numerical study of surface integral formulations for low-contrast objects,” IEEE Antennas Wirel. Propag. Lett.4(1), 482–485 (2005).
[CrossRef]

Martin, O. J. F.

Mautz, J. R.

J. R. Mautz and R. F. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag.33, 71–80 (1979).

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Newcomb, S. B.

M. Salaün, B. Corbett, S. B. Newcomb, and M. E. Pemble, “Fabrication and characterization of three-dimensional silver/air inverted opal photonic crystals,” J. Mater. Chem.20(36), 7870–7874 (2010).
[CrossRef]

Ng, S. L.

J. Zhou, Y. Zhou, S. L. Ng, H. X. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, “Three-dimensional photonic band gap structure of a polymer-metal composite,” Appl. Phys. Lett.76, 3337–3339 (2000).

Novotny, L.

L. Novotny and N. F. van Hulst, “Antennas for Light,” Nat. Photonics5(2), 83–90 (2011).
[CrossRef]

Obelleiro, F.

M. G. Araújo, J. M. Taboada, J. Rivero, and F. Obelleiro, “Comparison of Surface Integral Equations for Left-Handed Materials,” Prog. Electromagn. Res.118, 425–440 (2011).
[CrossRef]

J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, “Method-of-moments formulation for the analysis of plasmonic nano-optical antennas,” J. Opt. Soc. Am. A28(7), 1341–1348 (2011).
[CrossRef] [PubMed]

Pemble, M. E.

M. Salaün, B. Corbett, S. B. Newcomb, and M. E. Pemble, “Fabrication and characterization of three-dimensional silver/air inverted opal photonic crystals,” J. Mater. Chem.20(36), 7870–7874 (2010).
[CrossRef]

Piestun, R.

Pohl, D. W.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Que, W. X.

J. Zhou, Y. Zhou, S. L. Ng, H. X. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, “Three-dimensional photonic band gap structure of a polymer-metal composite,” Appl. Phys. Lett.76, 3337–3339 (2000).

Rahmat-Samii, Y.

R. E. Hodges and Y. Rahmat-Samii, “The evaluation of MFIE integrals with the use of vector triangle basis functions,” Microw. Opt. Technol. Lett.14(1), 9–14 (1997).
[CrossRef]

Rao, S. M.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag.32(3), 276–281 (1984).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag.30(3), 409–418 (1982).
[CrossRef]

Rivero, J.

M. G. Araújo, J. M. Taboada, J. Rivero, and F. Obelleiro, “Comparison of Surface Integral Equations for Left-Handed Materials,” Prog. Electromagn. Res.118, 425–440 (2011).
[CrossRef]

J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, “Method-of-moments formulation for the analysis of plasmonic nano-optical antennas,” J. Opt. Soc. Am. A28(7), 1341–1348 (2011).
[CrossRef] [PubMed]

Saad, Y.

Y. Saad and M. Schultz, “Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAMJ. Sci. Statist. Comput.7(3), 856–869 (1986).
[CrossRef]

Salaün, M.

M. Salaün, B. Corbett, S. B. Newcomb, and M. E. Pemble, “Fabrication and characterization of three-dimensional silver/air inverted opal photonic crystals,” J. Mater. Chem.20(36), 7870–7874 (2010).
[CrossRef]

Schaubert, D. H.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag.32(3), 276–281 (1984).
[CrossRef]

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Schultz, M.

Y. Saad and M. Schultz, “Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAMJ. Sci. Statist. Comput.7(3), 856–869 (1986).
[CrossRef]

Schwartz, B. T.

Song, J. M.

T. W. Lloyd, J. M. Song, and M. Yang, “Numerical study of surface integral formulations for low-contrast objects,” IEEE Antennas Wirel. Propag. Lett.4(1), 482–485 (2005).
[CrossRef]

Taboada, J. M.

M. G. Araújo, J. M. Taboada, J. Rivero, and F. Obelleiro, “Comparison of Surface Integral Equations for Left-Handed Materials,” Prog. Electromagn. Res.118, 425–440 (2011).
[CrossRef]

J. M. Taboada, J. Rivero, F. Obelleiro, M. G. Araújo, and L. Landesa, “Method-of-moments formulation for the analysis of plasmonic nano-optical antennas,” J. Opt. Soc. Am. A28(7), 1341–1348 (2011).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove and M. E. Brodwin, “Numerical solution of steadystate electromagnetic scattering problems using the timedependent Maxwell’s equations,” IEEE Trans. Microw. Theory Tech.23(8), 623–630 (1975).
[CrossRef]

Taskinen, M.

P. Ylä-Oijala and M. Taskinen, “Improving conditioning of electromagnetic surface integral equations using normalized field quantities,” IEEE Trans. Antenn. Propag.55(1), 178–185 (2007).
[CrossRef]

P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci.40(6), RS6002 (2005).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Well-conditioned Müller formulation for electromagnetic scattering by dielectric objects,” IEEE Trans. Antenn. Propag.53(10), 3316–3323 (2005).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antenn. Propag.53(3), 1168–1173 (2005).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Calculation of CFIE impedance matrix elements with RWG andn^× RWG functions,” IEEE Trans. Antenn. Propag.51(8), 1837–1846 (2003).
[CrossRef]

van Hulst, N. F.

