Abstract

We revisit the Green’s function integral equation for modelling light scattering with discretization strategies as well as numerical integration recipes borrowed from finite element method. The finite element based Green’s function integral equation is implemented by introducing auxiliary variables, which are used to discretize the Green’s function integral equation. The merits of introducing finite element techniques into Green’s function integral equation are apparent. Firstly, the finite element discretization provides a better geometric approximation of the scatterers, compared with that of the conventional discretization method using staircase approximation. Secondly, the accuracy of numerical integral inside one element associated with Green’s function integral equations can be improved by using more quadrature points, where the singular terms confined inside each triangle can be approximated analytically. We then illustrate the advantages of our finite element based Green’s function integral equation method via a few concrete examples in modelling light scattering by optically large and complex scatterers in 2-dimensional scenarios.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  31. T. Søndergaard and S. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi (b) 245(1), 9–19 (2008).
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  33. J. Jung, T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Theoretical analysis and experimental demonstration of resonant light scattering from metal nanostrips on quartz,” J. Opt. Soc. Am. B 26(1), 121–124 (2009).
    [Crossref]
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    [Crossref]
  39. S. C. Lee, “Dependent scattering of an obliquely incident plane wave by a collection of parallel cylinders,” J. Appl. Phys. 68(10), 4952–4957 (1990).
    [Crossref]
  40. E. M. Loebl, Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).
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    [Crossref]

2018 (2)

M. A. Yurkin and M. I. Mishchenko, “Volume integral equation for electromagnetic scattering: Rigorous derivation and analysis for a set of multilayered particles with piecewise-smooth boundaries in a passive host medium,” Phys. Rev. A 97(4), 043824 (2018).
[Crossref]

S. Arslanagić and R. W. Ziolkowski, “Highly subwavelength, superdirective cylindrical nanoantenna,” Phys. Rev. Lett. 120(23), 237401 (2018).
[Crossref]

2017 (1)

2016 (1)

D. Chen, W. Cai, B. Zinser, and M. H. Cho, “Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers,” J. Comput. Phys. 321, 303–320 (2016).
[Crossref]

2015 (2)

J. Waxenegger, A. Trügler, and U. Hohenester, “Plasmonics simulations with the MNPBEM toolbox: Consideration of substrates and layer structures,” Comput. Phys. Commun. 193, 138–150 (2015).
[Crossref]

T. V. Raziman, W. R. C. Somerville, O. J. F. Martin, and E. C. Le Ru, “Accuracy of surface integral equation matrix elements in plasmonic calculations,” J. Opt. Soc. Am. B 32(3), 485–492 (2015).
[Crossref]

2014 (1)

U. Hohenester, “Simulating electron energy loss spectroscopy with the MNPBEM toolbox,” Comput. Phys. Commun. 185(3), 1177–1187 (2014).
[Crossref]

2013 (1)

T. Søndergaard and S. I. Bozhevolnyi, “Theoretical analysis of plasmonic black gold: periodic arrays of ultra-sharp grooves,” New J. Phys. 15(1), 013034 (2013).
[Crossref]

2012 (5)

J. Schäfer, S. C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

V. Siahpoush and T. Søndegaard, ard J. Jung, “Green’s function approach to investigate the excitation of surface plasmon polaritons in a nanometer-thin metal film,” Phys. Rev. B 85(7), 075305 (2012).
[Crossref]

T. Søndergaard, V. Siahpoush, and J. Jung, “Coupling light into and out from the surface plasmon polaritons of a nanometer-thin metal film with a metal nanostrip,” Phys. Rev. B 86(8), 085455 (2012).
[Crossref]

S. B. Wang, H. H. Zheng, J. J. Xiao, Z. F. Lin, and C. T. Chan, “Fast multipole boundary element method for three dimensional electromagnetic scattering problem,” Int. J. Comput. Mater. Sci. Eng. 1(04), 1250038 (2012).

