Abstract

We introduce a 3-dimensional electromagnetic eigenmodal algorithm for the theoretical analysis of resonating nano-optical structures. The method, a variant of the Jacobi–Davidson algorithm, solves the electric field vector wave, or curl-curl, equation for the electromagnetic eigenmodes of resonant optical structures with a finite element method. In particular, the method includes transparent boundary conditions that enable the analysis of resonating structures in unbounded space. We demonstrate the performance of the method. First, we calculate the modes of several dielectric resonator antennas and compare them to theoretically determined results. Second, we calculate the modes of a nano-cuboid and compare them to theoretically determined results. Third, we numerically analyze spherical nanoparticles and compare the result to the theoretical Mie solution. Fourth, we analyze optical dipole antenna configurations in order to assess the method’s capability for solving technologically relevant problems.

© 2012 OSA

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  1. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
    [CrossRef]
  2. L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007).
    [CrossRef] [PubMed]
  3. P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photon. 1, 438–483 (2009).
    [CrossRef]
  4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [CrossRef] [PubMed]
  5. H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
    [CrossRef] [PubMed]
  6. D. W. Pohl, S. G. Rodrigo, and L. Novotny, “Stacked optical antennas,” Appl. Phys. Lett. 98, 023111 (2011).
    [CrossRef]
  7. A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657 (2009).
    [CrossRef]
  8. M. F. Garcia-Parajo, “Optical antennas focus in on biology,” Nat. Photon. 2, 201–203, (2008).
    [CrossRef]
  9. P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325, 594–597 (2009).
    [CrossRef] [PubMed]
  10. G. W. Hanson and A. B. Yakovlev, Operator Theory for Electromagnetics – An Introduction (Springer, 2002).
    [PubMed]
  11. Ch. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House Books, Boston, 1990).
  12. J. Jin, The Finite Element Method in Electromagnetics (John Wiley, New York, 2002).
  13. P. Monk, Finite Element Methods for Maxwell’s Equations (Oxford University Press, Oxford, 2003).
    [CrossRef] [PubMed]
  14. J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics – Antennas, Microwave Circuits and Scattering Applications (IEEE Press, New York, 1998).
  15. A. Okaya and L. F. Barash, “The dielectric microwave resonator,” Proc. IRE 50, 2081–2092 (1962).
    [CrossRef]
  16. R. K. Mongia and A. Ittipiboon, “Theoretical and experimental investigations on rectangular dielectric resonator antennas,” IEEE Trans. Antennas Propag. 45, 1348–1356 (1997).
    [CrossRef]
  17. C. Bohren and D. Huffmann, Absorption and Scattering of Light by Small Particles (John Wiley, New York, 1983).
  18. S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics (John Wiley, New York, 1993).
  19. A. Dhawan, S. J. Norton, M. D. Gerhold, and T. Vo-Dinh, “Comparison of FDTD numerical computations and analytical multipole expansion method for plasmonics-active nanosphere dimers,” Opt. Express 17, 9688–9703 (2009).
    [CrossRef] [PubMed]
  20. X. Cui and D. Erni, “The influence of particle shapes on the optical response of nearly touching plasmonic nanoparticle dimers,” J. Comput. Theor. Nanosci. 47, 1610–1615 (2010).
    [CrossRef]
  21. J. M. McMahon, A. I. Henry, K. L. Wustholz, M. J. Natan, R. G. Freeman, R. P. Van Duyne, and G. C. Schatz, “Gold nanoparticle dimer plasmonics: finite element method calculations of the electromagnetic enhancement to surface-enhanced Raman spectroscopy,” Anal. Bioanal. Chem. 394, 1819–1825 (2009).
    [CrossRef] [PubMed]
  22. J. Smajic, C. Hafner, L. Raguin, K. Tavzarashvili, and M. Mishrikey, “Comparison of numerical methods for the analysis of plasmonic structures,” J. Comput. Theor. Nanosci. 6, 763–774 (2009).
    [CrossRef]
  23. J. Smajic, C. Hafner, K. Tavzarashvili, and R. Vahldieck, “Numerical analysis of channel plasmon polaritons enhanced optical antennas,” J. Comput. Theor. Nanosci. 5, 725–734 (2008).
    [CrossRef]
  24. C. G. Khoury, S. J. Norton, and T. Vo-Dinh, “Plasmonics of 3-D nanoshell dimers using multipole expansion and finite element method,” ACS Nano 3, 2776–2788 (2009).
    [CrossRef] [PubMed]
  25. A. M. Kern and O. J. F. Martin, “Modeling near-field properties of plasmonic nanoparticles: a surface integral approach,” in Plasmonic: Nanoimaging, Nanofabrication, and their Applications V, V. M. Shalaev and D. P. Tsai, eds., Proc. SPIE7395, 739518 (2009).
  26. A. M. Kern and O. J. F. Martin, “Excitation and reemission of molecules near realistic plasmonic nanostructures,” Nano Lett. 11, 482–487 (2011).
    [CrossRef] [PubMed]
  27. M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9, 399–404 (2009).
    [CrossRef]
  28. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  29. G. M. Hale and M. R. Querry, “Optical constants of water in the 200 nm to 200 μm wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef] [PubMed]
  30. R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A: Gen. Phys. 3, 233245 (1970).
    [CrossRef]
  31. R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299, 309–312 (2002).
    [CrossRef]
  32. T. G. Philbin, “Electromagnetic energy momentum in dispersive media,” Phys. Rev. A 83, 013823 (2011).
    [CrossRef]
  33. F. D. Nunes, T. C. Vasconcelos, M. Bezerra, and J. Weiner, “Electromagnetic energy density in dispersive and dissipative media,” J. Opt. Soc. Am. B 28, 1544–1552 (2011).
    [CrossRef]
  34. L. Brillouin, Wave Propagation and Group Velocity (Academic Press, New York, 1960).
  35. A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
    [CrossRef]
  36. C. Geuzaine and J.-F. Remacle, “Gmsh: A 3-D finite element mesh generator with built-in pre- and postprocessing facilities,” Int. J. Numer. Methods Eng. 79, 1309–1331 (2009).
    [CrossRef]
  37. F. Tisseur and K. Meerbergen, “The quadratic eigenvalue problem,” SIAM Rev.  43, 235–286 (2001).
    [CrossRef]
  38. P. Arbenz and M. E. Hochstenbach, “A Jacobi–Davidson method for solving complex symmetric eigenvalue problems,” SIAM J. Sci. Comput. 25, 1655–1673 (2004).
    [CrossRef]
  39. Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (SIAM, Philadelphia PA, 2000).
    [CrossRef]
  40. D. R. Fokkema, G. L. G. Sleijpen, and H. A. Van der Vorst, “Jacobi–Davidson style QR and QZ algorithms for the partial reduction of matrix pencils,” SIAM J. Sci. Comput. 20, 94–125 (1996).
    [CrossRef]
  41. R. Geus, “The Jacobi–Davidson algorithm for solving large sparse symmetric eigenvalue problems.” PhD Thesis No. 14734, ETH Zurich 2002.
  42. P. Arbenz, M. Bečka, R. Geus, U. Hetmaniuk, and T. Mengotti, “On a parallel multilevel preconditioned Maxwell eigensolver,” Parallel Comput. 32, 157–165 (2006).
    [CrossRef]
  43. P. Arbenz and R. Geus, “Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems,” Appl. Numer. Math. 54, 107–121 (2005).
    [CrossRef]
  44. Trilinos Project Home Page, http://trilinos.sandia.gov/ .
  45. Paraview Home Page, http://www.paraview.org/ .
  46. Home Page of the Swiss National Supercomputing Centre (CSCS), http://www.cscs.ch/ .
  47. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002)
    [CrossRef] [PubMed]
  48. R. Fuchs and K. L. Kliewer, “Optical modes of vibration in an ionic crystal spheres,” J. Opt. Soc. Am. 58, 319–330 (1968)
    [CrossRef]
  49. S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
    [CrossRef] [PubMed]
  50. H. Fischer and O. J. F. Martin, “Engineering the optical response of plasmonic nanoantennas,” Opt. Express 16, 9144–9154 (2008).
    [CrossRef] [PubMed]

