Abstract

The optical response of dense finite arrays of nanoparticles can be efficiently analyzed with the help of macro basis functions obtained by employing the array scanning method. This is demonstrated by analyzing optical collimation in arrays of silver nanorods. The accuracy of the solution obtained with the proposed method has been validated by comparison with solutions obtained employing the Krylov subspace iterative method. The relative error in the electric field distribution on an observation plane above the finite array is of the order of 25dB, while the number of unknowns is reduced by a factor of 32.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2013

N. Ozdemir, D. Gonzalez-Ovejero, and C. Craeye, “On the relationship between multiple-scattering macro basis functions and Krylov subspace approaches,” IEEE Trans. Antennas Propag. 61, 2088–2098 (2013).

2012

2011

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. A 28, 1341–1348 (2011).
[CrossRef]

M. G. Araújo, J. M. Tabaoda, D. M. Solís, J. Rivero, and F. Obelleiro, “Comparison of surface integral equations for left-handed materials,” Prog. Electromagn. Res. 118, 425–440 (2011).
[CrossRef]

D. Gonzalez-Ovejero and C. Craeye, “Interpolatory macro basis functions analysis of non-periodic arrays,” IEEE Trans. Antennas Propag. 59, 3117–3122 (2011).
[CrossRef]

2010

2009

A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A 26, 732–740 (2009).
[CrossRef]

N. Guérin, C. Craeye, and X. Dardenne, “Accelerated computation of the free space Green’s function gradient of infinite phased arrays of dipoles,” IEEE Trans. Antennas Propag. 57, 3430–3434 (2009).
[CrossRef]

C. Craeye, T. Gilles, and X. Dardenne, “Efficient full-wave characterization of arrays of antennas embedded in finite dielectric volumes,” Radio Sci. 44, RS1S90 (2009).
[CrossRef]

2008

C. Craeye and R. Sarkis, “Finite array analysis through combination of macro basis functions and array scanning methods,” ACES J. 23, 256–261 (2008).

X. Dardenne and C. Craeye, “Method of moments simulation of infinitely periodic structures combining metal with dielectric objects,” IEEE Trans. Antennas Propag. 56, 2372–2380 (2008).
[CrossRef]

C. Delgado, M. F. Cátedra, and R. Mittra, “Efficient multilevel approach for the generation of characteristic basis functions for large structures,” IEEE Trans. Antennas Propag. 56, 2134–2137 (2008).

S. Kawata, A. Ono, and P. Verma, “Subwavelength color imaging with a metallic nanolens,” Nat. Photonics 2, 438–442 (2008).
[CrossRef]

X. Radu, A. Lapeyronnie, and C. Craeye, “Numerical and experimental analysis of a wire medium collimator for MRI,” Electromagnetics 28, 531–543 (2008).
[CrossRef]

2007

L. Matekovits, V. A. Laza, and G. Vecchi, “Analysis of large complex structures with the synthetic-functions approach,” IEEE Trans. Antennas Propag. 55, 2509–2521 (2007).
[CrossRef]

W. B. Ewe, H. S. Chou, and E. P. Li, “Volume integral equation analysis of surface plasmon resonance of nanoparticles,” Opt. Express 15, 18200–18208 (2007).
[CrossRef]

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propag. 55, 1644–1655 (2007).
[CrossRef]

2006

P. Belov, Y. Zhao, S. Sudhakaran, A. Alomainy, and Y. Hao, “Experimental study of the subwavelength imaging by a wire medium slab,” Appl. Phys. Lett. 89, 262109 (2006).
[CrossRef]

2005

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95, 267–407 (2005).

2003

J. Yeo, V. Prakash, and R. Mittra, “Efficient analysis of a class of microstrip antennas using the characteristic basis function method (CBFM),” Microw. Opt. Technol. Lett. 39, 456–464 (2003).
[CrossRef]

2002

2001

J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Trans. Antennas Propag. 43, 61–77 (2001).
[CrossRef]

J. P. Kottman, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

2000

J. P. Kottman and O. J. F. Martin, “Accurate solution of the volume integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
[CrossRef]

J. P. Kottman, O. J. F. Martin, D. R. Smith, and S. Schultz, “Spectral response of plasmon resonant nanoparticles with a non-regular shape,” Opt. Express 6, 213–219 (2000).
[CrossRef]

E. Suter and J. R. Mosig, “A sub-domain multilevel approach for the efficient MoM analysis of large planar antennas,” Microw. Opt. Technol. Lett. 26, 270–277 (2000).

M. Bebendorf, “Approximation of boundary element matrices,” Numer. Math. 86, 565–589 (2000).
[CrossRef]

1998

1997

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

1996

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: Adaptive integral method for solving large scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225–1251 (1996).
[CrossRef]

1995

W. H. Yang, G. C. Schatz, and R. P. V. Duyne, “Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shape,” J. Chem. Phys. 103, 869–875 (1995).
[CrossRef]

1993

R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: A pedestrian prescription,” IEEE Trans. Antennas Propag. 35, 7–12 (1993).
[CrossRef]

S. Singh and R. Singh, “On the use of Levins T-transform in accelerating the summation of series representing the free-space periodic Green’s functions,” IEEE Trans. Microw. Theory 41, 884–886 (1993).