U. Hohenester and A. Trügler, “MNPBEM-A Matlab toolbox for the simulation of plasmonic nanoparticles,” Comput. Phys. Commun. 183(2), 370–381 (2012).
[Crossref]

2011 (2)

J. Jung, T. Søndergarrd, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

R. Rodríguez-Oliveros and J. A. Sánchez-Gil, “Localized surface-plasmon resonances on single and coupled nanoparticles through surface integral equations for flexible surfaces,” Opt. Express 19(13), 12208–12219 (2011).
[Crossref] [PubMed]

2010 (1)

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

2009 (2)

2008 (3)

V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. J. García de Abajo“Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20(22), 4288–4293 (2008).
[Crossref]

J. Jung and T. Søndergaard, “Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B 77(24), 245310 (2008).
[Crossref]

T. Søndergaard and S. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi (b) 245(1), 9–19 (2008).
[Crossref]

2007 (2)

T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancements,” Phys. Rev. B 75(7), 073402 (2007).
[Crossref]

T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi (b) 244(10), 3448–3462 (2007).
[Crossref]

2002 (1)

F. J. García de Abajo and A. Howie“Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys, Rev. B 65(11), 115418 (2002).
[Crossref]

2000 (1)

J. P. Kottmann and O. J. F. Martin, “Accurate solution of the volume integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48(11), 1719–1726 (2000).
[Crossref]

1997 (1)

1995 (1)

S. N. Chandler-Wilde and D. C. Hothersall, “Efficient calculation of the Green function for acoustic propagation above a homogeneous impedance plane,” J. Sound Vibr. 180(5), 705–724 (1995).
[Crossref]

1994 (1)

1991 (1)

R. Kress, “Boundary integral equations in time-harmonic acoustic scattering,” Mathl. Comput. Modelling 15(3–5), 229–243 (1991).
[Crossref]

1990 (1)

S. C. Lee, “Dependent scattering of an obliquely incident plane wave by a collection of parallel cylinders,” J. Appl. Phys. 68(10), 4952–4957 (1990).
[Crossref]

Arslanagic, S.

S. Arslanagić and R. W. Ziolkowski, “Highly subwavelength, superdirective cylindrical nanoantenna,” Phys. Rev. Lett. 120(23), 237401 (2018).
[Crossref]

Beermann, J.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles(Wiley, 2008).

Boltasseva, A.

Bozhevolnyi, S.

T. Søndergaard and S. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi (b) 245(1), 9–19 (2008).
[Crossref]

T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancements,” Phys. Rev. B 75(7), 073402 (2007).
[Crossref]

Bozhevolnyi, S. I.

Cai, W.

D. Chen, W. Cai, B. Zinser, and M. H. Cho, “Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers,” J. Comput. Phys. 321, 303–320 (2016).
[Crossref]

Carbó-Argibay, E.

V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. J. García de Abajo“Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20(22), 4288–4293 (2008).
[Crossref]

Chan, C. T.

S. B. Wang, H. H. Zheng, J. J. Xiao, Z. F. Lin, and C. T. Chan, “Fast multipole boundary element method for three dimensional electromagnetic scattering problem,” Int. J. Comput. Mater. Sci. Eng. 1(04), 1250038 (2012).

Chandler-Wilde, S. N.

S. N. Chandler-Wilde and D. C. Hothersall, “Efficient calculation of the Green function for acoustic propagation above a homogeneous impedance plane,” J. Sound Vibr. 180(5), 705–724 (1995).
[Crossref]

Chen, D.

D. Chen, W. Cai, B. Zinser, and M. H. Cho, “Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers,” J. Comput. Phys. 321, 303–320 (2016).
[Crossref]

Chen, Y. T.

Y. T. Chen, Y. Zhang, and A. F. Koenderink, “General point dipole theory for periodic metasurfaces: magnetoelectric scattering lattices coupled to planar photonic structures,” Opt. Express 25(18), 21358–21378 (2017).
[Crossref] [PubMed]

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

Chew, W. C.

W. C. Chew, M. S. Tong, and B. Hu, Integral Equation Methods for Electromagnetic and Elastic Waves (Morgan & Claypool Publishers, 2009).

Cho, M. H.

D. Chen, W. Cai, B. Zinser, and M. H. Cho, “Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers,” J. Comput. Phys. 321, 303–320 (2016).
[Crossref]

Dereux, A.

Economou, E. N.

E. N. Economou, Green’s Functions in Quantum Physics(Springer, 1983).
[Crossref]

García de Abajo, F. J.

