Abstract

The existence of gap states within the first stop band is theoretically investigated for surface-plasmon polaritons propagating along metal surfaces structured with finite arrays of nano-grooves/ridges with imperfections. By means of rigorous calculations of all scattering channels on the basis of the reduced Rayleigh equation, it is shown that a mismatch of the grating period, rather than simple vacant/defect sites, favors the opening of gap states (located at midgap for half-period shifts) as a phase step does in distributed feedback gratings. Quality factors of the resulting surface-plasmon polaritons' resonances are limited by radiative leakage and ohmic losses.

© 2007 Optical Society of America

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References

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  1. H. Raether, Surface Polaritons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
    [CrossRef] [PubMed]
  3. J. Takahara and T. Kobayashi, Opt. Photon. News 15(10), 54 (2004).
    [CrossRef]
  4. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
    [CrossRef]
  5. J. A. Sánchez-Gil and A. A. Maradudin, Appl. Phys. Lett. 86, 251106 (2005).
    [CrossRef]
  6. F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, Phys. Rev. B 72, 161405(R) (2005).
    [CrossRef]
  7. T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, Phys. Rev. B 73, 045320 (2006).
    [CrossRef]
  8. M. Kretschmann and A. A. Maradudin, Phys. Rev. B 66, 245408 (2002).
    [CrossRef]
  9. M. Kretschman, T. A. Leskova, and A. A. Maradudin, Opt. Commun. 215, 205 (2004).
    [CrossRef]
  10. S. I. Bozhevolnyi, V. Volkov, K. Leosson, and J. Erland, Opt. Lett. 26, 734 (2001).
    [CrossRef]
  11. H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
    [CrossRef]
  12. Y.-H. Liau, S. Egusa, and N. F. Scherer, Opt. Lett. 27, 857 (2002).
    [CrossRef]
  13. J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Phys. Rev. B 70, 235406 (2004).
    [CrossRef]
  14. J. Gómez Rivas, M. Kuttge, P. Haring Bolivar, H. Kurz, and J. A. Sánchez-Gil, Phys. Rev. Lett. 93, 256804 (2004).
    [CrossRef]
  15. C. Marquart, S. Bozhevolnyi, and K. Leosson, Opt. Express 13, 3303 (2005).
    [CrossRef] [PubMed]
  16. J. Gómez Rivas, M. Kuttge, H. Kurz, P. Haring Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
    [CrossRef]
  17. J. A. Sánchez-Gil and A. A. Maradudin, Phys. Rev. B 60, 8359 (1999).
    [CrossRef]
  18. E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).
  19. R.Kashyap, ed., Fiber Bragg Gratings (Academic, 1999).
  20. P. Berini, Opt. Lett. 24, 1011 (1999).
    [CrossRef]
  21. I. I. Smolyaninov, C. C. Davis, J. Elliot, and A. V. Zayats, Opt. Lett. 30, 382 (2005).
    [CrossRef] [PubMed]
  22. I. V. Novikov and A. A. Maradudin, Phys. Rev. B 66, 035403 (2002).
    [CrossRef]
  23. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
    [CrossRef] [PubMed]
  24. K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, Opt. Express 14, 314 (2006).
    [CrossRef] [PubMed]

2006 (3)

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, Phys. Rev. B 73, 045320 (2006).
[CrossRef]

J. Gómez Rivas, M. Kuttge, H. Kurz, P. Haring Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, Opt. Express 14, 314 (2006).
[CrossRef] [PubMed]

2005 (6)

I. I. Smolyaninov, C. C. Davis, J. Elliot, and A. V. Zayats, Opt. Lett. 30, 382 (2005).
[CrossRef] [PubMed]

C. Marquart, S. Bozhevolnyi, and K. Leosson, Opt. Express 13, 3303 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

J. A. Sánchez-Gil and A. A. Maradudin, Appl. Phys. Lett. 86, 251106 (2005).
[CrossRef]

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, Phys. Rev. B 72, 161405(R) (2005).
[CrossRef]

2004 (4)

J. Takahara and T. Kobayashi, Opt. Photon. News 15(10), 54 (2004).
[CrossRef]

M. Kretschman, T. A. Leskova, and A. A. Maradudin, Opt. Commun. 215, 205 (2004).
[CrossRef]

J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Phys. Rev. B 70, 235406 (2004).
[CrossRef]

J. Gómez Rivas, M. Kuttge, P. Haring Bolivar, H. Kurz, and J. A. Sánchez-Gil, Phys. Rev. Lett. 93, 256804 (2004).
[CrossRef]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

2002 (4)

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

M. Kretschmann and A. A. Maradudin, Phys. Rev. B 66, 245408 (2002).
[CrossRef]

I. V. Novikov and A. A. Maradudin, Phys. Rev. B 66, 035403 (2002).
[CrossRef]

Y.-H. Liau, S. Egusa, and N. F. Scherer, Opt. Lett. 27, 857 (2002).
[CrossRef]

2001 (1)

1999 (2)

P. Berini, Opt. Lett. 24, 1011 (1999).
[CrossRef]

J. A. Sánchez-Gil and A. A. Maradudin, Phys. Rev. B 60, 8359 (1999).
[CrossRef]

Aussenegg, F. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Baudrion, A.-L.