1992

N. Engheta, W. D. Murphy, V. Rokhlin, and S. M. Vassiliou, “The Fast Multipole Method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).
[CrossRef]

1986

K. E. Jordan, G. R. Richter, and P. Sheng, “An efficient numerical evaluation of the Green’s function for the Helmholtz operator on periodic structures,” J. Comput. Phys. 63, 222–235 (1986).
[CrossRef]

1982

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

1980

A. W. Glisson and D. R. Wilton, “Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces,” IEEE Trans. Antennas Propag. 28, 593–603 (1980).
[CrossRef]

1979

B. A. Munk and G. A. Burrel, “Plane-wave expansion for arrays of arbitrarily oriented piecewise linear elements and its application in determining the impedance of a single linear antenna in a lossy-half space,” IEEE Trans. Antennas Propag. 27, 331–343 (1979).
[CrossRef]

1977

Y. Chang and R. Harrington, “A surface formulation for characteristic modes of material bodies,” IEEE Trans. Antennas Propag. 25, 789–795 (1977).
[CrossRef]

T. K. Wu and L. L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Sci. 12, 709–718 (1977).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Alomainy, A.

P. Belov, Y. Zhao, S. Sudhakaran, A. Alomainy, and Y. Hao, “Experimental study of the subwavelength imaging by a wire medium slab,” Appl. Phys. Lett. 89, 262109 (2006).
[CrossRef]

Araújo, M. G.

Bebendorf, M.

M. Bebendorf, “Approximation of boundary element matrices,” Numer. Math. 86, 565–589 (2000).
[CrossRef]

Belov, P.

P. Belov, Y. Zhao, S. Sudhakaran, A. Alomainy, and Y. Hao, “Experimental study of the subwavelength imaging by a wire medium slab,” Appl. Phys. Lett. 89, 262109 (2006).
[CrossRef]

Bleszynski, E.

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: Adaptive integral method for solving large scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225–1251 (1996).
[CrossRef]

Bleszynski, M.

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: Adaptive integral method for solving large scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225–1251 (1996).
[CrossRef]

Bohren, C. F.

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

Burrel, G. A.

B. A. Munk and G. A. Burrel, “Plane-wave expansion for arrays of arbitrarily oriented piecewise linear elements and its application in determining the impedance of a single linear antenna in a lossy-half space,” IEEE Trans. Antennas Propag. 27, 331–343 (1979).
[CrossRef]

Capolino, F.

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propag. 55, 1644–1655 (2007).
[CrossRef]

C. Craeye, X. Radu, A. Schuchinsky, and F. Capolino, “Fundamentals of method of moments for metamaterials,” in Handbook of Metamaterials, F. Capolino, ed. (Taylor & Francis, 2009).

Cátedra, M. F.

C. Delgado, M. F. Cátedra, and R. Mittra, “Efficient multilevel approach for the generation of characteristic basis functions for large structures,” IEEE Trans. Antennas Propag. 56, 2134–2137 (2008).

Chang, Y.

Y. Chang and R. Harrington, “A surface formulation for characteristic modes of material bodies,” IEEE Trans. Antennas Propag. 25, 789–795 (1977).
[CrossRef]

Chou, H. S.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Coifman, R.

R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: A pedestrian prescription,” IEEE Trans. Antennas Propag. 35, 7–12 (1993).
[CrossRef]

Craeye, C.

N. Ozdemir, D. Gonzalez-Ovejero, and C. Craeye, “On the relationship between multiple-scattering macro basis functions and Krylov subspace approaches,” IEEE Trans. Antennas Propag. 61, 2088–2098 (2013).

D. Gonzalez-Ovejero and C. Craeye, “Interpolatory macro basis functions analysis of non-periodic arrays,” IEEE Trans. Antennas Propag. 59, 3117–3122 (2011).
[CrossRef]

C. Craeye, T. Gilles, and X. Dardenne, “Efficient full-wave characterization of arrays of antennas embedded in finite dielectric volumes,” Radio Sci. 44, RS1S90 (2009).
[CrossRef]

N. Guérin, C. Craeye, and X. Dardenne, “Accelerated computation of the free space Green’s function gradient of infinite phased arrays of dipoles,” IEEE Trans. Antennas Propag. 57, 3430–3434 (2009).
[CrossRef]

X. Dardenne and C. Craeye, “Method of moments simulation of infinitely periodic structures combining metal with dielectric objects,” IEEE Trans. Antennas Propag. 56, 2372–2380 (2008).
[CrossRef]

C. Craeye and R. Sarkis, “Finite array analysis through combination of macro basis functions and array scanning methods,” ACES J. 23, 256–261 (2008).