V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. J. García de Abajo“Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20(22), 4288–4293 (2008).
[Crossref]

F. J. García de Abajo and A. Howie“Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys, Rev. B 65(11), 115418 (2002).
[Crossref]

Gibson, W. C.

W. C. Gibson, The Method of Moments in Electromagnetics (CRC, 2015).

Girard, C.

Gregersen, N.

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

A. V. Lavrinenko, J. Lægsgaard, N. Gregersen, F. Schmidt, and T. Søndergaard, Numerical Methods in Photonics (CRC, 2014).
[Crossref]

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods(Macmillan, 1968).

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2012).
[Crossref]

Hohenester, U.

J. Waxenegger, A. Trügler, and U. Hohenester, “Plasmonics simulations with the MNPBEM toolbox: Consideration of substrates and layer structures,” Comput. Phys. Commun. 193, 138–150 (2015).
[Crossref]

U. Hohenester, “Simulating electron energy loss spectroscopy with the MNPBEM toolbox,” Comput. Phys. Commun. 185(3), 1177–1187 (2014).
[Crossref]

U. Hohenester and A. Trügler, “MNPBEM-A Matlab toolbox for the simulation of plasmonic nanoparticles,” Comput. Phys. Commun. 183(2), 370–381 (2012).
[Crossref]

Hothersall, D. C.

S. N. Chandler-Wilde and D. C. Hothersall, “Efficient calculation of the Green function for acoustic propagation above a homogeneous impedance plane,” J. Sound Vibr. 180(5), 705–724 (1995).
[Crossref]

Howie, A.

F. J. García de Abajo and A. Howie“Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys, Rev. B 65(11), 115418 (2002).
[Crossref]

Hu, B.

W. C. Chew, M. S. Tong, and B. Hu, Integral Equation Methods for Electromagnetic and Elastic Waves (Morgan & Claypool Publishers, 2009).

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles(Wiley, 2008).

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics(Wiley, 2002).

Jung, J.

T. Søndergaard, V. Siahpoush, and J. Jung, “Coupling light into and out from the surface plasmon polaritons of a nanometer-thin metal film with a metal nanostrip,” Phys. Rev. B 86(8), 085455 (2012).
[Crossref]

J. Jung, T. Søndergarrd, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

J. Jung, T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Theoretical analysis and experimental demonstration of resonant light scattering from metal nanostrips on quartz,” J. Opt. Soc. Am. B 26(1), 121–124 (2009).
[Crossref]

J. Jung and T. Søndergaard, “Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B 77(24), 245310 (2008).
[Crossref]

Kern, A. M.

Kienle, A.

J. Schäfer, S. C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

Koenderink, A. F.

Kottmann, J. P.

J. P. Kottmann and O. J. F. Martin, “Accurate solution of the volume integral equation for high-permittivity scatterers,” IEEE Trans. Antennas Propag. 48(11), 1719–1726 (2000).
[Crossref]

Kress, R.

R. Kress, “Boundary integral equations in time-harmonic acoustic scattering,” Mathl. Comput. Modelling 15(3–5), 229–243 (1991).
[Crossref]

Kumagai, N.

N. Morita, N. Kumagai, and J. R. Mautz, Integral Equation Methods for Electromagnetics (Aetech House, 1990).

Lægsgaard, J.

A. V. Lavrinenko, J. Lægsgaard, N. Gregersen, F. Schmidt, and T. Søndergaard, Numerical Methods in Photonics (CRC, 2014).
[Crossref]

Larsen, A. N.

J. Jung, T. Søndergarrd, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

Lavrinenko, A. V.

A. V. Lavrinenko, J. Lægsgaard, N. Gregersen, F. Schmidt, and T. Søndergaard, Numerical Methods in Photonics (CRC, 2014).
[Crossref]

Le Ru, E. C.

Lee, S. C.

J. Schäfer, S. C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

S. C. Lee, “Dependent scattering of an obliquely incident plane wave by a collection of parallel cylinders,” J. Appl. Phys. 68(10), 4952–4957 (1990).
[Crossref]

Lin, Z. F.