2011

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

D. W. Pohl, S. G. Rodrigo, and L. Novotny, “Stacked optical antennas,” Appl. Phys. Lett. 98, 023111 (2011).
[CrossRef]

A. M. Kern and O. J. F. Martin, “Excitation and reemission of molecules near realistic plasmonic nanostructures,” Nano Lett. 11, 482–487 (2011).
[CrossRef] [PubMed]

T. G. Philbin, “Electromagnetic energy momentum in dispersive media,” Phys. Rev. A 83, 013823 (2011).
[CrossRef]

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[CrossRef]

F. D. Nunes, T. C. Vasconcelos, M. Bezerra, and J. Weiner, “Electromagnetic energy density in dispersive and dissipative media,” J. Opt. Soc. Am. B 28, 1544–1552 (2011).
[CrossRef]

2010

S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
[CrossRef] [PubMed]

X. Cui and D. Erni, “The influence of particle shapes on the optical response of nearly touching plasmonic nanoparticle dimers,” J. Comput. Theor. Nanosci. 47, 1610–1615 (2010).
[CrossRef]

2009

J. M. McMahon, A. I. Henry, K. L. Wustholz, M. J. Natan, R. G. Freeman, R. P. Van Duyne, and G. C. Schatz, “Gold nanoparticle dimer plasmonics: finite element method calculations of the electromagnetic enhancement to surface-enhanced Raman spectroscopy,” Anal. Bioanal. Chem. 394, 1819–1825 (2009).
[CrossRef] [PubMed]

J. Smajic, C. Hafner, L. Raguin, K. Tavzarashvili, and M. Mishrikey, “Comparison of numerical methods for the analysis of plasmonic structures,” J. Comput. Theor. Nanosci. 6, 763–774 (2009).
[CrossRef]

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9, 399–404 (2009).
[CrossRef]

C. G. Khoury, S. J. Norton, and T. Vo-Dinh, “Plasmonics of 3-D nanoshell dimers using multipole expansion and finite element method,” ACS Nano 3, 2776–2788 (2009).
[CrossRef] [PubMed]

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657 (2009).
[CrossRef]

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325, 594–597 (2009).
[CrossRef] [PubMed]

A. Dhawan, S. J. Norton, M. D. Gerhold, and T. Vo-Dinh, “Comparison of FDTD numerical computations and analytical multipole expansion method for plasmonics-active nanosphere dimers,” Opt. Express 17, 9688–9703 (2009).
[CrossRef] [PubMed]

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photon. 1, 438–483 (2009).
[CrossRef]

C. Geuzaine and J.-F. Remacle, “Gmsh: A 3-D finite element mesh generator with built-in pre- and postprocessing facilities,” Int. J. Numer. Methods Eng. 79, 1309–1331 (2009).
[CrossRef]

2008

H. Fischer and O. J. F. Martin, “Engineering the optical response of plasmonic nanoantennas,” Opt. Express 16, 9144–9154 (2008).
[CrossRef] [PubMed]

M. F. Garcia-Parajo, “Optical antennas focus in on biology,” Nat. Photon. 2, 201–203, (2008).
[CrossRef]

J. Smajic, C. Hafner, K. Tavzarashvili, and R. Vahldieck, “Numerical analysis of channel plasmon polaritons enhanced optical antennas,” J. Comput. Theor. Nanosci. 5, 725–734 (2008).
[CrossRef]

2007

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007).
[CrossRef] [PubMed]