L. Novotny and N. F. van Hulst, “Antennas for Light,” Nat. Photonics5(2), 83–90 (2011).
[CrossRef]

Waylonis, J. E.

Weiland, T.

T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Arch. Elektron. Übertragungstech.31, 116–120 (1977).

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Wilton, D. R.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag.32(3), 276–281 (1984).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag.30(3), 409–418 (1982).
[CrossRef]

Yang, M.

T. W. Lloyd, J. M. Song, and M. Yang, “Numerical study of surface integral formulations for low-contrast objects,” IEEE Antennas Wirel. Propag. Lett.4(1), 482–485 (2005).
[CrossRef]

Ylä-Oijala, P.

P. Ylä-Oijala and M. Taskinen, “Improving conditioning of electromagnetic surface integral equations using normalized field quantities,” IEEE Trans. Antenn. Propag.55(1), 178–185 (2007).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antenn. Propag.53(3), 1168–1173 (2005).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Well-conditioned Müller formulation for electromagnetic scattering by dielectric objects,” IEEE Trans. Antenn. Propag.53(10), 3316–3323 (2005).
[CrossRef]

P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci.40(6), RS6002 (2005).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Calculation of CFIE impedance matrix elements with RWG andn^× RWG functions,” IEEE Trans. Antenn. Propag.51(8), 1837–1846 (2003).
[CrossRef]

Zhang, H. X.

J. Zhou, Y. Zhou, S. L. Ng, H. X. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, “Three-dimensional photonic band gap structure of a polymer-metal composite,” Appl. Phys. Lett.76, 3337–3339 (2000).

Zhou, J.

J. Zhou, Y. Zhou, S. L. Ng, H. X. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, “Three-dimensional photonic band gap structure of a polymer-metal composite,” Appl. Phys. Lett.76, 3337–3339 (2000).

Zhou, Y.

J. Zhou, Y. Zhou, S. L. Ng, H. X. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, “Three-dimensional photonic band gap structure of a polymer-metal composite,” Appl. Phys. Lett.76, 3337–3339 (2000).

Appl. Phys. Lett.

J. Zhou, Y. Zhou, S. L. Ng, H. X. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, “Three-dimensional photonic band gap structure of a polymer-metal composite,” Appl. Phys. Lett.76, 3337–3339 (2000).

Arch. Elektr. Uebertrag.

J. R. Mautz and R. F. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag.33, 71–80 (1979).

Arch. Elektron. Übertragungstech.

T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Arch. Elektron. Übertragungstech.31, 116–120 (1977).

IEEE Antennas Wirel. Propag. Lett.

Ö. Ergül, “Fast and Accurate Analysis of Homogenized Metamaterials With the Surface Integral Equations and the Multilevel Fast Multipole Algorithm,” IEEE Antennas Wirel. Propag. Lett.10, 1286–1289 (2011).
[CrossRef]

T. W. Lloyd, J. M. Song, and M. Yang, “Numerical study of surface integral formulations for low-contrast objects,” IEEE Antennas Wirel. Propag. Lett.4(1), 482–485 (2005).
[CrossRef]

IEEE Trans. Antenn. Propag.

P. Ylä-Oijala and M. Taskinen, “Improving conditioning of electromagnetic surface integral equations using normalized field quantities,” IEEE Trans. Antenn. Propag.55(1), 178–185 (2007).
[CrossRef]

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag.32(3), 276–281 (1984).
[CrossRef]

R. D. Graglia, “On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,” IEEE Trans. Antenn. Propag.41(10), 1448–1455 (1993).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Calculation of CFIE impedance matrix elements with RWG andn^× RWG functions,” IEEE Trans. Antenn. Propag.51(8), 1837–1846 (2003).
[CrossRef]

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antenn. Propag.57(1), 176–187 (2009).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Well-conditioned Müller formulation for electromagnetic scattering by dielectric objects,” IEEE Trans. Antenn. Propag.53(10), 3316–3323 (2005).
[CrossRef]

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antenn. Propag.53(3), 1168–1173 (2005).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag.30(3), 409–418 (1982).
[CrossRef]

IEEE Trans. Microw. Antennas Propag.

Y. A. Liu and W. C. Chew, “Stability of surface integral equation for left-handed materials,” IEEE Trans. Microw. Antennas Propag.1(1), 84–89 (2007).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

A. Taflove and M. E. Brodwin, “Numerical solution of steadystate electromagnetic scattering problems using the timedependent Maxwell’s equations,” IEEE Trans. Microw. Theory Tech.23(8), 623–630 (1975).
[CrossRef]

J. Mater. Chem.

M. Salaün, B. Corbett, S. B. Newcomb, and M. E. Pemble, “Fabrication and characterization of three-dimensional silver/air inverted opal photonic crystals,” J. Mater. Chem.20(36), 7870–7874 (2010).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Microw. Opt. Technol. Lett.