S. B. Wang, H. H. Zheng, J. J. Xiao, Z. F. Lin, and C. T. Chan, “Fast multipole boundary element method for three dimensional electromagnetic scattering problem,” Int. J. Comput. Mater. Sci. Eng. 1(04), 1250038 (2012).

Liz-Marzán, L. M.

V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. J. García de Abajo“Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20(22), 4288–4293 (2008).
[Crossref]

Lodahl, P.

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

Loebl, E. M.

E. M. Loebl, Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

Mait, J. N.

Martin, O. J.

Martin, O. J. F.

Mautz, J. R.

N. Morita, N. Kumagai, and J. R. Mautz, Integral Equation Methods for Electromagnetics (Aetech House, 1990).

Mirotznik, M. S.

Mishchenko, M. I.

M. A. Yurkin and M. I. Mishchenko, “Volume integral equation for electromagnetic scattering: Rigorous derivation and analysis for a set of multilayered particles with piecewise-smooth boundaries in a passive host medium,” Phys. Rev. A 97(4), 043824 (2018).
[Crossref]

Morita, N.

N. Morita, N. Kumagai, and J. R. Mautz, Integral Equation Methods for Electromagnetics (Aetech House, 1990).

Mørk, J.

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

Myroshnychenko, V.

V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. J. García de Abajo“Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20(22), 4288–4293 (2008).
[Crossref]

Nielsen, B. B.

J. Jung, T. Søndergarrd, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

Nielsen, T. R.

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2012).
[Crossref]

Pastoriza-Santos, I.

V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. J. García de Abajo“Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20(22), 4288–4293 (2008).
[Crossref]

Pedersen, K.

J. Jung, T. Søndergarrd, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

Pedersen, T. G.

J. Jung, T. Søndergarrd, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

Pérez-Juste, J.

V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. J. García de Abajo“Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20(22), 4288–4293 (2008).
[Crossref]

Prather, D. W.

Raziman, T. V.

Rodríguez-Oliveros, R.

Sánchez-Gil, J. A.

Schäfer, J.

J. Schäfer, S. C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

Schmidt, F.

A. V. Lavrinenko, J. Lægsgaard, N. Gregersen, F. Schmidt, and T. Søndergaard, Numerical Methods in Photonics (CRC, 2014).
[Crossref]

Siahpoush, V.

T. Søndergaard, V. Siahpoush, and J. Jung, “Coupling light into and out from the surface plasmon polaritons of a nanometer-thin metal film with a metal nanostrip,” Phys. Rev. B 86(8), 085455 (2012).
[Crossref]

V. Siahpoush and T. Søndegaard, ard J. Jung, “Green’s function approach to investigate the excitation of surface plasmon polaritons in a nanometer-thin metal film,” Phys. Rev. B 85(7), 075305 (2012).
[Crossref]

Somerville, W. R. C.

Søndegaard, T.

V. Siahpoush and T. Søndegaard, ard J. Jung, “Green’s function approach to investigate the excitation of surface plasmon polaritons in a nanometer-thin metal film,” Phys. Rev. B 85(7), 075305 (2012).
[Crossref]

Søndergaard, T.

T. Søndergaard and S. I. Bozhevolnyi, “Theoretical analysis of plasmonic black gold: periodic arrays of ultra-sharp grooves,” New J. Phys. 15(1), 013034 (2013).
[Crossref]

T. Søndergaard, V. Siahpoush, and J. Jung, “Coupling light into and out from the surface plasmon polaritons of a nanometer-thin metal film with a metal nanostrip,” Phys. Rev. B 86(8), 085455 (2012).
[Crossref]

J. Jung, T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Theoretical analysis and experimental demonstration of resonant light scattering from metal nanostrips on quartz,” J. Opt. Soc. Am. B 26(1), 121–124 (2009).
[Crossref]

T. Søndergaard and S. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi (b) 245(1), 9–19 (2008).
[Crossref]

J. Jung and T. Søndergaard, “Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B 77(24), 245310 (2008).
[Crossref]

T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi (b) 244(10), 3448–3462 (2007).
[Crossref]

T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancements,” Phys. Rev. B 75(7), 073402 (2007).
[Crossref]

A. V. Lavrinenko, J. Lægsgaard, N. Gregersen, F. Schmidt, and T. Søndergaard, Numerical Methods in Photonics (CRC, 2014).
[Crossref]

T. Søndergaard, Green’s Function Integral Equation Methods in Nano-Optics (CRC, 2018).

Søndergarrd, T.