2006

P. Arbenz, M. Bečka, R. Geus, U. Hetmaniuk, and T. Mengotti, “On a parallel multilevel preconditioned Maxwell eigensolver,” Parallel Comput. 32, 157–165 (2006).
[CrossRef]

2005

P. Arbenz and R. Geus, “Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems,” Appl. Numer. Math. 54, 107–121 (2005).
[CrossRef]

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

2004

P. Arbenz and M. E. Hochstenbach, “A Jacobi–Davidson method for solving complex symmetric eigenvalue problems,” SIAM J. Sci. Comput. 25, 1655–1673 (2004).
[CrossRef]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

2002

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002)
[CrossRef] [PubMed]

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299, 309–312 (2002).
[CrossRef]

2001

F. Tisseur and K. Meerbergen, “The quadratic eigenvalue problem,” SIAM Rev.  43, 235–286 (2001).
[CrossRef]

1997

R. K. Mongia and A. Ittipiboon, “Theoretical and experimental investigations on rectangular dielectric resonator antennas,” IEEE Trans. Antennas Propag. 45, 1348–1356 (1997).
[CrossRef]

1996

D. R. Fokkema, G. L. G. Sleijpen, and H. A. Van der Vorst, “Jacobi–Davidson style QR and QZ algorithms for the partial reduction of matrix pencils,” SIAM J. Sci. Comput. 20, 94–125 (1996).
[CrossRef]

1973

1972

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

1970

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A: Gen. Phys. 3, 233245 (1970).
[CrossRef]

1968

1962

A. Okaya and L. F. Barash, “The dielectric microwave resonator,” Proc. IRE 50, 2081–2092 (1962).
[CrossRef]

Aouani, H.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

Arbenz, P.

P. Arbenz, M. Bečka, R. Geus, U. Hetmaniuk, and T. Mengotti, “On a parallel multilevel preconditioned Maxwell eigensolver,” Parallel Comput. 32, 157–165 (2006).
[CrossRef]

P. Arbenz and R. Geus, “Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems,” Appl. Numer. Math. 54, 107–121 (2005).
[CrossRef]

P. Arbenz and M. E. Hochstenbach, “A Jacobi–Davidson method for solving complex symmetric eigenvalue problems,” SIAM J. Sci. Comput. 25, 1655–1673 (2004).
[CrossRef]

Avlasevich, Y.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657 (2009).
[CrossRef]

Bai, Z.

Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (SIAM, Philadelphia PA, 2000).
[CrossRef]

Barash, L. F.

A. Okaya and L. F. Barash, “The dielectric microwave resonator,” Proc. IRE 50, 2081–2092 (1962).
[CrossRef]

Barchiesi, D.

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Becka, M.

P. Arbenz, M. Bečka, R. Geus, U. Hetmaniuk, and T. Mengotti, “On a parallel multilevel preconditioned Maxwell eigensolver,” Parallel Comput. 32, 157–165 (2006).
[CrossRef]

Bezerra, M.

Bharadwaj, P.

Bohren, C.

C. Bohren and D. Huffmann, Absorption and Scattering of Light by Small Particles (John Wiley, New York, 1983).

Bonod, N.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic Press, New York, 1960).

Chatterjee, A.

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics – Antennas, Microwave Circuits and Scattering Applications (IEEE Press, New York, 1998).

Chen, C. H.

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9, 399–404 (2009).
[CrossRef]

Chen, H. Y.

S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
[CrossRef] [PubMed]

Christy, R. W.

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

Chu, M. W.

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9, 399–404 (2009).
[CrossRef]

Cui, X.

X. Cui and D. Erni, “The influence of particle shapes on the optical response of nearly touching plasmonic nanoparticle dimers,” J. Comput. Theor. Nanosci. 47, 1610–1615 (2010).
[CrossRef]

de la Chapelle, M. L.

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Demmel, J.

Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (SIAM, Philadelphia PA, 2000).
[CrossRef]

Deng, J. P.

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9, 399–404 (2009).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Deutsch, B.

Devaux, E.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

Dhawan, A.

Dongarra, J.

Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (SIAM, Philadelphia PA, 2000).
[CrossRef]

Duzer, T. V.

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics (John Wiley, New York, 1993).

Ebbesen, T. W.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Erni, D.

X. Cui and D. Erni, “The influence of particle shapes on the optical response of nearly touching plasmonic nanoparticle dimers,” J. Comput. Theor. Nanosci. 47, 1610–1615 (2010).
[CrossRef]

Fan, S.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657 (2009).
[CrossRef]

Feldmann, J.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002)
[CrossRef] [PubMed]

Fischer, H.

Fokkema, D. R.

D. R. Fokkema, G. L. G. Sleijpen, and H. A. Van der Vorst, “Jacobi–Davidson style QR and QZ algorithms for the partial reduction of matrix pencils,” SIAM J. Sci. Comput. 20, 94–125 (1996).
[CrossRef]

Franzl, T.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002)
[CrossRef] [PubMed]

Freeman, R. G.

J. M. McMahon, A. I. Henry, K. L. Wustholz, M. J. Natan, R. G. Freeman, R. P. Van Duyne, and G. C. Schatz, “Gold nanoparticle dimer plasmonics: finite element method calculations of the electromagnetic enhancement to surface-enhanced Raman spectroscopy,” Anal. Bioanal. Chem. 394, 1819–1825 (2009).
[CrossRef] [PubMed]

Fuchs, R.

García de Abajo, F. J.

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9, 399–404 (2009).
[CrossRef]

Garcia-Parajo, M. F.

M. F. Garcia-Parajo, “Optical antennas focus in on biology,” Nat. Photon. 2, 201–203, (2008).
[CrossRef]

Gerhold, M. D.

Geus, R.