X. Radu, A. Lapeyronnie, and C. Craeye, “Numerical and experimental analysis of a wire medium collimator for MRI,” Electromagnetics 28, 531–543 (2008).
[CrossRef]

N. A. Ozdemir, R. M. Mateos, and C. Craeye, “Efficient integral-equation analysis of broadband metamaterials,” in Proceedings of the Fourth International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamorphose-VI, 2010), pp. 389–391.

N. Ozdemir and C. Craeye, “Efficient analysis of periodic structures involving finite dielectric material based on the array scanning method,” in International Conference on Electromagnetics in Advanced Applications Digest (IEEE, 2009), pp. 938–942.

N. A. Ozdemir and C. Craeye, “Multiple-scattering-based macro basis functions for the method of moments analysis of 3-D dielectric structures,” in Proceedings of the 26th Annual Review of Progress in Applied Computational Electromagnetics (ACES, 2010), pp. 195–200.

C. Craeye, X. Radu, A. Schuchinsky, and F. Capolino, “Fundamentals of method of moments for metamaterials,” in Handbook of Metamaterials, F. Capolino, ed. (Taylor & Francis, 2009).

N. A. Ozdemir, C. Simovski, D. Morits, and C. Craeye, “Efficient method of moments analysis of an infinite array of triangular nanoclusters in the optical frequency range,” in International Conference on Electromagnetics in Advanced Applications Digest (IEEE, 2011), pp. 359–362.

Dardenne, X.

N. Guérin, C. Craeye, and X. Dardenne, “Accelerated computation of the free space Green’s function gradient of infinite phased arrays of dipoles,” IEEE Trans. Antennas Propag. 57, 3430–3434 (2009).
[CrossRef]

C. Craeye, T. Gilles, and X. Dardenne, “Efficient full-wave characterization of arrays of antennas embedded in finite dielectric volumes,” Radio Sci. 44, RS1S90 (2009).
[CrossRef]

X. Dardenne and C. Craeye, “Method of moments simulation of infinitely periodic structures combining metal with dielectric objects,” IEEE Trans. Antennas Propag. 56, 2372–2380 (2008).
[CrossRef]

Delgado, C.

C. Delgado, M. F. Cátedra, and R. Mittra, “Efficient multilevel approach for the generation of characteristic basis functions for large structures,” IEEE Trans. Antennas Propag. 56, 2134–2137 (2008).

Djurisic, A. B.

Duyne, R. P. V.

W. H. Yang, G. C. Schatz, and R. P. V. Duyne, “Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shape,” J. Chem. Phys. 103, 869–875 (1995).
[CrossRef]

Elazar, J. M.

Engheta, N.

N. Engheta, W. D. Murphy, V. Rokhlin, and S. M. Vassiliou, “The Fast Multipole Method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).
[CrossRef]

Erni, D. E.

Ewe, W. B.

Felsen, L. B.

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propag. 55, 1644–1655 (2007).
[CrossRef]

Gallinet, B.

García-Tuñón, I.

Gilles, T.

C. Craeye, T. Gilles, and X. Dardenne, “Efficient full-wave characterization of arrays of antennas embedded in finite dielectric volumes,” Radio Sci. 44, RS1S90 (2009).
[CrossRef]

Glisson, A. W.

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

A. W. Glisson and D. R. Wilton, “Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces,” IEEE Trans. Antennas Propag. 28, 593–603 (1980).
[CrossRef]

Gonzalez-Ovejero, D.

N. Ozdemir, D. Gonzalez-Ovejero, and C. Craeye, “On the relationship between multiple-scattering macro basis functions and Krylov subspace approaches,” IEEE Trans. Antennas Propag. 61, 2088–2098 (2013).

D. Gonzalez-Ovejero and C. Craeye, “Interpolatory macro basis functions analysis of non-periodic arrays,” IEEE Trans. Antennas Propag. 59, 3117–3122 (2011).
[CrossRef]

Guérin, N.

N. Guérin, C. Craeye, and X. Dardenne, “Accelerated computation of the free space Green’s function gradient of infinite phased arrays of dipoles,” IEEE Trans. Antennas Propag. 57, 3430–3434 (2009).
[CrossRef]

Hafner, C.

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, 2005).

Hao, Y.

P. Belov, Y. Zhao, S. Sudhakaran, A. Alomainy, and Y. Hao, “Experimental study of the subwavelength imaging by a wire medium slab,” Appl. Phys. Lett. 89, 262109 (2006).
[CrossRef]

Harrington, R.

Y. Chang and R. Harrington, “A surface formulation for characteristic modes of material bodies,” IEEE Trans. Antennas Propag. 25, 789–795 (1977).
[CrossRef]

Harrington, R. F.

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

R. F. Harrington, Time-Harmonic Electromagnetic Fields (IEEE, 2001).

Hecht, B.

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

Huffman, D. R.

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

Jackson, D. R.