J. Jung, T. Søndergarrd, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

Tong, M. S.

W. C. Chew, M. S. Tong, and B. Hu, Integral Equation Methods for Electromagnetic and Elastic Waves (Morgan & Claypool Publishers, 2009).

Trügler, A.

J. Waxenegger, A. Trügler, and U. Hohenester, “Plasmonics simulations with the MNPBEM toolbox: Consideration of substrates and layer structures,” Comput. Phys. Commun. 193, 138–150 (2015).
[Crossref]

U. Hohenester and A. Trügler, “MNPBEM-A Matlab toolbox for the simulation of plasmonic nanoparticles,” Comput. Phys. Commun. 183(2), 370–381 (2012).
[Crossref]

Wang, S. B.

S. B. Wang, H. H. Zheng, J. J. Xiao, Z. F. Lin, and C. T. Chan, “Fast multipole boundary element method for three dimensional electromagnetic scattering problem,” Int. J. Comput. Mater. Sci. Eng. 1(04), 1250038 (2012).

Waxenegger, J.

J. Waxenegger, A. Trügler, and U. Hohenester, “Plasmonics simulations with the MNPBEM toolbox: Consideration of substrates and layer structures,” Comput. Phys. Commun. 193, 138–150 (2015).
[Crossref]

Xiao, J. J.

S. B. Wang, H. H. Zheng, J. J. Xiao, Z. F. Lin, and C. T. Chan, “Fast multipole boundary element method for three dimensional electromagnetic scattering problem,” Int. J. Comput. Mater. Sci. Eng. 1(04), 1250038 (2012).

Yurkin, M. A.

M. A. Yurkin and M. I. Mishchenko, “Volume integral equation for electromagnetic scattering: Rigorous derivation and analysis for a set of multilayered particles with piecewise-smooth boundaries in a passive host medium,” Phys. Rev. A 97(4), 043824 (2018).
[Crossref]

Zhang, Y.

Zheng, H. H.

S. B. Wang, H. H. Zheng, J. J. Xiao, Z. F. Lin, and C. T. Chan, “Fast multipole boundary element method for three dimensional electromagnetic scattering problem,” Int. J. Comput. Mater. Sci. Eng. 1(04), 1250038 (2012).

Zinser, B.

D. Chen, W. Cai, B. Zinser, and M. H. Cho, “Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers,” J. Comput. Phys. 321, 303–320 (2016).
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Ziolkowski, R. W.

S. Arslanagić and R. W. Ziolkowski, “Highly subwavelength, superdirective cylindrical nanoantenna,” Phys. Rev. Lett. 120(23), 237401 (2018).
[Crossref]

Adv. Mater. (1)

V. Myroshnychenko, E. Carbó-Argibay, I. Pastoriza-Santos, J. Pérez-Juste, L. M. Liz-Marzán, and F. J. García de Abajo“Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20(22), 4288–4293 (2008).
[Crossref]

Comput. Phys. Commun. (3)

U. Hohenester and A. Trügler, “MNPBEM-A Matlab toolbox for the simulation of plasmonic nanoparticles,” Comput. Phys. Commun. 183(2), 370–381 (2012).
[Crossref]

U. Hohenester, “Simulating electron energy loss spectroscopy with the MNPBEM toolbox,” Comput. Phys. Commun. 185(3), 1177–1187 (2014).
[Crossref]

J. Waxenegger, A. Trügler, and U. Hohenester, “Plasmonics simulations with the MNPBEM toolbox: Consideration of substrates and layer structures,” Comput. Phys. Commun. 193, 138–150 (2015).
[Crossref]

IEEE Trans. Antennas Propag. (1)

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[Crossref]

Int. J. Comput. Mater. Sci. Eng. (1)

S. B. Wang, H. H. Zheng, J. J. Xiao, Z. F. Lin, and C. T. Chan, “Fast multipole boundary element method for three dimensional electromagnetic scattering problem,” Int. J. Comput. Mater. Sci. Eng. 1(04), 1250038 (2012).

