Abstract

Abstract

General properties of retardation-based resonances involving slow surface plasmon-polariton (SPP) modes supported by metal nanostructures are considered. Explicit relations for the dispersion of SPP modes propagating along thin metal strips embedded in dielectric and in narrow gaps between metal surfaces are obtained. Strip and gap subwavelength resonant structures are compared with respect to the achievable scattering and local-field enhancements lending thereby their distinction as nano-antennas and nano-resonators, respectively. It is shown that, in the limit of extremely thin strips and narrow gaps, both structures exhibit the same Q factor of the resonance which is primarily determined by the complex dielectric function of metal.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, Berlin, 1995).
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  3. F. Wang and Y. R. Shen, "General properties of local plasmons in metal nanostructures," Phys. Rev. Lett. 97, 206806 (2006).
    [CrossRef] [PubMed]
  4. D. R. Fredkin and I. D. Mayergouz, "Resonant behaviour of dielectric objects (electrostatic resonances)," Phys. Rev. Lett. 91, 253902 (2003).
    [CrossRef]
  5. N. Engheta, A. Salandrino, and A. AluÌ, "Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).
    [CrossRef] [PubMed]
  6. T. Søndergaard and S. I. Bozhevolnyi, "Slow-plasmon resonant nanostructures: scattering and field enhancements," Phys. Rev. B 75, 073402 (2007).
    [CrossRef]
  7. T. Søndergaard and S. I. Bozhevolnyi, "Metal nano-strip optical resonators," Opt. Express 15, 4198-4204 (2007).
    [CrossRef] [PubMed]
  8. T. Søndergaard and S. I. Bozhevolnyi, "Strip and gap plasmon polariton resonances," Phys. Status Solidi(b), submitted.
  9. E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
    [CrossRef]
  10. H. Räther, Surface Plasmons (Springer, 1988).
  11. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A 21, 2442-2446 (2004).
    [CrossRef]
  12. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).
  13. R. Gordon, "Light in a subwavelength slit in a metal: propagation and reflection," Phys. Rev. B 73, 153405 (2006).
    [CrossRef]
  14. Y. Kurokawa and H. T. Miyazaki, "Metal-insulator-metal plasmon nanocavities: analysis of optical properties," Phys. Rev. B 75, 035411 (2007).
    [CrossRef]
  15. G. Lévêque and O. J. F. Martin, "Tunable composite nanoparticle for plasmonics," Opt. Lett. 31, 2750-2752 (2006).
    [CrossRef] [PubMed]
  16. V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
    [CrossRef]
  17. V. A. Podoloskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735-745 (2003).
    [CrossRef]
  18. L. Novotny, "Effective wavelength scaling for optical antennas," Phys. Rev. Lett. 98, 266802 (2007).
    [CrossRef] [PubMed]
  19. M. I. Haftel, C. Schlockermann, and G. Blumberg, "Role of cylindrical surface plasmons in enhanced transmission," Appl. Phys. Lett. 88, 193104 (2006).
    [CrossRef]
  20. M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, "Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium," Opt. Lett. 31, 3022 (2006).
    [CrossRef] [PubMed]

2007

T. Søndergaard and S. I. Bozhevolnyi, "Slow-plasmon resonant nanostructures: scattering and field enhancements," Phys. Rev. B 75, 073402 (2007).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, "Metal nano-strip optical resonators," Opt. Express 15, 4198-4204 (2007).
[CrossRef] [PubMed]

Y. Kurokawa and H. T. Miyazaki, "Metal-insulator-metal plasmon nanocavities: analysis of optical properties," Phys. Rev. B 75, 035411 (2007).
[CrossRef]

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

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

2006

M. I. Haftel, C. Schlockermann, and G. Blumberg, "Role of cylindrical surface plasmons in enhanced transmission," Appl. Phys. Lett. 88, 193104 (2006).
[CrossRef]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, "Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium," Opt. Lett. 31, 3022 (2006).
[CrossRef] [PubMed]

R. Gordon, "Light in a subwavelength slit in a metal: propagation and reflection," Phys. Rev. B 73, 153405 (2006).
[CrossRef]

G. Lévêque and O. J. F. Martin, "Tunable composite nanoparticle for plasmonics," Opt. Lett. 31, 2750-2752 (2006).
[CrossRef] [PubMed]

F. Wang and Y. R. Shen, "General properties of local plasmons in metal nanostructures," Phys. Rev. Lett. 97, 206806 (2006).
[CrossRef] [PubMed]

2004

2003

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

D. R. Fredkin and I. D. Mayergouz, "Resonant behaviour of dielectric objects (electrostatic resonances)," Phys. Rev. Lett. 91, 253902 (2003).
[CrossRef]

V. A. Podoloskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735-745 (2003).
[CrossRef]

1969

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Adegoke, J.