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propag. 55, 1644–1655 (2007).
[CrossRef]

Jaroszewicz, T.

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: Adaptive integral method for solving large scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225–1251 (1996).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Jordan, K. E.

K. E. Jordan, G. R. Richter, and P. Sheng, “An efficient numerical evaluation of the Green’s function for the Helmholtz operator on periodic structures,” J. Comput. Phys. 63, 222–235 (1986).
[CrossRef]

Kato, J.

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95, 267–407 (2005).

Kawata, S.

S. Kawata, A. Ono, and P. Verma, “Subwavelength color imaging with a metallic nanolens,” Nat. Photonics 2, 438–442 (2008).
[CrossRef]

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95, 267–407 (2005).

Kern, A. M.

Kottman, J. P.

J. P. Kottman, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

J. P. Kottman, O. J. F. Martin, D. R. Smith, and S. Schultz, “Spectral response of plasmon resonant nanoparticles with a non-regular shape,” Opt. Express 6, 213–219 (2000).
[CrossRef]

J. P. Kottman and O. J. F. Martin, “Accurate solution of the volume integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
[CrossRef]

Landesa, L.

Lapeyronnie, A.

X. Radu, A. Lapeyronnie, and C. Craeye, “Numerical and experimental analysis of a wire medium collimator for MRI,” Electromagnetics 28, 531–543 (2008).
[CrossRef]

Laza, V. A.

L. Matekovits, V. A. Laza, and G. Vecchi, “Analysis of large complex structures with the synthetic-functions approach,” IEEE Trans. Antennas Propag. 55, 2509–2521 (2007).
[CrossRef]

Li, E. P.

Majewski, M. L.

Martin, O. J. F.

Matekovits, L.

L. Matekovits, V. A. Laza, and G. Vecchi, “Analysis of large complex structures with the synthetic-functions approach,” IEEE Trans. Antennas Propag. 55, 2509–2521 (2007).
[CrossRef]

Mateos, R. M.

N. A. Ozdemir, R. M. Mateos, and C. Craeye, “Efficient integral-equation analysis of broadband metamaterials,” in Proceedings of the Fourth International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamorphose-VI, 2010), pp. 389–391.

Miller, E. K.

J. Poggio and E. K. Miller, “Integral equation solutions of three dimensional scattering problems,” in Computer Techniques for Electromagnetics, R. Mittra, ed. (Pergamon, 1973), pp. 159–264.

Mittra, R.

C. Delgado, M. F. Cátedra, and R. Mittra, “Efficient multilevel approach for the generation of characteristic basis functions for large structures,” IEEE Trans. Antennas Propag. 56, 2134–2137 (2008).

J. Yeo, V. Prakash, and R. Mittra, “Efficient analysis of a class of microstrip antennas using the characteristic basis function method (CBFM),” Microw. Opt. Technol. Lett. 39, 456–464 (2003).
[CrossRef]

Moreno, E.

Morits, D.

N. A. Ozdemir, C. Simovski, D. Morits, and C. Craeye, “Efficient method of moments analysis of an infinite array of triangular nanoclusters in the optical frequency range,” in International Conference on Electromagnetics in Advanced Applications Digest (IEEE, 2011), pp. 359–362.

Mosig, J. R.

E. Suter and J. R. Mosig, “A sub-domain multilevel approach for the efficient MoM analysis of large planar antennas,” Microw. Opt. Technol. Lett. 26, 270–277 (2000).

Munk, B. A.

B. A. Munk and G. A. Burrel, “Plane-wave expansion for arrays of arbitrarily oriented piecewise linear elements and its application in determining the impedance of a single linear antenna in a lossy-half space,” IEEE Trans. Antennas Propag. 27, 331–343 (1979).
[CrossRef]

Murphy, W. D.

N. Engheta, W. D. Murphy, V. Rokhlin, and S. M. Vassiliou, “The Fast Multipole Method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).
[CrossRef]

Nelson, R. O.

J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Trans. Antennas Propag. 43, 61–77 (2001).
[CrossRef]

Novotny, L.

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

Obelleiro, F.

Ono, A.

S. Kawata, A. Ono, and P. Verma, “Subwavelength color imaging with a metallic nanolens,” Nat. Photonics 2, 438–442 (2008).
[CrossRef]

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95, 267–407 (2005).

Ozdemir, N.

N. Ozdemir, D. Gonzalez-Ovejero, and C. Craeye, “On the relationship between multiple-scattering macro basis functions and Krylov subspace approaches,” IEEE Trans. Antennas Propag. 61, 2088–2098 (2013).

N. Ozdemir and C. Craeye, “Efficient analysis of periodic structures involving finite dielectric material based on the array scanning method,” in International Conference on Electromagnetics in Advanced Applications Digest (IEEE, 2009), pp. 938–942.

Ozdemir, N. A.