P. Arbenz, M. Bečka, R. Geus, U. Hetmaniuk, and T. Mengotti, “On a parallel multilevel preconditioned Maxwell eigensolver,” Parallel Comput. 32, 157–165 (2006).
[CrossRef]

P. Arbenz and R. Geus, “Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems,” Appl. Numer. Math. 54, 107–121 (2005).
[CrossRef]

R. Geus, “The Jacobi–Davidson algorithm for solving large sparse symmetric eigenvalue problems.” PhD Thesis No. 14734, ETH Zurich 2002.

Geuzaine, C.

C. Geuzaine and J.-F. Remacle, “Gmsh: A 3-D finite element mesh generator with built-in pre- and postprocessing facilities,” Int. J. Numer. Methods Eng. 79, 1309–1331 (2009).
[CrossRef]

Grimault, A. S.

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Gwo, S.

S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
[CrossRef] [PubMed]

Hafner, C.

J. Smajic, C. Hafner, L. Raguin, K. Tavzarashvili, and M. Mishrikey, “Comparison of numerical methods for the analysis of plasmonic structures,” J. Comput. Theor. Nanosci. 6, 763–774 (2009).
[CrossRef]

J. Smajic, C. Hafner, K. Tavzarashvili, and R. Vahldieck, “Numerical analysis of channel plasmon polaritons enhanced optical antennas,” J. Comput. Theor. Nanosci. 5, 725–734 (2008).
[CrossRef]

Hafner, Ch.

Ch. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House Books, Boston, 1990).

Hale, G. M.

Hanson, G. W.

G. W. Hanson and A. B. Yakovlev, Operator Theory for Electromagnetics – An Introduction (Springer, 2002).
[PubMed]

He, C. L.

S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
[CrossRef] [PubMed]

Henry, A. I.

J. M. McMahon, A. I. Henry, K. L. Wustholz, M. J. Natan, R. G. Freeman, R. P. Van Duyne, and G. C. Schatz, “Gold nanoparticle dimer plasmonics: finite element method calculations of the electromagnetic enhancement to surface-enhanced Raman spectroscopy,” Anal. Bioanal. Chem. 394, 1819–1825 (2009).
[CrossRef] [PubMed]

Hetmaniuk, U.

P. Arbenz, M. Bečka, R. Geus, U. Hetmaniuk, and T. Mengotti, “On a parallel multilevel preconditioned Maxwell eigensolver,” Parallel Comput. 32, 157–165 (2006).
[CrossRef]

Hochstenbach, M. E.

P. Arbenz and M. E. Hochstenbach, “A Jacobi–Davidson method for solving complex symmetric eigenvalue problems,” SIAM J. Sci. Comput. 25, 1655–1673 (2004).
[CrossRef]

Huffmann, D.

C. Bohren and D. Huffmann, Absorption and Scattering of Light by Small Particles (John Wiley, New York, 1983).

Ittipiboon, A.

R. K. Mongia and A. Ittipiboon, “Theoretical and experimental investigations on rectangular dielectric resonator antennas,” IEEE Trans. Antennas Propag. 45, 1348–1356 (1997).
[CrossRef]

Jin, J.

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

Johnson, P. B.

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

Kanehara, M.

S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
[CrossRef] [PubMed]

Kempel, L. C.

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics – Antennas, Microwave Circuits and Scattering Applications (IEEE Press, New York, 1998).

Kern, A. M.

A. M. Kern and O. J. F. Martin, “Excitation and reemission of molecules near realistic plasmonic nanostructures,” Nano Lett. 11, 482–487 (2011).
[CrossRef] [PubMed]

A. M. Kern and O. J. F. Martin, “Modeling near-field properties of plasmonic nanoparticles: a surface integral approach,” in Plasmonic: Nanoimaging, Nanofabrication, and their Applications V, V. M. Shalaev and D. P. Tsai, eds., Proc. SPIE7395, 739518 (2009).

Khoury, C. G.

C. G. Khoury, S. J. Norton, and T. Vo-Dinh, “Plasmonics of 3-D nanoshell dimers using multipole expansion and finite element method,” ACS Nano 3, 2776–2788 (2009).
[CrossRef] [PubMed]

Kinkhabwala, A.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657 (2009).
[CrossRef]

Kliewer, K. L.

Kobori, H.

S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
[CrossRef] [PubMed]

Li, C.

S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
[CrossRef] [PubMed]

Lin, M. H.

S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
[CrossRef] [PubMed]

Lindquist, N. C.

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325, 594–597 (2009).
[CrossRef] [PubMed]

Loudon, R.

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A: Gen. Phys. 3, 233245 (1970).
[CrossRef]

Macías, D.

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Mahboub, O.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

Martin, O. J. F.

A. M. Kern and O. J. F. Martin, “Excitation and reemission of molecules near realistic plasmonic nanostructures,” Nano Lett. 11, 482–487 (2011).
[CrossRef] [PubMed]

H. Fischer and O. J. F. Martin, “Engineering the optical response of plasmonic nanoantennas,” Opt. Express 16, 9144–9154 (2008).
[CrossRef] [PubMed]

A. M. Kern and O. J. F. Martin, “Modeling near-field properties of plasmonic nanoparticles: a surface integral approach,” in Plasmonic: Nanoimaging, Nanofabrication, and their Applications V, V. M. Shalaev and D. P. Tsai, eds., Proc. SPIE7395, 739518 (2009).

McMahon, J. M.

J. M. McMahon, A. I. Henry, K. L. Wustholz, M. J. Natan, R. G. Freeman, R. P. Van Duyne, and G. C. Schatz, “Gold nanoparticle dimer plasmonics: finite element method calculations of the electromagnetic enhancement to surface-enhanced Raman spectroscopy,” Anal. Bioanal. Chem. 394, 1819–1825 (2009).
[CrossRef] [PubMed]

Meerbergen, K.

F. Tisseur and K. Meerbergen, “The quadratic eigenvalue problem,” SIAM Rev.  43, 235–286 (2001).
[CrossRef]

Mengotti, T.

