Abstract

We have theoretically investigated the dynamics of the scattering of surface-plasmon polariton (SPP) pulses by single nanoscale metal defects through a rigorous calculation of the time dependence of the reflected and transmitted SPP and of the angular distribution of the scattered light. SPP resonances that occur at deep Gaussian grooves are probed with SPP pulses, the resonant scattering being unequivocally manifested by (a) the exponential tails of the scattered SPP and light pulses and (b) the delay time of the transmitted SPP pulse.

© 2003 Optical Society of America

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  1. H. Raether, Surface Polaritons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  2. S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. Lett. 77, 2670 (1996).
    [CrossRef] [PubMed]
  3. I. I. Smolyaninov, D. L. Mazzoni, and C. C. Davis, Phys. Rev. Lett. 77, 3877 (1996).
    [CrossRef] [PubMed]
  4. S. Bozhevolnyi and F. A. Pudonin, Phys. Rev. Lett. 78, 2823 (1997).
    [CrossRef]
  5. A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, Phys. Rev. Lett. 78, 4269 (1997).
    [CrossRef]
  6. J. A. Sánchez-Gil, Appl. Phys. Lett. 73, 3509 (1998).
    [CrossRef]
  7. J. A. Sánchez-Gil and A. A. Maradudin, Phys. Rev. B 60, 8359 (1999).
    [CrossRef]
  8. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
    [CrossRef]
  9. A. Dogariu, T. Thio, L. J. Wang, T. W. Ebbesen, and H. J. Lezec, Opt. Lett. 26, 450 (2001).
    [CrossRef]
  10. S. I. Bozhevolnyi, J. E. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, Phys. Rev. Lett. 86, 3008 (2001).
    [CrossRef] [PubMed]
  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. A. A. Maradudin, in Topics in Condensed Matter Physics, M. P. Das, ed. (Nova Science, Hauppauge, N.Y., 1995).
  14. Drude's free-electron approximation describes correctly the metal response for frequencies below the onset of the highly absorbing, interband transitions (at l~400 nm for Ag). The (weak) absorptive contribution to Drude's formula is also neglected, since it does not introduce significant effects in the scattering process (defect size < <labs), and subsequent dissipative losses in the SPP propagation can be independently accounted for (labs~24μm for Ag at l=650 nm).

2002

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

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

2001

S. I. Bozhevolnyi, J. E. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, Phys. Rev. Lett. 86, 3008 (2001).
[CrossRef] [PubMed]

A. Dogariu, T. Thio, L. J. Wang, T. W. Ebbesen, and H. J. Lezec, Opt. Lett. 26, 450 (2001).
[CrossRef]

1999

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

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

J. A. Sánchez-Gil, Appl. Phys. Lett. 73, 3509 (1998).
[CrossRef]

1997

S. Bozhevolnyi and F. A. Pudonin, Phys. Rev. Lett. 78, 2823 (1997).
[CrossRef]

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, Phys. Rev. Lett. 78, 4269 (1997).
[CrossRef]

1996

S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. Lett. 77, 2670 (1996).
[CrossRef] [PubMed]

I. I. Smolyaninov, D. L. Mazzoni, and C. C. Davis, Phys. Rev. Lett. 77, 3877 (1996).
[CrossRef] [PubMed]

1995

A. A. Maradudin, in Topics in Condensed Matter Physics, M. P. Das, ed. (Nova Science, Hauppauge, N.Y., 1995).

1988

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

Aussenegg, F. R.

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

Barnes, W. L.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. Lett. 77, 2670 (1996).
[CrossRef] [PubMed]

Bozhevolnyi, S.

S. Bozhevolnyi and F. A. Pudonin, Phys. Rev. Lett. 78, 2823 (1997).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, J. E. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, Phys. Rev. Lett. 86, 3008 (2001).
[CrossRef] [PubMed]

Davis, C. C.

I. I. Smolyaninov, D. L. Mazzoni, and C. C. Davis, Phys. Rev. Lett. 77, 3877 (1996).
[CrossRef] [PubMed]

Ditlbacher, H.

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

Dogariu, A.

Ebbesen, T. W.

A. Dogariu, T. Thio, L. J. Wang, T. W. Ebbesen, and H. J. Lezec, Opt. Lett. 26, 450 (2001).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Egusa, S.

Erland, J. E.

S. I. Bozhevolnyi, J. E. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, Phys. Rev. Lett. 86, 3008 (2001).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Hvam, J. M.

S. I. Bozhevolnyi, J. E. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, Phys. Rev. Lett. 86, 3008 (2001).
[CrossRef] [PubMed]

Kitson, S. C.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. Lett. 77, 2670 (1996).
[CrossRef] [PubMed]

Krenn, J. R.

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

S. I. Bozhevolnyi, J. E. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, Phys. Rev. Lett. 86, 3008 (2001).
[CrossRef] [PubMed]

Lezec, H. J.

A. Dogariu, T. Thio, L. J. Wang, T. W. Ebbesen, and H. J. Lezec, Opt. Lett. 26, 450 (2001).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Liau, Y.-H.

Maradudin, A. A.