J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Berini, P.

Bolivar, P. Haring

J. Gómez Rivas, M. Kuttge, H. Kurz, P. Haring Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

J. Gómez Rivas, M. Kuttge, P. Haring Bolivar, H. Kurz, and J. A. Sánchez-Gil, Phys. Rev. Lett. 93, 256804 (2004).
[CrossRef]

Boltasseva, A.

K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, Opt. Express 14, 314 (2006).
[CrossRef] [PubMed]

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, Phys. Rev. B 73, 045320 (2006).
[CrossRef]

Bozhevolnyi, S.

Bozhevolnyi, S. I.

Davis, C. C.

Dereux, A.

J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Phys. Rev. B 70, 235406 (2004).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Devaux, E.

J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Ditlbacher, H.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Ebbesen, T.

J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Egusa, S.

Elliot, J.

Erland, J.

García-Vidal, F. J.

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, Phys. Rev. B 72, 161405(R) (2005).
[CrossRef]

Girard, C.

J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Gómez Rivas, J.

J. Gómez Rivas, M. Kuttge, H. Kurz, P. Haring Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

González, M. U.

J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Hofer, F.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Hohenau, A.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Kobayashi, T.

J. Takahara and T. Kobayashi, Opt. Photon. News 15(10), 54 (2004).
[CrossRef]

Kreibig, U.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Krenn, J. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Kretschman, M.

M. Kretschman, T. A. Leskova, and A. A. Maradudin, Opt. Commun. 215, 205 (2004).
[CrossRef]

Kretschmann, M.

M. Kretschmann and A. A. Maradudin, Phys. Rev. B 66, 245408 (2002).
[CrossRef]

Kurz, H.

J. Gómez Rivas, M. Kuttge, H. Kurz, P. Haring Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

J. Gómez Rivas, M. Kuttge, P. Haring Bolivar, H. Kurz, and J. A. Sánchez-Gil, Phys. Rev. Lett. 93, 256804 (2004).
[CrossRef]

Kuttge, M.

J. Gómez Rivas, M. Kuttge, H. Kurz, P. Haring Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

J. Gómez Rivas, M. Kuttge, P. Haring Bolivar, H. Kurz, and J. A. Sánchez-Gil, Phys. Rev. Lett. 93, 256804 (2004).
[CrossRef]

Lacroute, Y.

J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Leitner, A.

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Leosson, K.

Leskova, T. A.

M. Kretschman, T. A. Leskova, and A. A. Maradudin, Opt. Commun. 215, 205 (2004).
[CrossRef]

Liau, Y.-H.

López-Tejeira, F.

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, Phys. Rev. B 72, 161405(R) (2005).
[CrossRef]

Maradudin, A. A.

J. A. Sánchez-Gil and A. A. Maradudin, Appl. Phys. Lett. 86, 251106 (2005).
[CrossRef]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

M. Kretschman, T. A. Leskova, and A. A. Maradudin, Opt. Commun. 215, 205 (2004).
[CrossRef]

I. V. Novikov and A. A. Maradudin, Phys. Rev. B 66, 035403 (2002).
[CrossRef]

M. Kretschmann and A. A. Maradudin, Phys. Rev. B 66, 245408 (2002).
[CrossRef]

J. A. Sánchez-Gil and A. A. Maradudin, Phys. Rev. B 60, 8359 (1999).
[CrossRef]

Marquart, C.

Martín-Moreno, L.

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, Phys. Rev. B 72, 161405(R) (2005).
[CrossRef]

Nikolajsen, T.

Novikov, I. V.

I. V. Novikov and A. A. Maradudin, Phys. Rev. B 66, 035403 (2002).
[CrossRef]

Raether, H.

H. Raether, Surface Polaritons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Rivas, J. Gómez

J. Gómez Rivas, M. Kuttge, P. Haring Bolivar, H. Kurz, and J. A. Sánchez-Gil, Phys. Rev. Lett. 93, 256804 (2004).
[CrossRef]

Rogers, M.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Sánchez-Gil, J. A.