P. Arbenz, M. Bečka, R. Geus, U. Hetmaniuk, and T. Mengotti, “On a parallel multilevel preconditioned Maxwell eigensolver,” Parallel Comput. 32, 157–165 (2006).
[CrossRef]

Mishrikey, M.

J. Smajic, C. Hafner, L. Raguin, K. Tavzarashvili, and M. Mishrikey, “Comparison of numerical methods for the analysis of plasmonic structures,” J. Comput. Theor. Nanosci. 6, 763–774 (2009).
[CrossRef]

Moerner, W. E.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657 (2009).
[CrossRef]

Mongia, R. K.

R. K. Mongia and A. Ittipiboon, “Theoretical and experimental investigations on rectangular dielectric resonator antennas,” IEEE Trans. Antennas Propag. 45, 1348–1356 (1997).
[CrossRef]

Monk, P.

P. Monk, Finite Element Methods for Maxwell’s Equations (Oxford University Press, Oxford, 2003).
[CrossRef] [PubMed]

Mou, C. Y.

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9, 399–404 (2009).
[CrossRef]

Müllen, K.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657 (2009).
[CrossRef]

Myroshnychenko, V.

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9, 399–404 (2009).
[CrossRef]

Nagpal, P.

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325, 594–597 (2009).
[CrossRef] [PubMed]

Natan, M. J.

J. M. McMahon, A. I. Henry, K. L. Wustholz, M. J. Natan, R. G. Freeman, R. P. Van Duyne, and G. C. Schatz, “Gold nanoparticle dimer plasmonics: finite element method calculations of the electromagnetic enhancement to surface-enhanced Raman spectroscopy,” Anal. Bioanal. Chem. 394, 1819–1825 (2009).
[CrossRef] [PubMed]

Norris, D. J.

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325, 594–597 (2009).
[CrossRef] [PubMed]

Norton, S. J.

Novotny, L.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[CrossRef]

D. W. Pohl, S. G. Rodrigo, and L. Novotny, “Stacked optical antennas,” Appl. Phys. Lett. 98, 023111 (2011).
[CrossRef]

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photon. 1, 438–483 (2009).
[CrossRef]

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007).
[CrossRef] [PubMed]

Nunes, F. D.

Oh, S.-H.

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325, 594–597 (2009).
[CrossRef] [PubMed]

Okaya, A.

A. Okaya and L. F. Barash, “The dielectric microwave resonator,” Proc. IRE 50, 2081–2092 (1962).
[CrossRef]

Philbin, T. G.

T. G. Philbin, “Electromagnetic energy momentum in dispersive media,” Phys. Rev. A 83, 013823 (2011).
[CrossRef]

Pohl, D. W.

D. W. Pohl, S. G. Rodrigo, and L. Novotny, “Stacked optical antennas,” Appl. Phys. Lett. 98, 023111 (2011).
[CrossRef]

Popov, E.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

Querry, M. R.

Raguin, L.

J. Smajic, C. Hafner, L. Raguin, K. Tavzarashvili, and M. Mishrikey, “Comparison of numerical methods for the analysis of plasmonic structures,” J. Comput. Theor. Nanosci. 6, 763–774 (2009).
[CrossRef]

Ramo, S.

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics (John Wiley, New York, 1993).

Remacle, J.-F.

C. Geuzaine and J.-F. Remacle, “Gmsh: A 3-D finite element mesh generator with built-in pre- and postprocessing facilities,” Int. J. Numer. Methods Eng. 79, 1309–1331 (2009).
[CrossRef]

Rigneault, H.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

Rodrigo, S. G.

D. W. Pohl, S. G. Rodrigo, and L. Novotny, “Stacked optical antennas,” Appl. Phys. Lett. 98, 023111 (2011).
[CrossRef]

Ruhe, A.

Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (SIAM, Philadelphia PA, 2000).
[CrossRef]

Ruppin, R.

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299, 309–312 (2002).
[CrossRef]

Schatz, G. C.

J. M. McMahon, A. I. Henry, K. L. Wustholz, M. J. Natan, R. G. Freeman, R. P. Van Duyne, and G. C. Schatz, “Gold nanoparticle dimer plasmonics: finite element method calculations of the electromagnetic enhancement to surface-enhanced Raman spectroscopy,” Anal. Bioanal. Chem. 394, 1819–1825 (2009).
[CrossRef] [PubMed]

Sleijpen, G. L. G.

D. R. Fokkema, G. L. G. Sleijpen, and H. A. Van der Vorst, “Jacobi–Davidson style QR and QZ algorithms for the partial reduction of matrix pencils,” SIAM J. Sci. Comput. 20, 94–125 (1996).
[CrossRef]

Smajic, J.

J. Smajic, C. Hafner, L. Raguin, K. Tavzarashvili, and M. Mishrikey, “Comparison of numerical methods for the analysis of plasmonic structures,” J. Comput. Theor. Nanosci. 6, 763–774 (2009).
[CrossRef]

J. Smajic, C. Hafner, K. Tavzarashvili, and R. Vahldieck, “Numerical analysis of channel plasmon polaritons enhanced optical antennas,” J. Comput. Theor. Nanosci. 5, 725–734 (2008).
[CrossRef]

Sönnichsen, C.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002)
[CrossRef] [PubMed]

Tavzarashvili, K.

J. Smajic, C. Hafner, L. Raguin, K. Tavzarashvili, and M. Mishrikey, “Comparison of numerical methods for the analysis of plasmonic structures,” J. Comput. Theor. Nanosci. 6, 763–774 (2009).
[CrossRef]

J. Smajic, C. Hafner, K. Tavzarashvili, and R. Vahldieck, “Numerical analysis of channel plasmon polaritons enhanced optical antennas,” J. Comput. Theor. Nanosci. 5, 725–734 (2008).
[CrossRef]

Teranishi, T.