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J. Comput. Phys. (1)

D. Chen, W. Cai, B. Zinser, and M. H. Cho, “Accurate and efficient Nyström volume integral equation method for the Maxwell equations for multiple 3-D scatterers,” J. Comput. Phys. 321, 303–320 (2016).
[Crossref]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (2)

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

J. Schäfer, S. C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

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S. N. Chandler-Wilde and D. C. Hothersall, “Efficient calculation of the Green function for acoustic propagation above a homogeneous impedance plane,” J. Sound Vibr. 180(5), 705–724 (1995).
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R. Kress, “Boundary integral equations in time-harmonic acoustic scattering,” Mathl. Comput. Modelling 15(3–5), 229–243 (1991).
[Crossref]

New J. Phys. (1)

T. Søndergaard and S. I. Bozhevolnyi, “Theoretical analysis of plasmonic black gold: periodic arrays of ultra-sharp grooves,” New J. Phys. 15(1), 013034 (2013).
[Crossref]

Opt. Express (2)

Phys, Rev. B (1)

F. J. García de Abajo and A. Howie“Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys, Rev. B 65(11), 115418 (2002).
[Crossref]

Phys. Rev. A (1)

M. A. Yurkin and M. I. Mishchenko, “Volume integral equation for electromagnetic scattering: Rigorous derivation and analysis for a set of multilayered particles with piecewise-smooth boundaries in a passive host medium,” Phys. Rev. A 97(4), 043824 (2018).
[Crossref]

Phys. Rev. B (6)

V. Siahpoush and T. Søndegaard, ard J. Jung, “Green’s function approach to investigate the excitation of surface plasmon polaritons in a nanometer-thin metal film,” Phys. Rev. B 85(7), 075305 (2012).
[Crossref]

T. Søndergaard, V. Siahpoush, and J. Jung, “Coupling light into and out from the surface plasmon polaritons of a nanometer-thin metal film with a metal nanostrip,” Phys. Rev. B 86(8), 085455 (2012).
[Crossref]

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

J. Jung and T. Søndergaard, “Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B 77(24), 245310 (2008).
[Crossref]

J. Jung, T. Søndergarrd, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancements,” Phys. Rev. B 75(7), 073402 (2007).
[Crossref]

Phys. Rev. Lett. (1)

S. Arslanagić and R. W. Ziolkowski, “Highly subwavelength, superdirective cylindrical nanoantenna,” Phys. Rev. Lett. 120(23), 237401 (2018).
[Crossref]

Phys. Status Solidi (b) (2)

T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi (b) 244(10), 3448–3462 (2007).
[Crossref]

T. Søndergaard and S. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi (b) 245(1), 9–19 (2008).
[Crossref]

Other (13)

J. Jin, The Finite Element Method in Electromagnetics(Wiley, 2002).

T. Søndergaard, Green’s Function Integral Equation Methods in Nano-Optics (CRC, 2018).

E. N. Economou, Green’s Functions in Quantum Physics(Springer, 1983).
[Crossref]

A. V. Lavrinenko, J. Lægsgaard, N. Gregersen, F. Schmidt, and T. Søndergaard, Numerical Methods in Photonics (CRC, 2014).
[Crossref]

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2012).
[Crossref]

W. C. Chew, M. S. Tong, and B. Hu, Integral Equation Methods for Electromagnetic and Elastic Waves (Morgan & Claypool Publishers, 2009).

W. C. Gibson, The Method of Moments in Electromagnetics (CRC, 2015).

R. F. Harrington, Field Computation by Moment Methods(Macmillan, 1968).

N. Morita, N. Kumagai, and J. R. Mautz, Integral Equation Methods for Electromagnetics (Aetech House, 1990).

The matlab scripts of the practical impelemntation can be requested via yuntian@hust.edu.cn

E. M. Loebl, Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles(Wiley, 2008).

Comsol, “Comsol Multiphysics Modeling Software,” https://www.comsol.com/ .