Bahoura, M.

Barnes, W. L.

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

Blumberg, G.

M. I. Haftel, C. Schlockermann, and G. Blumberg, "Role of cylindrical surface plasmons in enhanced transmission," Appl. Phys. Lett. 88, 193104 (2006).
[CrossRef]

Bozhevolnyi, S. I.

T. Søndergaard and S. I. Bozhevolnyi, "Slow-plasmon resonant nanostructures: scattering and field enhancements," Phys. Rev. B 75, 073402 (2007).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, "Metal nano-strip optical resonators," Opt. Express 15, 4198-4204 (2007).
[CrossRef] [PubMed]

T. Søndergaard and S. I. Bozhevolnyi, "Strip and gap plasmon polariton resonances," Phys. Status Solidi(b), submitted.

Brongersma, M. L.

Catrysse, P. B.

Dereux, A.

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

Drachev, V. P.

Ebbesen, T. W.

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

Economou, E. N.

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Fredkin, D. R.

D. R. Fredkin and I. D. Mayergouz, "Resonant behaviour of dielectric objects (electrostatic resonances)," Phys. Rev. Lett. 91, 253902 (2003).
[CrossRef]

Gordon, R.

R. Gordon, "Light in a subwavelength slit in a metal: propagation and reflection," Phys. Rev. B 73, 153405 (2006).
[CrossRef]

Haftel, M. I.

M. I. Haftel, C. Schlockermann, and G. Blumberg, "Role of cylindrical surface plasmons in enhanced transmission," Appl. Phys. Lett. 88, 193104 (2006).
[CrossRef]

Kurokawa, Y.

Y. Kurokawa and H. T. Miyazaki, "Metal-insulator-metal plasmon nanocavities: analysis of optical properties," Phys. Rev. B 75, 035411 (2007).
[CrossRef]

Lévêque, G.

Martin, O. J. F.

Mayergouz, I. D.

D. R. Fredkin and I. D. Mayergouz, "Resonant behaviour of dielectric objects (electrostatic resonances)," Phys. Rev. Lett. 91, 253902 (2003).
[CrossRef]

Miyazaki, H. T.

Y. Kurokawa and H. T. Miyazaki, "Metal-insulator-metal plasmon nanocavities: analysis of optical properties," Phys. Rev. B 75, 035411 (2007).
[CrossRef]

Noginov, M. A.

Novotny, L.

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

Podoloskiy, V. A.

Ritzo, B. A.

Sarychev, A. K.

Schlockermann, C.

M. I. Haftel, C. Schlockermann, and G. Blumberg, "Role of cylindrical surface plasmons in enhanced transmission," Appl. Phys. Lett. 88, 193104 (2006).
[CrossRef]

Selker, M. D.

Shalaev, V. M.

Shen, Y. R.

F. Wang and Y. R. Shen, "General properties of local plasmons in metal nanostructures," Phys. Rev. Lett. 97, 206806 (2006).
[CrossRef] [PubMed]

Small, C. E.

Søndergaard, T.

T. Søndergaard and S. I. Bozhevolnyi, "Slow-plasmon resonant nanostructures: scattering and field enhancements," Phys. Rev. B 75, 073402 (2007).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, "Metal nano-strip optical resonators," Opt. Express 15, 4198-4204 (2007).
[CrossRef] [PubMed]

T. Søndergaard and S. I. Bozhevolnyi, "Strip and gap plasmon polariton resonances," Phys. Status Solidi(b), submitted.

Wang, F.

F. Wang and Y. R. Shen, "General properties of local plasmons in metal nanostructures," Phys. Rev. Lett. 97, 206806 (2006).
[CrossRef] [PubMed]

Zhu, G.

Zia, R.

Appl. Phys. Lett.

