Abstract

We investigate theoretically the near-field dynamics of the scattering of a surface-plasmon polariton (SPP) pulse impinging normally on a rectangular groove on an otherwise planar metal surface. Our formulation is based on solving the reduced Rayleigh equation (derived through the use of an impedance boundary condition) for every component of the spectral decomposition of the incoming SPP pulse. Numerical calculations are carried out of the time dependence of the near-field resonant scattering effects produced at the rectangular groove. The scattering process is tracked through the (time-resolved) repartition of the incoming SPP electromagnetic energy into reflected and transmitted SPP pulses, and into pulsed scattered light. Furthermore, we directly show evidence of the excitation of single resonances, as manifested by the concentration of electric field intensity within the groove, and its subsequent leakage, over the resonance lifetime. The near-field formation of oscillations caused by the interference between two adjacent resonances simultaneously excited is also considered.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. T. A. Leskova and N. I. Gapotchenko, �??Fabry-Perot type interferometer for surface polaritons: resonance effects,�?? Solid State Commun. 53, 351 (1985).
    [CrossRef]
  2. B. Rothenhausler and W. Knoll, �??Surface plasmon interferometry in the visible,�?? Appl. Phys. Lett. 52, 1554 (1988).
    [CrossRef]
  3. B. Rothenhausler and W. Knoll, �??Interferometric determination of the complex wave vector of plasmon surface polaritons,�?? J. Opt. Soc. Am. B 5, 1401 (1988).
    [CrossRef]
  4. F. Pincemin, A. A. Maradudin, A. D. Boardman, and J.-J. Greffet, �??Scattering of a surface plasmon polariton by a surface defect,�?? Phys. Rev. B 50, 15261 (1994).
    [CrossRef]
  5. A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, �??Scattering of surface plasmon polaritons by a circularly symmetric surface defect,�?? Phys. Rev. Lett. 78, 4269 (1997).
    [CrossRef]
  6. J. A. Sanchez-Gil, �??Surface defect scattering of surface plasmon polaritons: Mirrors and light emitters,�?? Appl. Phys. Lett. 73, 3509 (1998).
    [CrossRef]
  7. J. A. Sanchez-Gil and A. A. Maradudin, �??Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,�?? Phys. Rev. B 60, 8359 (1999).
  8. T. A. Leskova, A. A. Maradudin, and W. Zierau, �??Surface plasmon polariton propagation near an index step,�?? Proc. SPIE 4100, 1 (2000).
    [CrossRef]
  9. Z. Schlesinger and A. J. Sievers, �??Infrared surface wave interferometry,�?? Appl. Phys. Lett. 36, 409 (1980).
    [CrossRef]
  10. B. Rothenh¨ausler and W. Knoll, �??On the influence of the propagation length of plasmon surface polaritons in the visible energy range for the optical characterization of heterogeneous thin films,�?? Surf. Sci. 191, 585 (1987).
    [CrossRef]
  11. B. Rothenhausler and W. Knoll, �??Total internal diffraction of plasmon surface polaritons,�?? Appl. Phys. Lett. 51, 783 (1987).
    [CrossRef]
  12. B. Rothenhausler and W. Knoll, �??Surface plasmon microscopy,�?? Nature 332, 615 (1988)
    [CrossRef]
  13. C. E. H. Berger, R. P. H. Koioyman, and J. Greve, �??Surface plasmon propagation near an index step,�?? Opt. Commun. 167, 183 (1999).
    [CrossRef]
  14. I. Smolyaninov, D. L. Mazzoni, and C. C. Davis, �??Imaging of surface plasmon scattering by lithographically created individual surface defects,�?? Phys. Rev. Lett. 78, 2823 (1997).
  15. I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and C. C. Davis, �??Experimental study of surface plasmon scattering by individual surface defects,�?? Phys. Rev. B 56, 1601 (1997).
    [CrossRef]
  16. A. Dogariu, T. Thio, L. J. Wang, T. W. Ebbesen, and H. J. Lezec, �??Delay in light transmission through small apertures,�?? Opt. Lett. 26, 450 (2001).
    [CrossRef]
  17. Y.-H. Liau, S. Egusa, and N. F. Scherer, �??Ultrafast interferometric measurements of plasmonic transport in photonic crystals,�?? Opt. Lett. 27, 857 (2002).
    [CrossRef]
  18. J. A. Sanchez-Gil and A. A. Maradudin, �??Resonant scattering of surface-plasmon polariton pulses by nanoscale metal defects,�?? Opt. Lett. 28, 2255 (2003).
    [CrossRef] [PubMed]
  19. H. Raether, Surface Polaritons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  20. A. A. Maradudin, �??An impedance boundary condition for a rough surface,�?? in Topics in Condensed Matter Physics, ed. M. P. Das (Nova, New York, 1994), p. 33.
  21. Note that, strictly speaking, such a linear mapping of the surface corrugation into the surface impedance on the plane may not be correct, as discussed in Ref. [7], in the case of rectangular defects, due to the influence of higher-order terms in the slope. Nonetheless, this should not affect the results for the resonant scattering process, except for, presumably, the actual position and strength of resonances.
  22. In our two-dimensional geometry, a near-field area at constant height converts into a single line; we actually merge in a single map all such line scans, from the vacuum-metal interface up to a certain, maximum height.
  23. We have verified that both resonances are decoupled by separately probing each with surface plasmon polariton pulses appropriately tuned.
  24. W. L. Barnes, A. Dereux, and T.W. Ebbesen, �??Surface plasmon sub-wavelength optics,�?? Nature 424, 824 (2003).
    [CrossRef] [PubMed]

