Abstract

We develop a transformation optics theory for the nonlocal media in the hydrodynamic Drude model by generalizing the free-electron current density equation to a transformation invariant form. Applying the transformation optics theory, perfectly matched layers (PMLs) for the nonlocal media are theoretically formulated and implemented in frequency domain with finite element method. The nonlocal PMLs are shown to absorb outgoing surface and volume plasmons without inducing unphysical reflections. The effectiveness of the nonlocal PMLs is quantitatively demonstrated by the behaviors that the numerical errors continuously approach zero with increasing linear mesh density.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization

Jean Paul Hugonin and Philippe Lalanne
J. Opt. Soc. Am. A 22(9) 1844-1849 (2005)

Unified perfectly matched layer for finite-difference time-domain modeling of dispersive optical materials

Indika Udagedara, Malin Premaratne, Ivan D. Rukhlenko, Haroldo T. Hattori, and Govind P. Agrawal
Opt. Express 17(23) 21179-21190 (2009)

R-matrix propagator with perfectly matched layers for the study of integrated optical components

J. Merle Elson and Phuc Tran
J. Opt. Soc. Am. A 16(12) 2983-2989 (1999)

References

  • View by:
  • |
  • |
  • |

  1. W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
    [Crossref] [PubMed]
  2. A. Varas, P. García-González, J. Feist, F. J. García-Vidal, and A. Rubio, “Quantum plasmonics: from jellium models to ab initio calculations,” Nanophotonics 5(3), 409–426 (2016).
    [Crossref]
  3. J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012).
    [Crossref] [PubMed]
  4. S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014).
    [Crossref] [PubMed]
  5. F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
    [Crossref] [PubMed]
  6. S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
    [Crossref] [PubMed]
  7. M. K. Dezfouli, C. Tserkezis, N. A. Mortensen, and S. Hughes, “Nonlocal quasinormal modes for three-dimensional plasmonic resonators,” https://arXiv:1707.05750 .
  8. G. Toscano, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20(4), 4176–4188 (2012).
    [Crossref] [PubMed]
  9. F. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C 112(46), 17983–17987 (2008).
    [Crossref]
  10. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
    [Crossref]
  11. S. D. Gedney, “An anisotropic perfectly matched layer - absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
    [Crossref]
  12. W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
    [Crossref]
  13. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref] [PubMed]
  14. H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
    [Crossref] [PubMed]
  15. A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett. 108(10), 106802 (2012).
    [Crossref] [PubMed]
  16. M. Moccia, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Dispersion engineering via nonlocal transformation optics,” Optica 3(2), 179–188 (2016).
    [Crossref]
  17. K. Dharamvir, B. Singla, K. N. Pathak, and V. V. Paranjape, “Plasmon excitations in a metallic slab,” Phys. Rev. B Condens. Matter 48(16), 12330–12333 (1993).
    [Crossref] [PubMed]
  18. C. David and J. Christensen, “Extraordinary optical transmission through nonlocal holey metal films,” Appl. Phys. Lett. 110(26), 261110 (2017).
    [Crossref]
  19. N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
    [Crossref] [PubMed]
  20. G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
    [Crossref] [PubMed]
  21. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-Domain Method, Second Edition, (Artech House, 2000).

2017 (1)

C. David and J. Christensen, “Extraordinary optical transmission through nonlocal holey metal films,” Appl. Phys. Lett. 110(26), 261110 (2017).
[Crossref]

2016 (4)

M. Moccia, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Dispersion engineering via nonlocal transformation optics,” Optica 3(2), 179–188 (2016).
[Crossref]

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

A. Varas, P. García-González, J. Feist, F. J. García-Vidal, and A. Rubio, “Quantum plasmonics: from jellium models to ab initio calculations,” Nanophotonics 5(3), 409–426 (2016).
[Crossref]

2015 (2)

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
[Crossref] [PubMed]

G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
[Crossref] [PubMed]

2014 (2)

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref] [PubMed]

S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014).
[Crossref] [PubMed]

2012 (3)

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett. 108(10), 106802 (2012).
[Crossref] [PubMed]

G. Toscano, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20(4), 4176–4188 (2012).
[Crossref] [PubMed]

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012).
[Crossref] [PubMed]

2010 (1)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

2008 (1)

F. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C 112(46), 17983–17987 (2008).
[Crossref]

2006 (1)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

1996 (1)

S. D. Gedney, “An anisotropic perfectly matched layer - absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[Crossref]

1994 (2)

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[Crossref]

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[Crossref]

1993 (1)

K. Dharamvir, B. Singla, K. N. Pathak, and V. V. Paranjape, “Plasmon excitations in a metallic slab,” Phys. Rev. B Condens. Matter 48(16), 12330–12333 (1993).
[Crossref] [PubMed]

Aizpurua, J.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

Alù, A.

Asger Mortensen, N.

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
[Crossref] [PubMed]

Bai, P.

S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014).
[Crossref] [PubMed]

Baumberg, J. J.

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

Benz, F.

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[Crossref]

Borisov, A. G.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

Bosman, M.