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Figures (5)

Fig. 1
Fig. 1 A circular disk is discretized into 15 triangles which are further used in (a) type-1 FEGIE and (b) type-2 FEGIE. (c) A small portion, indicated by light gray, of the circular disk of (b) with only 4 triangles and 6 vertices. In type-2 FEGIE, the dependent variables are the vertices indicated by the solid blue dots, while the auxiliary variables associated with each triangle are the quadrature points indicated by red diamonds inside the corresponding triangles.
Fig. 2
Fig. 2 (a) Triangle discretization of the dielectric rod. (b) Far-field pattern calculated using type-1 FEGIE, type-2 FEGIE, staircase GIE, and Mie theory. The radius of the scatterer is 0.6 μm, and the vacuum wavelength is 0.633 μm. The numbersof DOFs in type-1 FEGIE, type-2 FEGIE, and staircase are 1080, 595, and 1085, respectively.
Fig. 3
Fig. 3 Far-field pattern of the light scattering by (a) the 3-layered rod and (b) the 5-layered rod calculated using type-1 FEGIE, type-2 FEGIE, and Mie theory. For the 3-layered (5-layered) rod, the numbers of DOFs in type-1 FEGIE and type-2 FEGIE are 3186 (4812) and 1674 (2507).
Fig. 4
Fig. 4 (a) Far-field patterns of the light scattering by a complex scatterer with corrugated surface calculated using type-1 FEGIE, type-2 FEGIE, staircase GIE, and Mie theory. (b/c) Triangle/Staircase approximation of the surface-corrugated scatterer. The numbers of DOFs in type-1 FEGIE, type-2 FEGIE, staircase, and COMSOL are 2586, 1407, 2590, and 280525 respectively.
Fig. 5
Fig. 5 Farfield convergence versus the number of DOFs.

Tables (1)

Tables Icon

Table 1 Assembling Transformation

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

E ( r ) = i ω μ 0 Ω s g ¯ ( r , r ) J s ( r ) d V ,
[ × × k 0 2 ε ¯ b g ] E 0 ( r ) = 0 ,
[ × × k 0 2 ε ¯ r ( r ) ] E ( r ) = 0 ,
E ( r ) = E 0 ( r ) + r Ω g ¯ ( r , r ) k 0 2 ( ε ( r ) ε r e f ) E ( r ) d v .
E z ( r ) = E 0 z ( r ) + r Ω g ( r , r ) k 0 2 ( ε ( r ) ε r e f ) E z ( r ) d v ,
E i = E 0 , i + j g i j k 0 2 ( ε j ε r e f ) E j A j
( α ( i , r 1 ) l u l i α ( i , r 2 ) l u l i α ( i , r 3 ) l u l i ) = ( E 0 ( i , r 1 ) E 0 ( i , r 2 ) E 0 ( i , r 3 ) ) + j k 0 2 Δ ε A j 3 ( g ( i , r 1 ) ( j , r p ) α ( j , r p ) l u l j g ( i , r 2 ) ( j , r p ) α ( j , r p ) l u l j g ( i , r 3 ) ( j , r p ) α ( j , r p ) l u l j ) ,
( α ¯ 11 0 0 0 0 α ¯ 22 0 0 0 0 α ¯ 33 0 0 0 0 α ¯ 44 ) ( U 1 U 2 U 3 U 4 ) = ( E 01 E 02 E 03 E 04 ) + ( g ¯ 11 g ¯ 12 g ¯ 13 g ¯ 14 g ¯ 21 g ¯ 22 g ¯ 23 g ¯ 24 g ¯ 31 g ¯ 32 g ¯ 33 g ¯ 34 g ¯ 41 g ¯ 42 g ¯ 43 g ¯ 44 ) ( U 1 U 2 U 3 U 4 ) ,
( T ¯ a s m [ α ¯ i i ] T ¯ a s m T ) U g = T ¯ a s m E i n c + ( T ¯ a s m [ g ¯ i j ] T ¯ a s m T ) U g ,
g i i = 1 A i A i g ( r , r ) d A
g i i 1 2 i ( k 0 n r e f a ) 2 ( k 0 n r e f a H 1 ( 2 ) ( k 0 n r e f a ) 2 i π )
g f f ( r , r ) = 1 4 2 π k r e i π 4 e i k r e i k r r r
E S C f f ( r ) = 1 4 2 π k r e i π 4 e i k r k 0 2 ( ε ( r ) ε r e f ) E ( r ) e i k r r r d A

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