Appl. Phys. Lett.

B. Rothenhausler and W. Knoll, �??Surface plasmon interferometry in the visible,�?? Appl. Phys. Lett. 52, 1554 (1988).
[CrossRef]

J. A. Sanchez-Gil, �??Surface defect scattering of surface plasmon polaritons: Mirrors and light emitters,�?? Appl. Phys. Lett. 73, 3509 (1998).
[CrossRef]

Z. Schlesinger and A. J. Sievers, �??Infrared surface wave interferometry,�?? Appl. Phys. Lett. 36, 409 (1980).
[CrossRef]

B. Rothenhausler and W. Knoll, �??Total internal diffraction of plasmon surface polaritons,�?? Appl. Phys. Lett. 51, 783 (1987).
[CrossRef]

J. Opt. Soc. Am. B

B. Rothenhausler and W. Knoll, �??Interferometric determination of the complex wave vector of plasmon surface polaritons,�?? J. Opt. Soc. Am. B 5, 1401 (1988).
[CrossRef]

Nature

B. Rothenhausler and W. Knoll, �??Surface plasmon microscopy,�?? Nature 332, 615 (1988)
[CrossRef]

W. L. Barnes, A. Dereux, and T.W. Ebbesen, �??Surface plasmon sub-wavelength optics,�?? Nature 424, 824 (2003).
[CrossRef] [PubMed]

Opt. Commun.

C. E. H. Berger, R. P. H. Koioyman, and J. Greve, �??Surface plasmon propagation near an index step,�?? Opt. Commun. 167, 183 (1999).
[CrossRef]

Opt. Lett.

A. Dogariu, T. Thio, L. J. Wang, T. W. Ebbesen, and H. J. Lezec, �??Delay in light transmission through small apertures,�?? Opt. Lett. 26, 450 (2001).
[CrossRef]

Y.-H. Liau, S. Egusa, and N. F. Scherer, �??Ultrafast interferometric measurements of plasmonic transport in photonic crystals,�?? Opt. Lett. 27, 857 (2002).
[CrossRef]

J. A. Sanchez-Gil and A. A. Maradudin, �??Resonant scattering of surface-plasmon polariton pulses by nanoscale metal defects,�?? Opt. Lett. 28, 2255 (2003).
[CrossRef] [PubMed]

Phys. Rev. B

F. Pincemin, A. A. Maradudin, A. D. Boardman, and J.-J. Greffet, �??Scattering of a surface plasmon polariton by a surface defect,�?? Phys. Rev. B 50, 15261 (1994).
[CrossRef]

J. A. Sanchez-Gil and A. A. Maradudin, �??Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,�?? Phys. Rev. B 60, 8359 (1999).