S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
[Crossref] [PubMed]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref] [PubMed]

Carnegie, C.

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

Castaldi, G.

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Chew, W. C.

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[Crossref]

Chikkaraddy, R.

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

Christensen, J.

C. David and J. Christensen, “Extraordinary optical transmission through nonlocal holey metal films,” Appl. Phys. Lett. 110(26), 261110 (2017).
[Crossref]

Crozier, K. B.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

David, C.

C. David and J. Christensen, “Extraordinary optical transmission through nonlocal holey metal films,” Appl. Phys. Lett. 110(26), 261110 (2017).
[Crossref]

de Nijs, B.

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

Demetriadou, A.

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

Dharamvir, K.

K. Dharamvir, B. Singla, K. N. Pathak, and V. V. Paranjape, “Plasmon excitations in a metallic slab,” Phys. Rev. B Condens. Matter 48(16), 12330–12333 (1993).
[Crossref] [PubMed]

Dionne, J. A.

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012).
[Crossref] [PubMed]

Dreismann, A.

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

Engheta, N.

Esteban, R.

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

Evers, F.

G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
[Crossref] [PubMed]

Feist, J.

A. Varas, P. García-González, J. Feist, F. J. García-Vidal, and A. Rubio, “Quantum plasmonics: from jellium models to ab initio calculations,” Nanophotonics 5(3), 409–426 (2016).
[Crossref]

Fernández-Domínguez, A. I.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett. 108(10), 106802 (2012).
[Crossref] [PubMed]

Galdi, V.

García de Abajo, F. J.

F. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C 112(46), 17983–17987 (2008).
[Crossref]

García-González, P.

A. Varas, P. García-González, J. Feist, F. J. García-Vidal, and A. Rubio, “Quantum plasmonics: from jellium models to ab initio calculations,” Nanophotonics 5(3), 409–426 (2016).
[Crossref]

García-Vidal, F. J.

A. Varas, P. García-González, J. Feist, F. J. García-Vidal, and A. Rubio, “Quantum plasmonics: from jellium models to ab initio calculations,” Nanophotonics 5(3), 409–426 (2016).
[Crossref]

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett. 108(10), 106802 (2012).
[Crossref] [PubMed]

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer - absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[Crossref]

Jauho, A. P.

Koh, A. L.

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012).
[Crossref] [PubMed]

Kwiatkowski, A.

G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
[Crossref] [PubMed]

Lezec, H. J.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

Maier, S. A.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett. 108(10), 106802 (2012).
[Crossref] [PubMed]

Moccia, M.

Mortensen, N. A.

G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
[Crossref] [PubMed]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref] [PubMed]

G. Toscano, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20(4), 4176–4188 (2012).
[Crossref] [PubMed]

Nijhuis, C. A.

S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014).
[Crossref] [PubMed]

Nordlander, P.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

Ohadi, H.

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

Paranjape, V. V.

K. Dharamvir, B. Singla, K. N. Pathak, and V. V. Paranjape, “Plasmon excitations in a metallic slab,” Phys. Rev. B Condens. Matter 48(16), 12330–12333 (1993).
[Crossref] [PubMed]

Pathak, K. N.

K. Dharamvir, B. Singla, K. N. Pathak, and V. V. Paranjape, “Plasmon excitations in a metallic slab,” Phys. Rev. B Condens. Matter 48(16), 12330–12333 (1993).
[Crossref] [PubMed]

Pendry, J. B.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett. 108(10), 106802 (2012).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Raza, S.

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
[Crossref] [PubMed]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref] [PubMed]

G. Toscano, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20(4), 4176–4188 (2012).
[Crossref] [PubMed]

Rockstuhl, C.

G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
[Crossref] [PubMed]

Rubio, A.

A. Varas, P. García-González, J. Feist, F. J. García-Vidal, and A. Rubio, “Quantum plasmonics: from jellium models to ab initio calculations,” Nanophotonics 5(3), 409–426 (2016).
[Crossref]

Schmidt, M. K.

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

Scholl, J. A.

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012).
[Crossref] [PubMed]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Singla, B.

K. Dharamvir, B. Singla, K. N. Pathak, and V. V. Paranjape, “Plasmon excitations in a metallic slab,” Phys. Rev. B Condens. Matter 48(16), 12330–12333 (1993).
[Crossref] [PubMed]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Søndergaard, T.

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref] [PubMed]

Straubel, J.

G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
[Crossref] [PubMed]

Tan, S. F.

S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014).
[Crossref] [PubMed]

Toscano, G.

G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
[Crossref] [PubMed]

G. Toscano, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20(4), 4176–4188 (2012).
[Crossref] [PubMed]

Varas, A.

A. Varas, P. García-González, J. Feist, F. J. García-Vidal, and A. Rubio, “Quantum plasmonics: from jellium models to ab initio calculations,” Nanophotonics 5(3), 409–426 (2016).
[Crossref]

Weedon, W. H.

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[Crossref]

Wiener, A.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett. 108(10), 106802 (2012).
[Crossref] [PubMed]

Wu, L.