N. A. Ozdemir, R. M. Mateos, and C. Craeye, “Efficient integral-equation analysis of broadband metamaterials,” in Proceedings of the Fourth International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamorphose-VI, 2010), pp. 389–391.

N. A. Ozdemir and C. Craeye, “Multiple-scattering-based macro basis functions for the method of moments analysis of 3-D dielectric structures,” in Proceedings of the 26th Annual Review of Progress in Applied Computational Electromagnetics (ACES, 2010), pp. 195–200.

N. A. Ozdemir, C. Simovski, D. Morits, and C. Craeye, “Efficient method of moments analysis of an infinite array of triangular nanoclusters in the optical frequency range,” in International Conference on Electromagnetics in Advanced Applications Digest (IEEE, 2011), pp. 359–362.

Poggio, J.

J. Poggio and E. K. Miller, “Integral equation solutions of three dimensional scattering problems,” in Computer Techniques for Electromagnetics, R. Mittra, ed. (Pergamon, 1973), pp. 159–264.

Pohl, D. W.

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

Prakash, V.

J. Yeo, V. Prakash, and R. Mittra, “Efficient analysis of a class of microstrip antennas using the characteristic basis function method (CBFM),” Microw. Opt. Technol. Lett. 39, 456–464 (2003).
[CrossRef]

Radu, X.

X. Radu, A. Lapeyronnie, and C. Craeye, “Numerical and experimental analysis of a wire medium collimator for MRI,” Electromagnetics 28, 531–543 (2008).
[CrossRef]

C. Craeye, X. Radu, A. Schuchinsky, and F. Capolino, “Fundamentals of method of moments for metamaterials,” in Handbook of Metamaterials, F. Capolino, ed. (Taylor & Francis, 2009).

Rakic, A. D.

Rao, S. M.

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

Richter, G. R.

K. E. Jordan, G. R. Richter, and P. Sheng, “An efficient numerical evaluation of the Green’s function for the Helmholtz operator on periodic structures,” J. Comput. Phys. 63, 222–235 (1986).
[CrossRef]

Rivero, J.

Rokhlin, V.

R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: A pedestrian prescription,” IEEE Trans. Antennas Propag. 35, 7–12 (1993).
[CrossRef]

N. Engheta, W. D. Murphy, V. Rokhlin, and S. M. Vassiliou, “The Fast Multipole Method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).
[CrossRef]

Saad, Y.

Y. Saad, Iterative Methods for Sparse Linear Systems (SIAM, 2003).

Sarkis, R.

C. Craeye and R. Sarkis, “Finite array analysis through combination of macro basis functions and array scanning methods,” ACES J. 23, 256–261 (2008).

Schatz, G. C.

W. H. Yang, G. C. Schatz, and R. P. V. Duyne, “Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shape,” J. Chem. Phys. 103, 869–875 (1995).
[CrossRef]

Schuchinsky, A.

C. Craeye, X. Radu, A. Schuchinsky, and F. Capolino, “Fundamentals of method of moments for metamaterials,” in Handbook of Metamaterials, F. Capolino, ed. (Taylor & Francis, 2009).

Schultz, S.

J. P. Kottman, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

J. P. Kottman, O. J. F. Martin, D. R. Smith, and S. Schultz, “Spectral response of plasmon resonant nanoparticles with a non-regular shape,” Opt. Express 6, 213–219 (2000).
[CrossRef]

Sheng, P.

K. E. Jordan, G. R. Richter, and P. Sheng, “An efficient numerical evaluation of the Green’s function for the Helmholtz operator on periodic structures,” J. Comput. Phys. 63, 222–235 (1986).
[CrossRef]

Simovski, C.

N. A. Ozdemir, C. Simovski, D. Morits, and C. Craeye, “Efficient method of moments analysis of an infinite array of triangular nanoclusters in the optical frequency range,” in International Conference on Electromagnetics in Advanced Applications Digest (IEEE, 2011), pp. 359–362.

Singh, R.

S. Singh and R. Singh, “On the use of Levins T-transform in accelerating the summation of series representing the free-space periodic Green’s functions,” IEEE Trans. Microw. Theory 41, 884–886 (1993).

Singh, S.

S. Singh and R. Singh, “On the use of Levins T-transform in accelerating the summation of series representing the free-space periodic Green’s functions,” IEEE Trans. Microw. Theory 41, 884–886 (1993).

Smith, D. R.

J. P. Kottman, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

J. P. Kottman, O. J. F. Martin, D. R. Smith, and S. Schultz, “Spectral response of plasmon resonant nanoparticles with a non-regular shape,” Opt. Express 6, 213–219 (2000).
[CrossRef]

Solís, D. M.

M. G. Araújo, J. M. Tabaoda, D. M. Solís, J. Rivero, L. Landesa, and F. Obelleiro, “Comparison of surface integral equation formulations for electromagnetic analysis of plasmonic nanoscatterers,” Opt. Express 20, 9161–9171 (2012).
[CrossRef]

M. G. Araújo, J. M. Tabaoda, D. M. Solís, J. Rivero, and F. Obelleiro, “Comparison of surface integral equations for left-handed materials,” Prog. Electromagn. Res. 118, 425–440 (2011).
[CrossRef]

Sudhakaran, S.