S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
[CrossRef] [PubMed]

Tisseur, F.

F. Tisseur and K. Meerbergen, “The quadratic eigenvalue problem,” SIAM Rev.  43, 235–286 (2001).
[CrossRef]

Vahldieck, R.

J. Smajic, C. Hafner, K. Tavzarashvili, and R. Vahldieck, “Numerical analysis of channel plasmon polaritons enhanced optical antennas,” J. Comput. Theor. Nanosci. 5, 725–734 (2008).
[CrossRef]

van der Vorst, H.

Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (SIAM, Philadelphia PA, 2000).
[CrossRef]

Van der Vorst, H. A.

D. R. Fokkema, G. L. G. Sleijpen, and H. A. Van der Vorst, “Jacobi–Davidson style QR and QZ algorithms for the partial reduction of matrix pencils,” SIAM J. Sci. Comput. 20, 94–125 (1996).
[CrossRef]

Van Duyne, R. P.

J. M. McMahon, A. I. Henry, K. L. Wustholz, M. J. Natan, R. G. Freeman, R. P. Van Duyne, and G. C. Schatz, “Gold nanoparticle dimer plasmonics: finite element method calculations of the electromagnetic enhancement to surface-enhanced Raman spectroscopy,” Anal. Bioanal. Chem. 394, 1819–1825 (2009).
[CrossRef] [PubMed]

van Hulst, N.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[CrossRef]

Vasconcelos, T. C.

Vial, A.

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[CrossRef]

Vo-Dinh, T.

Volakis, J. L.

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics – Antennas, Microwave Circuits and Scattering Applications (IEEE Press, New York, 1998).

von Plessen, G.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002)
[CrossRef] [PubMed]

Weiner, J.

Wenger, J.

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

Whinnery, J. R.

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics (John Wiley, New York, 1993).

Wilk, T.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002)
[CrossRef] [PubMed]

Wustholz, K. L.

J. M. McMahon, A. I. Henry, K. L. Wustholz, M. J. Natan, R. G. Freeman, R. P. Van Duyne, and G. C. Schatz, “Gold nanoparticle dimer plasmonics: finite element method calculations of the electromagnetic enhancement to surface-enhanced Raman spectroscopy,” Anal. Bioanal. Chem. 394, 1819–1825 (2009).
[CrossRef] [PubMed]

Yakovlev, A. B.

G. W. Hanson and A. B. Yakovlev, Operator Theory for Electromagnetics – An Introduction (Springer, 2002).
[PubMed]

Yang, S. C.

S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
[CrossRef] [PubMed]

Yu, Z.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657 (2009).
[CrossRef]

ACS Nano

C. G. Khoury, S. J. Norton, and T. Vo-Dinh, “Plasmonics of 3-D nanoshell dimers using multipole expansion and finite element method,” ACS Nano 3, 2776–2788 (2009).
[CrossRef] [PubMed]

Adv. Opt. Photon.

Anal. Bioanal. Chem.

J. M. McMahon, A. I. Henry, K. L. Wustholz, M. J. Natan, R. G. Freeman, R. P. Van Duyne, and G. C. Schatz, “Gold nanoparticle dimer plasmonics: finite element method calculations of the electromagnetic enhancement to surface-enhanced Raman spectroscopy,” Anal. Bioanal. Chem. 394, 1819–1825 (2009).
[CrossRef] [PubMed]

Appl. Numer. Math.

P. Arbenz and R. Geus, “Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems,” Appl. Numer. Math. 54, 107–121 (2005).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

D. W. Pohl, S. G. Rodrigo, and L. Novotny, “Stacked optical antennas,” Appl. Phys. Lett. 98, 023111 (2011).
[CrossRef]

IEEE Trans. Antennas Propag.

R. K. Mongia and A. Ittipiboon, “Theoretical and experimental investigations on rectangular dielectric resonator antennas,” IEEE Trans. Antennas Propag. 45, 1348–1356 (1997).
[CrossRef]

Int. J. Numer. Methods Eng.

C. Geuzaine and J.-F. Remacle, “Gmsh: A 3-D finite element mesh generator with built-in pre- and postprocessing facilities,” Int. J. Numer. Methods Eng. 79, 1309–1331 (2009).
[CrossRef]

J. Comput. Theor. Nanosci.

J. Smajic, C. Hafner, L. Raguin, K. Tavzarashvili, and M. Mishrikey, “Comparison of numerical methods for the analysis of plasmonic structures,” J. Comput. Theor. Nanosci. 6, 763–774 (2009).
[CrossRef]

J. Smajic, C. Hafner, K. Tavzarashvili, and R. Vahldieck, “Numerical analysis of channel plasmon polaritons enhanced optical antennas,” J. Comput. Theor. Nanosci. 5, 725–734 (2008).
[CrossRef]

X. Cui and D. Erni, “The influence of particle shapes on the optical response of nearly touching plasmonic nanoparticle dimers,” J. Comput. Theor. Nanosci. 47, 1610–1615 (2010).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Phys. A: Gen. Phys.

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A: Gen. Phys. 3, 233245 (1970).
[CrossRef]

Nano Lett.

S. C. Yang, H. Kobori, C. L. He, M. H. Lin, H. Y. Chen, C. Li, M. Kanehara, T. Teranishi, and S. Gwo, “Plasmon hybridization in individual gold nanocrystal dimers: direct observation of bright and dark modes,” Nano Lett. 10, 632–637 (2010).
[CrossRef] [PubMed]

H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright unidirectional fluorescence emission of molecules in a nanoaperture with plasmonic corrugations,” Nano Lett. 11, 637–644 (2011).
[CrossRef] [PubMed]

A. M. Kern and O. J. F. Martin, “Excitation and reemission of molecules near realistic plasmonic nanostructures,” Nano Lett. 11, 482–487 (2011).
[CrossRef] [PubMed]

M. W. Chu, V. Myroshnychenko, C. H. Chen, J. P. Deng, C. Y. Mou, and F. J. García de Abajo, “Probing bright and dark surface-plasmon modes in individual and coupled noble metal nanoparticles using an electron beam,” Nano Lett. 9, 399–404 (2009).
[CrossRef]

Nat. Photon.