I. I. Smolyaninov, D. L. Mazzoni, J. Mait, and C. C. Davis, �??Experimental study of surface plasmon scattering by individual surface defects,�?? Phys. Rev. B 56, 1601 (1997).
[CrossRef]

Phys. Rev. Lett.

I. Smolyaninov, D. L. Mazzoni, and C. C. Davis, �??Imaging of surface plasmon scattering by lithographically created individual surface defects,�?? Phys. Rev. Lett. 78, 2823 (1997).

A. V. Shchegrov, I. V. Novikov, and A. A. Maradudin, �??Scattering of surface plasmon polaritons by a circularly symmetric surface defect,�?? Phys. Rev. Lett. 78, 4269 (1997).
[CrossRef]

Proc. SPIE

T. A. Leskova, A. A. Maradudin, and W. Zierau, �??Surface plasmon polariton propagation near an index step,�?? Proc. SPIE 4100, 1 (2000).
[CrossRef]

Solid State Commun.

T. A. Leskova and N. I. Gapotchenko, �??Fabry-Perot type interferometer for surface polaritons: resonance effects,�?? Solid State Commun. 53, 351 (1985).
[CrossRef]

Surf. Sci.

B. Rothenh¨ausler and W. Knoll, �??On the influence of the propagation length of plasmon surface polaritons in the visible energy range for the optical characterization of heterogeneous thin films,�?? Surf. Sci. 191, 585 (1987).
[CrossRef]

Other

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

A. A. Maradudin, �??An impedance boundary condition for a rough surface,�?? in Topics in Condensed Matter Physics, ed. M. P. Das (Nova, New York, 1994), p. 33.

Note that, strictly speaking, such a linear mapping of the surface corrugation into the surface impedance on the plane may not be correct, as discussed in Ref. [7], in the case of rectangular defects, due to the influence of higher-order terms in the slope. Nonetheless, this should not affect the results for the resonant scattering process, except for, presumably, the actual position and strength of resonances.

In our two-dimensional geometry, a near-field area at constant height converts into a single line; we actually merge in a single map all such line scans, from the vacuum-metal interface up to a certain, maximum height.

We have verified that both resonances are decoupled by separately probing each with surface plasmon polariton pulses appropriately tuned.

Supplementary Material (4)

» Media 1: AVI (304 KB)     
» Media 2: AVI (255 KB)     
» Media 3: AVI (320 KB)     
» Media 4: AVI (244 KB)     

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 (9)

Fig. 1.
Fig. 1.

Illustration of the scattering geometry. The dashed rectangle shows the configuration of the near-field region scanned in Figs. 3, 4, 7 and 9.

Fig. 2.
Fig. 2.

Spectral dependence of the monochromatic, SPP reflection (green curve) and transmission (red curve) coefficients (R SPP and T SPP, respectively), and total radiated energy S (blue curve) for a rectangular defect of half-width L=789 nm. Solid curves: Groove, h=-157 nm; Dashed curves: Ridge, h=157 nm. λp =2πc/ωp =157 nm (Ag). The spectral amplitudes (normalized to 1) of the SPP pulses considered below are superimposed (black curves).

Fig. 3.
Fig. 3.

(308 KB) Movie of the time evolution of the near (electric) field intensity (log scale) images in an area of 8λ×4λ perpendicular to the Ag surface for a rectangular groove (located at the bottom center, see Fig. 1) of half-width L=785 nm and depth h=-157 nm. The incident SPP pulse parameters are: ω 0/ωp =0.275 (λ0=571 nm) and Δω/ω 0=0.02. Front picture: t=0 (incoming SPP pulse maximum at x 1=0).

Fig. 4.
Fig. 4.

(260 KB) Same as in Fig. 3 but for a rectangular ridge (h=157 nm).

Fig. 5.
Fig. 5.

Pulse amplitudes for ω 0/ωp =0.275 and Δω/ω 0=0.035 at a distance x=400λ 0 scattered from rectangular defects of half-width L=785 nm and height h=±157 nm: Reflected (green curve) and transmitted (red curve) SPP, and radiated (blue curve) at θ=θmax . (a) Groove, θmax =46.6°; (b) Ridge, θmax =62.5°. The freely propagating SPP pulse is also shown (black curve).