P. Belov, Y. Zhao, S. Sudhakaran, A. Alomainy, and Y. Hao, “Experimental study of the subwavelength imaging by a wire medium slab,” Appl. Phys. Lett. 89, 262109 (2006).
[CrossRef]

Suter, E.

E. Suter and J. R. Mosig, “A sub-domain multilevel approach for the efficient MoM analysis of large planar antennas,” Microw. Opt. Technol. Lett. 26, 270–277 (2000).

Tabaoda, J. M.

M. G. Araújo, J. M. Tabaoda, D. M. Solís, J. Rivero, L. Landesa, and F. Obelleiro, “Comparison of surface integral equation formulations for electromagnetic analysis of plasmonic nanoscatterers,” Opt. Express 20, 9161–9171 (2012).
[CrossRef]

M. G. Araújo, J. M. Tabaoda, D. M. Solís, J. Rivero, and F. Obelleiro, “Comparison of surface integral equations for left-handed materials,” Prog. Electromagn. Res. 118, 425–440 (2011).
[CrossRef]

Taboada, J. M.

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, 2005).

Tsai, L. L.

T. K. Wu and L. L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Sci. 12, 709–718 (1977).
[CrossRef]

Vahldieck, R.

Vassiliou, S. M.

N. Engheta, W. D. Murphy, V. Rokhlin, and S. M. Vassiliou, “The Fast Multipole Method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).
[CrossRef]

Vecchi, G.

L. Matekovits, V. A. Laza, and G. Vecchi, “Analysis of large complex structures with the synthetic-functions approach,” IEEE Trans. Antennas Propag. 55, 2509–2521 (2007).
[CrossRef]

Verma, P.

S. Kawata, A. Ono, and P. Verma, “Subwavelength color imaging with a metallic nanolens,” Nat. Photonics 2, 438–442 (2008).
[CrossRef]

Wandzura, S.

R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: A pedestrian prescription,” IEEE Trans. Antennas Propag. 35, 7–12 (1993).
[CrossRef]

Wilton, D. R.

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propag. 55, 1644–1655 (2007).
[CrossRef]

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

A. W. Glisson and D. R. Wilton, “Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces,” IEEE Trans. Antennas Propag. 28, 593–603 (1980).
[CrossRef]

Wu, T. K.

T. K. Wu and L. L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Sci. 12, 709–718 (1977).
[CrossRef]

Yang, W. H.

W. H. Yang, G. C. Schatz, and R. P. V. Duyne, “Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shape,” J. Chem. Phys. 103, 869–875 (1995).
[CrossRef]

Yeo, J.

J. Yeo, V. Prakash, and R. Mittra, “Efficient analysis of a class of microstrip antennas using the characteristic basis function method (CBFM),” Microw. Opt. Technol. Lett. 39, 456–464 (2003).
[CrossRef]

Young, J. L.

J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Trans. Antennas Propag. 43, 61–77 (2001).
[CrossRef]

Zhao, Y.

P. Belov, Y. Zhao, S. Sudhakaran, A. Alomainy, and Y. Hao, “Experimental study of the subwavelength imaging by a wire medium slab,” Appl. Phys. Lett. 89, 262109 (2006).
[CrossRef]

ACES J.

C. Craeye and R. Sarkis, “Finite array analysis through combination of macro basis functions and array scanning methods,” ACES J. 23, 256–261 (2008).

Appl. Opt.

Appl. Phys. Lett.

P. Belov, Y. Zhao, S. Sudhakaran, A. Alomainy, and Y. Hao, “Experimental study of the subwavelength imaging by a wire medium slab,” Appl. Phys. Lett. 89, 262109 (2006).
[CrossRef]

Electromagnetics

X. Radu, A. Lapeyronnie, and C. Craeye, “Numerical and experimental analysis of a wire medium collimator for MRI,” Electromagnetics 28, 531–543 (2008).
[CrossRef]

IEEE Trans. Antennas Propag.

D. Gonzalez-Ovejero and C. Craeye, “Interpolatory macro basis functions analysis of non-periodic arrays,” IEEE Trans. Antennas Propag. 59, 3117–3122 (2011).
[CrossRef]

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

A. W. Glisson and D. R. Wilton, “Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces,” IEEE Trans. Antennas Propag. 28, 593–603 (1980).
[CrossRef]

J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Trans. Antennas Propag. 43, 61–77 (2001).
[CrossRef]

J. P. Kottman and O. J. F. Martin, “Accurate solution of the volume integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48, 1719–1726 (2000).
[CrossRef]

Y. Chang and R. Harrington, “A surface formulation for characteristic modes of material bodies,” IEEE Trans. Antennas Propag. 25, 789–795 (1977).
[CrossRef]