R. E. Hodges and Y. Rahmat-Samii, “The evaluation of MFIE integrals with the use of vector triangle basis functions,” Microw. Opt. Technol. Lett.14(1), 9–14 (1997).
[CrossRef]

Nat. Mater.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Nat. Photonics

L. Novotny and N. F. van Hulst, “Antennas for Light,” Nat. Photonics5(2), 83–90 (2011).
[CrossRef]

Phys. Rev. B

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Prog. Electromagn. Res.

M. G. Araújo, J. M. Taboada, J. Rivero, and F. Obelleiro, “Comparison of Surface Integral Equations for Left-Handed Materials,” Prog. Electromagn. Res.118, 425–440 (2011).
[CrossRef]

Radio Sci.

P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci.40(6), RS6002 (2005).
[CrossRef]

Science

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

SIAMJ. Sci. Statist. Comput.

Y. Saad and M. Schultz, “Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAMJ. Sci. Statist. Comput.7(3), 856–869 (1986).
[CrossRef]

Other

R. F. Harrington, Field Computation by Moment Method (IEEE Press, 1993).

A. Ishimaru, Electromagnetic Wave Propagation, Radiation and Scattering (Prentice-Hall, 1991).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

S. Kawata, ed., Near-Field Optis and Surface Plasmon Polaritons (Springer, 2010).

P. Biagioni, J. S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Physics Optics arXiv:1103.1568v1, (2011).

C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer, 1969).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley, 1983).

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Figures (9)

Fig. 1
Fig. 1

Normalized RMS error (erms) of the total near field calculation at λ0 = 548.6 nm vs. the number of unknowns (mesh size) for spheres with radius (up) r = λ0/2 and (down) r = λ0/4 made of (left) gold, (center) silver, and (right) aluminum. The spheres are illuminated by an x ^ polarized plane wave with θ inc = 180°. The fields are calculated on centered square XY planes of side 4r with 100 × 100 points resolution.

Fig. 2
Fig. 2

Normalized RMS error (erms) of the total near field calculation at λ0 = 548.6 nm vs. the number of unknowns (mesh size) for spheres with radius (up) r = λ0/8 and (down) r = λ0/16 made of (left) gold, (center) silver, and (right) aluminum. The spheres are illuminated by an x ^ polarized plane wave with θ inc = 180°. The fields are calculated on centered square XY planes of side 4r with 100 × 100 points resolution.

Fig. 3
Fig. 3

Total near electric field distribution (V/m) inside and outside a λ0/2 radius gold sphere in vacuum computed by the PMCHWT-MoM approach for a mesh size of λ0/40 in the XZ and YZ planes vs. the Mie’s series analytical reference. The spheres are illuminated by an x ^ polarized plane wave with θ inc = 180°. Fields inside the spheres are scaled up by a factor of 4 for visualization purposes.

Fig. 4
Fig. 4

Total near electric field distribution (V/m) inside and outside a λ0/8 radius gold sphere in vacuum computed by the PMCHWT-MoM approach for a mesh size of λ0/160 in the XZ and YZ planes vs. the Mie’s series analytical reference. The spheres are illuminated by an x ^ polarized plane wave with θ inc = 180°. Fields inside the spheres are scaled up by a factor of 4 for visualization purposes.

Fig. 7
Fig. 7

Absorption (Qa), scattering (Qs) and extinction (Qe) efficiencies vs. the product k0r for gold spheres at λ0 = 548.6 nm.

Fig. 5
Fig. 5

Normalized RMS error (erms) of the extinction efficiency calculation at λ0 = 548.6 nm vs. the number of unknowns (mesh size) for λ0/2 and λ0/4 radius spheres made of gold, silver and aluminum.

Fig. 6
Fig. 6

Normalized RMS error (erms) of the extinction efficiency calculation at λ0 = 548.6 nm vs. the number of unknowns (mesh size) for λ0/8 and λ0/16 radius spheres made of gold, silver and aluminum.

Fig. 8
Fig. 8

Resonance study for a gold sphere with radius 74.712 nm: (up) Absorption (Qa), scattering (Qs) and extinction (Qe) efficiencies vs. wavelength; (down) Normalized RMS error (erms) of the total near field calculation vs. wavelength.

Fig. 9
Fig. 9

MoM-GMRES iterative convergence of the formulations for the λ0/2 radius sphere made of gold, silver and aluminum with a mesh size of λ0/40.

Tables (1)

Tables Icon

Table 1 Parameters for Combining Equations Corresponding to Each Formulation Considered in the Comparative Study

Equations (3)

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i=1 2 a i 1 η i T-EFIE i + i=1 2 b i N-MFIE i
i=1 2 c i N-EFIE i + i=1 2 d i η i T-MFIE i ,
e rms = ( E Mie E f ) 2 /N max( E Mie ) .

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