Fig. 6.
Fig. 6.

Time dependence of the angular distribution of intensity scattered (for ω 0/ωp =0.275) from rectangular defects of half-width L=785 nm and height h=±157 nm. (a) Groove; (b) Ridge.

Fig. 7.
Fig. 7.

(328 KB) Same as in Fig. 3 but for different incident SPP pulse parameters: ω 0/ωp =0.247 (λ 0=636 nm) and Δω/ω 0=0.035.

Fig. 8.
Fig. 8.

Same as in Fig. 5(a) but for different incident SPP pulse parameters: ω 0/ωp =0.247 and Δω/ω 0=0.035. θmax =69.6°.

Fig. 9.
Fig. 9.

(252 KB) Movie of the time evolution of the near (electric) field intensity (log scale) images in an area of 8λ×4λ perpendicular to the Ag surface for a Gaussian groove (located at the bottom center, see Fig. 1) of 1/e-width a=157 nm and height δ=-785 nm. The incident SPP pulse parameters are: ω 0/ωp =0.239 (λ 0=657 nm) and Δω/ω 0=0.035. Front picture: t=0 (incoming SPP pulse maximum at x 1=0).

Equations (17)

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

H 2 ( i ) ( x 1 , x 3 ; t ) = d ω F ( ω ) exp [ ik ( ω ) x 1 β 0 ( ω ) x 3 ] exp ( i ω t ) ,
F ( ω ) = exp [ ( ω 2 ω 0 2 ) ( Δ ω ) 2 ] ( π Δ ω ) ,
k ( ω ) = ω c ( 1 1 ε ( ω ) ) 1 2 , β 0 ( ω ) ( k ( ω ) 2 ω 2 c 2 ) 1 2 = ω c [ ε ( ω ) ] 1 2 ,
H 2 ( sc ) ( x 1 , x 3 ; t ) = d ω F ( ω ) e i ω t d q 2 π R ( q , ω ) exp [ i ( q x 1 + α 0 ( q , ω ) x 3 ) ] ,
R ( q , ω ) = G 0 ( q , ω ) T ( q , ω ) ,
G 0 ( q , ω ) = i ε ( ω ) ε ( ω ) α 0 ( q , ω ) + i ( ω c ) [ ε ( ω ) ] 1 2 C ( q , ω ) ( 1 q k ( ω ) 1 q + k ( ω ) ) ,
T ( q , ω ) = V ( q k ( ω ) ) + d p 2 π V ( q p ) G 0 ( p , ω ) T ( p , ω ) ,
V ( q p ) β 0 ( ω ) s ̂ ( q p ) , s ̂ ( Q ) = d x 1 e i Q x 1 s ( x 1 ) .
H 2 ( x 1 , 0 ; t ) = H 2 ( i ) ( x 1 , 0 ; t ) + H 2 ( r ) ( x 1 , 0 ; t )
= H 2 ( i ) ( x 1 , 0 ; t ) + d ω F ( ω ) e i ω t ρ ( ω ) exp [ ik ( ω ) x 1 β 0 ( ω ) x 3 ] , x 1 0 ;
H 2 ( x 1 , 0 ; t ) = H 2 ( t ) ( x 1 , 0 ; t )
= d ω F ( ω ) e i ω t τ ( ω ) exp [ ik ( ω ) x 1 β 0 ( ω ) x 3 ] , x 1 0 ,
ρ ( ω ) = iT ( k R ( ω ) , ω ) C ( k R ( ω ) , ω )
τ ( ω ) = 1 + iT ( k R ( ω ) , ω ) C ( k R ( ω ) , ω ) ,
H 2 ( s ) ( r , θ ; t ) = e i π 4 cos θ 2 π r d ω F ( ω ) e i ω t ω c R ( ( ω c ) sin θ , ω ) exp ( i ω r c ) ,
I ( θ , t ) r H s 2 .
s ( x 1 , ω ) = 1 ε ( ω ) d ( ω ) ε ( ω ) h [ Θ ( x 1 + L ) Θ ( x 1 L ) ] ,

Metrics