X. Dardenne and C. Craeye, “Method of moments simulation of infinitely periodic structures combining metal with dielectric objects,” IEEE Trans. Antennas Propag. 56, 2372–2380 (2008).
[CrossRef]

N. Guérin, C. Craeye, and X. Dardenne, “Accelerated computation of the free space Green’s function gradient of infinite phased arrays of dipoles,” IEEE Trans. Antennas Propag. 57, 3430–3434 (2009).
[CrossRef]

N. Engheta, W. D. Murphy, V. Rokhlin, and S. M. Vassiliou, “The Fast Multipole Method (FMM) for electromagnetic scattering problems,” IEEE Trans. Antennas Propag. 40, 634–641 (1992).
[CrossRef]

R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: A pedestrian prescription,” IEEE Trans. Antennas Propag. 35, 7–12 (1993).
[CrossRef]

N. Ozdemir, D. Gonzalez-Ovejero, and C. Craeye, “On the relationship between multiple-scattering macro basis functions and Krylov subspace approaches,” IEEE Trans. Antennas Propag. 61, 2088–2098 (2013).

L. Matekovits, V. A. Laza, and G. Vecchi, “Analysis of large complex structures with the synthetic-functions approach,” IEEE Trans. Antennas Propag. 55, 2509–2521 (2007).
[CrossRef]

C. Delgado, M. F. Cátedra, and R. Mittra, “Efficient multilevel approach for the generation of characteristic basis functions for large structures,” IEEE Trans. Antennas Propag. 56, 2134–2137 (2008).

B. A. Munk and G. A. Burrel, “Plane-wave expansion for arrays of arbitrarily oriented piecewise linear elements and its application in determining the impedance of a single linear antenna in a lossy-half space,” IEEE Trans. Antennas Propag. 27, 331–343 (1979).
[CrossRef]

F. Capolino, D. R. Jackson, D. R. Wilton, and L. B. Felsen, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propag. 55, 1644–1655 (2007).
[CrossRef]

IEEE Trans. Microw. Theory

S. Singh and R. Singh, “On the use of Levins T-transform in accelerating the summation of series representing the free-space periodic Green’s functions,” IEEE Trans. Microw. Theory 41, 884–886 (1993).

J. Appl. Phys.

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1798–1806 (1997).
[CrossRef]

J. Chem. Phys.

W. H. Yang, G. C. Schatz, and R. P. V. Duyne, “Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shape,” J. Chem. Phys. 103, 869–875 (1995).
[CrossRef]

J. Comput. Phys.

K. E. Jordan, G. R. Richter, and P. Sheng, “An efficient numerical evaluation of the Green’s function for the Helmholtz operator on periodic structures,” J. Comput. Phys. 63, 222–235 (1986).
[CrossRef]

J. Opt. Soc. Am. A

Microw. Opt. Technol. Lett.

E. Suter and J. R. Mosig, “A sub-domain multilevel approach for the efficient MoM analysis of large planar antennas,” Microw. Opt. Technol. Lett. 26, 270–277 (2000).

J. Yeo, V. Prakash, and R. Mittra, “Efficient analysis of a class of microstrip antennas using the characteristic basis function method (CBFM),” Microw. Opt. Technol. Lett. 39, 456–464 (2003).
[CrossRef]

Nat. Photonics

S. Kawata, A. Ono, and P. Verma, “Subwavelength color imaging with a metallic nanolens,” Nat. Photonics 2, 438–442 (2008).
[CrossRef]

Numer. Math.

M. Bebendorf, “Approximation of boundary element matrices,” Numer. Math. 86, 565–589 (2000).
[CrossRef]

Opt. Express

Phys. Rev. B

J. P. Kottman, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett.

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95, 267–407 (2005).

Prog. Electromagn. Res.

M. G. Araújo, J. M. Tabaoda, D. M. Solís, J. Rivero, and F. Obelleiro, “Comparison of surface integral equations for left-handed materials,” Prog. Electromagn. Res. 118, 425–440 (2011).
[CrossRef]

Radio Sci.

T. K. Wu and L. L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Sci. 12, 709–718 (1977).
[CrossRef]

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: Adaptive integral method for solving large scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225–1251 (1996).
[CrossRef]

C. Craeye, T. Gilles, and X. Dardenne, “Efficient full-wave characterization of arrays of antennas embedded in finite dielectric volumes,” Radio Sci. 44, RS1S90 (2009).
[CrossRef]

Other

N. A. Ozdemir, R. M. Mateos, and C. Craeye, “Efficient integral-equation analysis of broadband metamaterials,” in Proceedings of the Fourth International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamorphose-VI, 2010), pp. 389–391.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (IEEE, 2001).

N. Ozdemir and C. Craeye, “Efficient analysis of periodic structures involving finite dielectric material based on the array scanning method,” in International Conference on Electromagnetics in Advanced Applications Digest (IEEE, 2009), pp. 938–942.