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

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, Phys. Rev. Lett. 78, 4269 (1997).
[CrossRef]

A. A. Maradudin, in Topics in Condensed Matter Physics, M. P. Das, ed. (Nova Science, Hauppauge, N.Y., 1995).

Mazzoni, D. L.

I. I. Smolyaninov, D. L. Mazzoni, and C. C. Davis, Phys. Rev. Lett. 77, 3877 (1996).
[CrossRef] [PubMed]

Novikov, I. V.

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, Phys. Rev. Lett. 78, 4269 (1997).
[CrossRef]

Pudonin, F. A.

S. Bozhevolnyi and F. A. Pudonin, Phys. Rev. Lett. 78, 2823 (1997).
[CrossRef]

Raether, H.

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

Sambles, J. R.

S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. Lett. 77, 2670 (1996).
[CrossRef] [PubMed]

Sánchez-Gil, J. A.

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

J. A. Sánchez-Gil, Appl. Phys. Lett. 73, 3509 (1998).
[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]

Shchegrov, A. V.

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, Phys. Rev. Lett. 78, 4269 (1997).
[CrossRef]

Skovgaard, P. M. W.

S. I. Bozhevolnyi, J. E. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, Phys. Rev. Lett. 86, 3008 (2001).
[CrossRef] [PubMed]

Smolyaninov, I. I.

I. I. Smolyaninov, D. L. Mazzoni, and C. C. Davis, Phys. Rev. Lett. 77, 3877 (1996).
[CrossRef] [PubMed]

Thio, T.

A. Dogariu, T. Thio, L. J. Wang, T. W. Ebbesen, and H. J. Lezec, Opt. Lett. 26, 450 (2001).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Wang, L. J.

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Appl. Phys. Lett.

J. A. Sánchez-Gil, Appl. Phys. Lett. 73, 3509 (1998).
[CrossRef]

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

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Opt. Lett.

Phys. Rev. B

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

Phys. Rev. Lett.

S. I. Bozhevolnyi, J. E. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam, Phys. Rev. Lett. 86, 3008 (2001).
[CrossRef] [PubMed]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. Lett. 77, 2670 (1996).
[CrossRef] [PubMed]

I. I. Smolyaninov, D. L. Mazzoni, and C. C. Davis, Phys. Rev. Lett. 77, 3877 (1996).
[CrossRef] [PubMed]

S. Bozhevolnyi and F. A. Pudonin, Phys. Rev. Lett. 78, 2823 (1997).
[CrossRef]

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, Phys. Rev. Lett. 78, 4269 (1997).
[CrossRef]

Other

A. A. Maradudin, in Topics in Condensed Matter Physics, M. P. Das, ed. (Nova Science, Hauppauge, N.Y., 1995).

Drude's free-electron approximation describes correctly the metal response for frequencies below the onset of the highly absorbing, interband transitions (at l~400 nm for Ag). The (weak) absorptive contribution to Drude's formula is also neglected, since it does not introduce significant effects in the scattering process (defect size < <labs), and subsequent dissipative losses in the SPP propagation can be independently accounted for (labs~24μm for Ag at l=650 nm).

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

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Figures (4)

Fig. 1
Fig. 1

Spectral dependence of the monochromatic SPP reflection (dashed–dotted curve) and transmission (solid curve) coefficients (RSPP and TSPP, respectively), and total radiated energy S (dashed curve) for a Gaussian defect of 1/e half-width a=157 nm: (a) ridge, δ=785 nm; (b) groove, δ=-785 nm. λp=2πc/ωp=157 nm (Ag). The spectral amplitudes (normalized to 1) of the SPP pulses considered below are superimposed (thicker curves).

Fig. 2
Fig. 2

Pulse intensities for ω0/ωp=0.239 and Δω=0.035ω0 at a distance x=400λ0 scattered from Gaussian defects of 1/e half-width a=157 nm and height δ=±785 nm: reflected (dashed–dotted curve) and transmitted (thin solid curve) SPP, and radiated (dashed curve) at θ=θmax, the freely propagating SPP pulse is also shown (thick solid curve), (a) ridge and (b) groove.

Fig. 3
Fig. 3

Time dependence of the angular distribution of intensity scattered (for ω0/ωp=0.239) from Gaussian defects of 1/e half-width a=157 nm and height δ=±785 nm: (a) ridge and (b) groove.

Fig. 4
Fig. 4

Modulus of the cross correlation (normalized to 1) of the incident and transmitted SPP pulses for ω0/ωp=0.239 and Δω=0.01ω0 from a Gaussian groove of 1/e half-width a=157 nm δ=-785 nm. The autocorrelation of the incident SPP pulse is also shown (thicker curve).

Equations (5)

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H2ix1,x3;t=-dωFωexpikωx1-β0ωx3×exp-iωt,
H2scx1,x3;t=-dωFωexp-iωt×-dq2πRq,ωexpiqx1+α0q,ωx3,
H2rx1,0;t=-dωFωexp-iωt×ρωexp-ikωx1-β0ωx3,  x10;
H2tx1,0;t=-dωFωexp-iωt×τωexpikωx1-β0ωx3,  x10.
H2sr,θ;t=exp-iτ4cos θ2τr-dωFωexp-ωt×ωcRω/csin θ,ω)expiωrc.

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