J. Gómez Rivas, M. Kuttge, H. Kurz, P. Haring Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

J. A. Sánchez-Gil and A. A. Maradudin, Appl. Phys. Lett. 86, 251106 (2005).
[CrossRef]

J. Gómez Rivas, M. Kuttge, P. Haring Bolivar, H. Kurz, and J. A. Sánchez-Gil, Phys. Rev. Lett. 93, 256804 (2004).
[CrossRef]

J. A. Sánchez-Gil and A. A. Maradudin, Phys. Rev. B 60, 8359 (1999).
[CrossRef]

Scherer, N. F.

Schider, G.

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

I. I. Smolyaninov, C. C. Davis, J. Elliot, and A. V. Zayats, Opt. Lett. 30, 382 (2005).
[CrossRef] [PubMed]

Søndergaard, T.

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, Phys. Rev. B 73, 045320 (2006).
[CrossRef]

Takahara, J.

J. Takahara and T. Kobayashi, Opt. Photon. News 15(10), 54 (2004).
[CrossRef]

Volkov, V.

Wagner, D.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Weeber, J. C.

J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

I. I. Smolyaninov, C. C. Davis, J. Elliot, and A. V. Zayats, Opt. Lett. 30, 382 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

J. A. Sánchez-Gil and A. A. Maradudin, Appl. Phys. Lett. 86, 251106 (2005).
[CrossRef]

J. Gómez Rivas, M. Kuttge, H. Kurz, P. Haring Bolivar, and J. A. Sánchez-Gil, Appl. Phys. Lett. 88, 082106 (2006).
[CrossRef]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. Kretschman, T. A. Leskova, and A. A. Maradudin, Opt. Commun. 215, 205 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Opt. Photon. News (1)

J. Takahara and T. Kobayashi, Opt. Photon. News 15(10), 54 (2004).
[CrossRef]

Phys. Rep. (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

Phys. Rev. B (6)

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, Phys. Rev. B 72, 161405(R) (2005).
[CrossRef]

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, Phys. Rev. B 73, 045320 (2006).
[CrossRef]

M. Kretschmann and A. A. Maradudin, Phys. Rev. B 66, 245408 (2002).
[CrossRef]

J. C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, Phys. Rev. B 70, 235406 (2004).
[CrossRef]

I. V. Novikov and A. A. Maradudin, Phys. Rev. B 66, 035403 (2002).
[CrossRef]

J. A. Sánchez-Gil and A. A. Maradudin, Phys. Rev. B 60, 8359 (1999).
[CrossRef]

Phys. Rev. Lett. (2)

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

J. Gómez Rivas, M. Kuttge, P. Haring Bolivar, H. Kurz, and J. A. Sánchez-Gil, Phys. Rev. Lett. 93, 256804 (2004).
[CrossRef]

Other (3)

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

R.Kashyap, ed., Fiber Bragg Gratings (Academic, 1999).

H. Raether, Surface Polaritons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

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Figures (3)

Fig. 1
Fig. 1

Spectral dependence of the SPP transmission coefficient for finite arrays of period d = 314 nm , consisting of N = 41 Gaussian grooves of depth h = 31.4 nm and 1 e half-width A = 31.4 nm : perfect grating (thin solid curve), center groove of depth 2 h (short-dashed curve), center groove removed (long-dashed curve). The thick solid curve also corresponds to removing the center groove but bringing both symmetric sides of the grating a half-period distance closer (equivalent to shifting apart both symmetric halves of a 40-groove array by d 2 ). The shadow region shows the first SPP gap of the unperturbed grating. Inset, illustration of the SPP scattering geometry.

Fig. 2
Fig. 2

SPP reflection (R, top) and transmission (T, in a log 10 scale, middle) coefficients and the normalized radiative losses (S, bottom) for finite arrays ( d = 314 nm ) of N = 40 Gaussian grooves (left column) or ridges (right column) of depth/height h = 31.4 nm and 1 e half-width A = 31.4 nm as a function of wavelength (in the first gap region) and of the total shift s of both symmetric sides with respect to the array center.

Fig. 3
Fig. 3

Near (electric) field intensity (log scale) images in an area of 16 μ m × 3 μ m (in vacuum) perpendicular to the Ag surface for the same Gaussian-groove array as in Fig. 2 with shift (a) s d = 0 and (b) s d = 0.5 . (c) Corresponding surface electric field intensities for s d = 0 (left curve) and s d = 0.5 (right curve). In all cases, a monochromatic SPP of wavelength λ = 658 nm [lying on the SPP gap center in (a) and on the SPP gap state in (b)] impinges from the negative x axes onto the groove array, located at the bottom center within the vertical lines.

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