M. I. Haftel, C. Schlockermann, and G. Blumberg, "Role of cylindrical surface plasmons in enhanced transmission," Appl. Phys. Lett. 88, 193104 (2006).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

Nature

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

Opt. Express

Opt. Lett.

Phys. Rev.

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Phys. Rev. B

R. Gordon, "Light in a subwavelength slit in a metal: propagation and reflection," Phys. Rev. B 73, 153405 (2006).
[CrossRef]

Y. Kurokawa and H. T. Miyazaki, "Metal-insulator-metal plasmon nanocavities: analysis of optical properties," Phys. Rev. B 75, 035411 (2007).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, "Slow-plasmon resonant nanostructures: scattering and field enhancements," Phys. Rev. B 75, 073402 (2007).
[CrossRef]

Phys. Rev. Lett.

F. Wang and Y. R. Shen, "General properties of local plasmons in metal nanostructures," Phys. Rev. Lett. 97, 206806 (2006).
[CrossRef] [PubMed]

D. R. Fredkin and I. D. Mayergouz, "Resonant behaviour of dielectric objects (electrostatic resonances)," Phys. Rev. Lett. 91, 253902 (2003).
[CrossRef]

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

Phys. Status Solidi

T. Søndergaard and S. I. Bozhevolnyi, "Strip and gap plasmon polariton resonances," Phys. Status Solidi(b), submitted.

Other

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, Berlin, 1995).

N. Engheta, A. Salandrino, and A. AluÌ, "Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

H. Räther, Surface Plasmons (Springer, 1988).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

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 (6)

Fig. 1.
Fig. 1.

The distributions of electric field components of the SR-SPP supported by a 10-nm-thick silver film in air at the light wavelength of 655 nm.

Fig. 2.
Fig. 2.

The effective indexes of SPP modes and their propagation lengths at the excitation light wavelength of 775 nm for a thin gold film surrounded by air.

Fig. 3.
Fig. 3.

The distributions of electric field components of the G-SPP supported by 50-nm-thick silver films separated by a 10-nm-wide air gap (at 655 nm). A finite (but quite large) film thickness was chosen for practical considerations.

Fig. 4.
Fig. 4.

The GSP mode effective index and propagation length at the excitation light wavelength of 775 nm for an air gap between thick gold layers.

Fig. 5.
Fig. 5.

Scattering spectra for a 10-nm-thick and 150-nm-wide silver strip (in air) and for two 10-nm-air-gap structures being 110-nm-long and having 25- and 50-nm-thick silver cladding layers. The structures are illuminated by a p-polarized plane wave propagating at 45° angle with respect to the x-axis.

Fig. 6.
Fig. 6.

Electric field magnitude distributions for (a) strip and (b) gap structures exhibiting the resonance at the wavelength of ~650 nm. The structures are illuminated by a plane wave propagating along the y-axis (for structure details see Fig. 5). The arrows indicate the electric field orientation and magnitude for the real part of the electric field (which is equivalent to a snapshot in time).

Equations (8)

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

tanh ( 1 ) ( α m t 2 ) = ( ε m α d ) ( ε d α m ) with α m , d = k l ( s ) rsp 2 ε m , d k 0 2 and k 0 = 2 π λ ,
k l ( s ) rsp k 0 ε d + ( ε d ε m ) ( ε d ε m ) 2 · tanh ( ) 2 ( 0.5 k 0 t ε d ε m ) .
tanh ( α d t 2 ) = ( ε d α m ) ( ε m α d ) with α m , d = k gsp 2 ε m , d k 0 2 ,
k gsp k 0 ε d + 0.5 ( k gsp 0 k 0 ) 2 + ( k gsp 0 k 0 ) 2 [ ε d ε m + 0.25 ( k gsp 0 k 0 ) 2 ] with k gsp 0 = 2 ε d t ε m .
k gsp k sp 1 4 ε d ε m ε m 2 ε d 2 exp ( α d t ) with α d = α 0 1 + 4 ε m 2 ε m 2 ε d 2 exp ( α 0 t ) ,
where α 0 = k sp 2 ε d k 0 2 = k 0 ε d ε m ε d .
w 2 π λ N eff = m π + φ .
Q π λ Im ( k sp ) 1 2 N eff Re ( ε m ) Im ( ε m ) .

Metrics