A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657 (2009).
[CrossRef]

M. F. Garcia-Parajo, “Optical antennas focus in on biology,” Nat. Photon. 2, 201–203, (2008).
[CrossRef]

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Opt. Express

Parallel Comput.

P. Arbenz, M. Bečka, R. Geus, U. Hetmaniuk, and T. Mengotti, “On a parallel multilevel preconditioned Maxwell eigensolver,” Parallel Comput. 32, 157–165 (2006).
[CrossRef]

Phys. Lett. A

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299, 309–312 (2002).
[CrossRef]

Phys. Rev. A

T. G. Philbin, “Electromagnetic energy momentum in dispersive media,” Phys. Rev. A 83, 013823 (2011).
[CrossRef]

Phys. Rev. B

A. Vial, A. S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B 71, 085416 (2005).
[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.

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007).
[CrossRef] [PubMed]

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002)
[CrossRef] [PubMed]

Proc. IRE

A. Okaya and L. F. Barash, “The dielectric microwave resonator,” Proc. IRE 50, 2081–2092 (1962).
[CrossRef]

Science

P. Nagpal, N. C. Lindquist, S.-H. Oh, and D. J. Norris, “Ultrasmooth patterned metals for plasmonics and metamaterials,” Science 325, 594–597 (2009).
[CrossRef] [PubMed]

SIAM J. Sci. Comput.

P. Arbenz and M. E. Hochstenbach, “A Jacobi–Davidson method for solving complex symmetric eigenvalue problems,” SIAM J. Sci. Comput. 25, 1655–1673 (2004).
[CrossRef]

D. R. Fokkema, G. L. G. Sleijpen, and H. A. Van der Vorst, “Jacobi–Davidson style QR and QZ algorithms for the partial reduction of matrix pencils,” SIAM J. Sci. Comput. 20, 94–125 (1996).
[CrossRef]

SIAM Rev

F. Tisseur and K. Meerbergen, “The quadratic eigenvalue problem,” SIAM Rev.  43, 235–286 (2001).
[CrossRef]

Other

A. M. Kern and O. J. F. Martin, “Modeling near-field properties of plasmonic nanoparticles: a surface integral approach,” in Plasmonic: Nanoimaging, Nanofabrication, and their Applications V, V. M. Shalaev and D. P. Tsai, eds., Proc. SPIE7395, 739518 (2009).

L. Brillouin, Wave Propagation and Group Velocity (Academic Press, New York, 1960).

R. Geus, “The Jacobi–Davidson algorithm for solving large sparse symmetric eigenvalue problems.” PhD Thesis No. 14734, ETH Zurich 2002.

Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (SIAM, Philadelphia PA, 2000).
[CrossRef]

Trilinos Project Home Page, http://trilinos.sandia.gov/ .

Paraview Home Page, http://www.paraview.org/ .

Home Page of the Swiss National Supercomputing Centre (CSCS), http://www.cscs.ch/ .

G. W. Hanson and A. B. Yakovlev, Operator Theory for Electromagnetics – An Introduction (Springer, 2002).
[PubMed]

Ch. Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House Books, Boston, 1990).

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

P. Monk, Finite Element Methods for Maxwell’s Equations (Oxford University Press, Oxford, 2003).
[CrossRef] [PubMed]

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics – Antennas, Microwave Circuits and Scattering Applications (IEEE Press, New York, 1998).

C. Bohren and D. Huffmann, Absorption and Scattering of Light by Small Particles (John Wiley, New York, 1983).

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics (John Wiley, New York, 1993).

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Figures (9)

Fig. 1
Fig. 1

A 3-D view of a typical computational domain Ω = Ω1 ∪ Ω2 ∪ Ω3. Ω1 is the optical device, Ω2 is the substrate, Ω3 is the environment. Γ13 is the interface between Ω1 and Ω2 ∪ Ω3, and Γ23 is the interface between Ω2 and Ω1 ∪ Ω3. Γ is the boundary of Ω.

Fig. 2
Fig. 2

(a) a 3-D sketch of the DRA (or nano-cuboid). (b): a DRA with a = b = 10 mm, d = 4 mm and εr = 20.0, resonance at 6.545GHz. The electric field distribution |E| of the T E 111 z mode in the antenna and its surrounding region is shown. (c): a gold cuboid with a = b = 100 nm, d = 40 nm, resonance at 935.1THz (where εr = −1.2308 + i5.8458). It shows the electric field distribution |E| of the T E 111 z mode in the cuboid and the surrounding region. (b) and (c) are visualized on the xy-plane through the center of the antenna. (d) 3 components of the electric field of the DRA (in (b)) plotted along the y-axis. (e) 3 components of the electric field of the gold cuboid (in (c)) plotted along the y-axis. Note that, Ex, Ey, and Ez are complex. For Ey and Ez (approximately zero), only real parts are shown. Ex is scaled such that ||Re(Ex)|| = 1.

Fig. 3
Fig. 3

Mie solutions of silver spheres with radii of (a) 30 nm and (b) 60 nm.

Fig. 4
Fig. 4

Numerical and Mie solutions of Q factors and radiative quantum yield (subfigure) of silver spheres with varying radius R.

Fig. 5
Fig. 5

(a) and (b) show the electric field distributions (|E|) in the vicinity of a silver sphere on the xy-plane. The radius of the sphere is 60 nm. (a): the mode when Qsca reaches maximum, Eres = 3.03 eV; (b): the mode when Qabs reaches maximum, Eres = 3.48 eV.