Y. Saad, Iterative Methods for Sparse Linear Systems (SIAM, 2003).

W. C. Chew, J. Jin, E. Michielssen, and J. Song, eds. Fast and Efficient Algorithms in Computational Electromagnetics (Artech House, 2001).

N. A. Ozdemir, C. Simovski, D. Morits, and C. Craeye, “Efficient method of moments analysis of an infinite array of triangular nanoclusters in the optical frequency range,” in International Conference on Electromagnetics in Advanced Applications Digest (IEEE, 2011), pp. 359–362.

J. Poggio and E. K. Miller, “Integral equation solutions of three dimensional scattering problems,” in Computer Techniques for Electromagnetics, R. Mittra, ed. (Pergamon, 1973), pp. 159–264.

N. A. Ozdemir and C. Craeye, “Multiple-scattering-based macro basis functions for the method of moments analysis of 3-D dielectric structures,” in Proceedings of the 26th Annual Review of Progress in Applied Computational Electromagnetics (ACES, 2010), pp. 195–200.

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

C. Craeye, X. Radu, A. Schuchinsky, and F. Capolino, “Fundamentals of method of moments for metamaterials,” in Handbook of Metamaterials, F. Capolino, ed. (Taylor & Francis, 2009).

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

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, 2005).

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Figures (5)

Fig. 1.
Fig. 1.

Unit cell of a 9×9 array of silver nanorods is shown on the right. The 9×9 array is excited at the center of the array below the element (5,5).

Fig. 2.
Fig. 2.

Total electric field distributions, obtained by employing iterative solutions of the MoM (|EFOM|) and ASM-MBF method |EMBF|, are shown together with the scaled error distributions on observation planes above a 16×16 array of nanorods. The electric field distributions in the first, second, third, and fourth rows correspond to the field distributions on an observation plane at d=0.25a, 0.50a, 0.75a,a, respectively, where the distance d is measured from the top face of the nanorod to the observation plane and a denotes the unit cell size, which also corresponds to the inter-element distance.

Fig. 3.
Fig. 3.

Normalized scattered far-field pattern, obtained by employing the iterative solution of the MoM (|EFOM|) and ASM-MBF method |EMBF|, are shown in both the E (left) and H (right) planes, together with the absolute error.

Fig. 4.
Fig. 4.

Total electric field distributions, obtained by employing the ASM-MBF method, on observation planes above 9×9 (left) and 16×16 (right) arrays of nanorods are shown. The electric field distributions in the first, second, third, and fourth rows correspond to the field distributions on an observation plane at d=0.25a, 0.50a, 0.75a,a, respectively, where the distance d is measured from the top face of the nanorod to the observation plane and a denotes the unit cell size, which also corresponds to the inter-element distance.

Fig. 5.
Fig. 5.

Scaled error distributions on observation planes above 9×9 (left) and 16×16 (right) arrays of nanorods are shown in the same color scale as the first row of Fig. 4. The distributions in the first, second, third, and fourth rows correspond to the scaled error distributions on an observation plane at d=0.25a, 0.50a, 0.75a,a, respectively, where the distance d is measured from the top face of the nanorod to the observation plane and a denotes the unit cell size, which also corresponds to the inter-element distance. (|EFOM|: iterative solution; |EMBF|: ASM-MBF solution.)

Equations (13)

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n^×(E⃗inc+kin2+·jωεinSGinJ⃗dS+kout2·jωεoutSGoutM⃗dS∫̶SM⃗×(Gin+Gout)dS)=0
n^×(H⃗inc+kin2+·jωμinSGinM⃗dS+kout2+·jωμoutSGoutM⃗dS+∫̶SJ⃗×(Gin+Gout)dS)=0,
[Z1,1Z1,NZN,1ZN,N][x1xN]=[b1bN],
Zi,i=[μoutZi,iEJ,outjkout+μinZi,iEJ,injkin,Zi,iEM,out+Zi,iEM,inZi,iEM,outZi,iEM,in,Zi,iEJ,outjkoutμout+Zi,iEJ,injkinμin].
Zi,j=[μoutZi,jEJ,outjkout,Zi,jEM,outZi,jEM,out,Zi,jEJ,outjkoutμout].
Zk,lEJ,out(in)=SiSjejkout(in)R4πR(kout(in)2F⃗k·F⃗l·F⃗k·F⃗l)dsds
Zk,lEM,out(in)=SiSj(ejkout(in)R4πR)×F⃗k·F⃗ldsds,
bi=[EiHi],
E(H)l=SiE⃗inc(H⃗inc)·F⃗lds.
[Z1,1Z1,NZN,1ZN,N][r1rN]=[b1bN],
Im,n=1MpNqp=0Mp1q=0Nq1I(ψx,p,ψy,q)ejmψx,pejnψy,q,
ψx,p=2πp/Mp,ψy,q=2πq/Nq.
QNbx(MpNq)=[I0,0IMp1,Nq1],

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