S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014).
[Crossref] [PubMed]

Wubs, M.

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
[Crossref] [PubMed]

G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
[Crossref] [PubMed]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref] [PubMed]

G. Toscano, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express 20(4), 4176–4188 (2012).
[Crossref] [PubMed]

Xu, H.

G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
[Crossref] [PubMed]

Yang, J. K. W.

S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014).
[Crossref] [PubMed]

Zhang, Y.

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

Zhu, W.

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

C. David and J. Christensen, “Extraordinary optical transmission through nonlocal holey metal films,” Appl. Phys. Lett. 110(26), 261110 (2017).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

S. D. Gedney, “An anisotropic perfectly matched layer - absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[Crossref]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[Crossref]

J. Phys. Chem. C (1)

F. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C 112(46), 17983–17987 (2008).
[Crossref]

J. Phys. Condens. Matter (1)

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
[Crossref] [PubMed]

Microw. Opt. Technol. Lett. (1)

W. C. Chew and W. H. Weedon, “A 3d perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7(13), 599–604 (1994).
[Crossref]

Nanophotonics (1)

A. Varas, P. García-González, J. Feist, F. J. García-Vidal, and A. Rubio, “Quantum plasmonics: from jellium models to ab initio calculations,” Nanophotonics 5(3), 409–426 (2016).
[Crossref]

Nat. Commun. (3)

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref] [PubMed]

G. Toscano, J. Straubel, A. Kwiatkowski, C. Rockstuhl, F. Evers, H. Xu, N. A. Mortensen, and M. Wubs, “Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics,” Nat. Commun. 6, 7132 (2015).
[Crossref] [PubMed]

Nat. Mater. (1)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Nature (1)

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012).
[Crossref] [PubMed]

Opt. Express (1)

Optica (1)

Phys. Rev. B Condens. Matter (1)

K. Dharamvir, B. Singla, K. N. Pathak, and V. V. Paranjape, “Plasmon excitations in a metallic slab,” Phys. Rev. B Condens. Matter 48(16), 12330–12333 (1993).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett. 108(10), 106802 (2012).
[Crossref] [PubMed]

Science (3)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014).
[Crossref] [PubMed]

F. Benz, M. K. Schmidt, A. Dreismann, R. Chikkaraddy, Y. Zhang, A. Demetriadou, C. Carnegie, H. Ohadi, B. de Nijs, R. Esteban, J. Aizpurua, and J. J. Baumberg, “Single-molecule optomechanics in “picocavities”,” Science 354(6313), 726–729 (2016).
[Crossref] [PubMed]

Other (2)

M. K. Dezfouli, C. Tserkezis, N. A. Mortensen, and S. Hughes, “Nonlocal quasinormal modes for three-dimensional plasmonic resonators,” https://arXiv:1707.05750 .

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-Domain Method, Second Edition, (Artech House, 2000).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 Schematic diagram of the setting for the computational domain containing a nonlocal medium. In the center region the free-electron current density (Jz) is visualized. (J) at the boundary shown in white needs to comply with the boundary conditions indicated in red.
Fig. 2
Fig. 2 The termination of a nonlocal medium by the conventional local PML and NL-PML. Ex and abs(E) of the surface ((a) and (b)) and volume ((c) and (d)) plasmon fields are displayed for the cases of local PML ((a) and (c)) and NL-PML ((b) and (d)), respectively.
Fig. 3
Fig. 3 The performance of the conventional and NL-PML is evaluated with the relative error |(E)-(E)0|2/|(E)0|2 (see text) against (a) γ1 and (b) normalized linear grid density d/dm (dm = 103/λp).
Fig. 4
Fig. 4 The NL-PML in cylindrical coordinate system: A thin metal film with a circular hole of radius λp/100. A vertically positioned dipole emitter (λp/100 above the center of the hole) is used to excite the system. Er and abs(E) are shown on the left and right, respectively.

Equations (6)

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

β 2 ( × J ) + ω ( ω + i γ 0 ) J = i ω ω p 2 ε 0 E ,
( α × J ) + ω ( ω + i γ 0 ) ξ ¯ ¯ J = i ω ω p 2 ε 0 E
E ' = ( Λ ¯ ¯ 1 ) T E , J ' = det ( Λ ¯ ¯ 1 ) Λ ¯ ¯ J ,
ε ¯ ¯ ' = ε 0 Λ ¯ ¯ Λ ¯ ¯ T det ( Λ ¯ ¯ 1 ) , μ ¯ ¯ ' = μ 0 Λ ¯ ¯ Λ ¯ ¯ T det ( Λ ¯ ¯ 1 ) ,
α ' = det ( Λ ¯ ¯ ) α , ξ ¯ ¯ ' = ( Λ ¯ ¯ T ) 1 ξ ¯ ¯ Λ ¯ ¯ 1 det ( Λ ¯ ¯ ) .
α = β 2 / ( 1 + i γ 1 ) , ξ ¯ ¯ = d i a g ( 1 + i γ 1 , 1 / ( 1 + i γ 1 ) , 1 / ( 1 + i γ 1 ) ) .

Metrics