Fig. 6
Fig. 6

The nano-optical dipole antenna. (a) geometry; (b) 3-D sketch.

Fig. 7
Fig. 7

(a)–(c): Numerical analysis of a gold, nano-optical dipole antenna (model (1)). The gap width is 20 nm and the resonance is at 665.7 nm; (a) magnetic and (b) electric field distribution (|H| and |E|) in the vicinity of the antenna surface; (c) electric field distribution |E| around the gap; (a), (b), and (c) are evaluated on the xy-plane through the center of the antenna arms. (d) plots the electric field amplitudes |E| along the x-axis, associated with 3 material arrangements.

Fig. 8
Fig. 8

Numerical analysis of a gold nano-optical antenna (model (2)): (a) gap width = 5 nm, resonance at 796.3 nm. It shows the electric field distribution |E| (visualized on the xy-plane) in the vicinity of the antenna surface; (b) plots of the electric field amplitude |E| along the x-axis with varying gap width g.

Fig. 9
Fig. 9

(a) Charge profiles; (b) the dark mode of the gold nano-optical antenna (gap width g = 10 nm) in vacuum: resonance at 557.4 nm. The electric field distribution |E| (visualized on the xy-plane) in the vicinity of the antenna surface is shown; (c) the gold nano-optical antenna (gap width g = 5 nm) in vacuum. The electric field amplitude |E| along the x-axis is plotted, associated with the bright mode (resonance at 713.9 nm) and the dark mode (resonance at 532.1 nm), respectively.

Tables (5)

Tables Icon

Table 1 T E 111 z mode of DRAs (f : resonant frequency computed by femaxx; fMI: theoretically determined resonant frequency [16]; Diff.: relative difference of f and fMI; QMI: theoretically determined the Q factor [16].)

Tables Icon

Table 2 Numerical figures of merit for the T E 111 z mode of the nano-cuboid where λ : resonant wavelength computed by femaxx; f : resonant frequency computed by femaxx; fMI: theoretically determined resonant frequency [16]; Diff.: relative difference of f and fMI; QMI: theoretically determined Q factor [16].

Tables Icon

Table 3 Results of the numerical analysis and the semi-analytical Mie solutions of the silver sphere hovering in vacuum, where: Eres1: resonant energy computed by femaxx; Ediff: the relative difference between Eres1 and E res 1 mie. Qdiff: the relative difference between Q1 and Q res 1 mie.

Tables Icon

Table 4 Numerical analysis of a gold nano-optical antenna (#p: number of cores; N: number of tetrahedra; dofs: degrees of freedom; λ : resonant wavelength computed by femaxx; Q1 and Q2: quality factors by Eq. (5) and Eq. (10), respectively;

Tables Icon

Table 5 Dark modes vs. bright modes

Equations (20)

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× ( μ r 1 × E ( x ) ) + i k 0 σ Z 0 E ( x ) k 0 2 ε r E ( x ) = 0 , ( ε r E ( x ) ) = 0 , x Ω .
ε r = { ε r ( Re ( k 0 ) ) , x Ω 1 , ε sub , x Ω 2 , ε env , x Ω 3 .
n × × E ( x ) = i k n × ( n × E ( x ) ) ,
H ( x ) = 1 i ω ˜ μ 0 μ r × E ( x ) = i k 0 Z 0 μ r × E ( x ) .
Q 1 = | ω / 2 α | .
U = ε 0 4 Ω ( Re ( ε r ) + 2 ω Im ( ε r ) γ e ) | E ( x ) | 2 d x + μ 0 4 Ω | H ( x ) | 2 d x .
U s = ε 0 4 Ω ( Re ( ε r ) + ω d ( Re ( ε r ) ) d ω | E ( x ) | 2 d x + μ 0 4 Ω | H ( x ) | 2 d x .
U d = ε 0 2 Ω 1 Im ( ε r ) | E ( x ) | 2 d x .
P r = 1 2 Γ Re ( E ( x ) × H ( x ) * ) d x .
Q 2 = ω U s ω U d + P r .
η = P r P r + ω U d .
U s = ε 0 2 Ω Re ( ε r ) | E ( x ) | 2 d x , U d = 0 ,
Ω f ( x ) ( × μ r 1 × E ( x ) ) d x = Ω μ r 1 × f × E d x Γ μ r 1 n ( f × × E ) d x = Ω μ r 1 × f × E d x + i Γ k μ r 1 ( n × f ) ( n × E ) d x .
Ω ε r ( E ( x ) ) q ( x ) d x = Ω ε r E ( x ) ( q ( x ) ) d x = 0.
Ω μ r 1 × f × E d x + i k 0 [ Γ ε r μ r ( n × f ) ( n × E ) d x + Ω σ Z 0 f E d x ] + k 0 2 Ω ε r f E d x = 0 , Ω ε r E q d x = 0.
T ( λ ) x = A x + λ R x λ 2 M x = 0 , C T x = 0 ,
a i j = Ω μ r 1 ( × N i ) ( × N j ) d x , 1 i , j n , m i j = Ω ε r N i N j d x , 1 i , j n , r i j = i Γ ε r / μ r ( n × N i ) ( n × N J ) d x + i Ω σ Z 0 N i N j d x , 1 i , j n , c i = Ω ε r N i ( x ) N ( x ) d x , 1 i n , 1 m ,
𝒜 x [ A O O I ] ( x 1 x 2 ) = λ [ R M I O ] ( x 1 x 2 ) λ x , 𝒞 T x [ C O O C ] T x = 0 .
𝒜 Q = Z T A , Q = Z T B , 𝒞 T Q = O ,
( Z ˜ Z ˜ * ) ( 𝒜 λ ˜ 𝒝 ) ( Q ˜ Q ˜ * ) t = r Q ˜ * t = 0 , 𝒞 T t = 0 ,

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