Abstract

We apply the technique of far-field interferometry to measure the properties of surface waves generated by two-dimensional (2D) single subwavelength slit-groove structures on gold films. The effective surface index of refraction n surf measured for the surface wave propagating over a distance of more than 12 μm is determined to be n surf = 1.016± 0.004, to within experimental uncertainty close to the expected bound surface plasmon-polariton (SPP) value for a Au/Air interface of n spp = 1.018. We compare these measurements to finite-difference-time-domain (FDTD) numerical simulations of the optical field transmission through these devices. We find excellent agreement between the measurements and the simulations for n surf. The measurements also show that the surface wave propagation parameter k surf exhibits transient behavior close to the slit, evolving smoothly from greater values asymptotically toward k spp over the first 2–3 μm of slit-groove distance x sg. This behavior is confirmed by the FDTD simulations.

© 2007 Optical Society of America

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  1. Permanent address: Physikalisches Institut, Universit¨at Bonn, Wegelerstrasse 8, 53115 Bonn, Germany.
  2. G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by Far-Field Interferometry," Phys. Rev. Lett. 96, 213901-1-4 (2006).
    [CrossRef]
  3. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nat. Phys. 2, 262-267 (2006).
    [CrossRef]
  4. H. Raether,Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, Berlin, 1988).
  5. P. Lalanne and J. P. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Phys. 2, 551-556 (2006).
    [CrossRef]
  6. G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, Comment on "The Response of Nanostructured Surfaces in the Near Field,"Nat. Phys. 2, 792 (2006).
    [CrossRef]
  7. G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, "Surface quality and surface waves on subwavelength-structured silver films," Phys. Rev. E 75, 016612-1-4 (2007).
    [CrossRef]
  8. Y. Xie, A. Zakharian, J. Moloney, and M. Mansuripur, "Transmission of light through slit apertures in metallic films," Opt. Express 12, 6106-6121 (2004).
    [CrossRef] [PubMed]
  9. Y. Xie, A. Zakharian, J. Moloney, and M. Mansuripur, "Transmission of light through a periodic array of slits in a thick metallic film," Opt. Express 13, 4485-4491 (2005).
    [CrossRef] [PubMed]
  10. A. Zakharian, J. Moloney, and M. Mansuripur, "Transmission of light through small elliptical apertures," Opt. Express 12, 2631-2648 (2004).
    [CrossRef] [PubMed]
  11. P. Johnson and R. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  12. Present experimental results. Value of nsurf determined from data in the far-zone
  13. Present FDTD simulations. Value of nsurf determined from FDTD simulations in the far-zone
  14. Measurements from Ref. [2] predominantly in the transient near-zone.
  15. Measurements from Ref. [3] predominantly in the transient near-zone.
  16. Value ofnsurf determined from FDTD simulations of Refs. [7, 6] in the far-zone.
  17. H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (2004).
    [CrossRef] [PubMed]
  18. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, "Transmission of light through periodic arrays of sub-wavelength slits in metallic hosts," Opt. Express 14, 6400-6413 (2004).
    [CrossRef]

2006

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nat. Phys. 2, 262-267 (2006).
[CrossRef]

P. Lalanne and J. P. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Phys. 2, 551-556 (2006).
[CrossRef]

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, Comment on "The Response of Nanostructured Surfaces in the Near Field,"Nat. Phys. 2, 792 (2006).
[CrossRef]

2005

2004

1972

P. Johnson and R. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Alloschery, O.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nat. Phys. 2, 262-267 (2006).
[CrossRef]

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, Comment on "The Response of Nanostructured Surfaces in the Near Field,"Nat. Phys. 2, 792 (2006).
[CrossRef]

Christy, R.

P. Johnson and R. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Gay, G.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, Comment on "The Response of Nanostructured Surfaces in the Near Field,"Nat. Phys. 2, 792 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nat. Phys. 2, 262-267 (2006).
[CrossRef]

Hugonin, J. P.

P. Lalanne and J. P. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Phys. 2, 551-556 (2006).
[CrossRef]

Johnson, P.

P. Johnson and R. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Lalanne, P.

P. Lalanne and J. P. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Phys. 2, 551-556 (2006).
[CrossRef]

Lezec, H. J.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nat. Phys. 2, 262-267 (2006).
[CrossRef]

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, Comment on "The Response of Nanostructured Surfaces in the Near Field,"Nat. Phys. 2, 792 (2006).
[CrossRef]

H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (2004).
[CrossRef] [PubMed]

Mansuripur, M.

Moloney, J.

Moloney, J. V.

O’Dwyer, C.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, Comment on "The Response of Nanostructured Surfaces in the Near Field,"Nat. Phys. 2, 792 (2006).
[CrossRef]

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nat. Phys. 2, 262-267 (2006).
[CrossRef]

Seideman, T.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, Comment on "The Response of Nanostructured Surfaces in the Near Field,"Nat. Phys. 2, 792 (2006).
[CrossRef]

Sukharev, M.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, Comment on "The Response of Nanostructured Surfaces in the Near Field,"Nat. Phys. 2, 792 (2006).
[CrossRef]

Thio, T.

Viaris de Lesegno, B.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nat. Phys. 2, 262-267 (2006).
[CrossRef]

Weiner, J.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nat. Phys. 2, 262-267 (2006).
[CrossRef]

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, Comment on "The Response of Nanostructured Surfaces in the Near Field,"Nat. Phys. 2, 792 (2006).
[CrossRef]

Xie, Y.

Zakharian, A.

Zakharian, A. R.

Nat. Phys.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner and H. J. Lezec, "The optical response of nanostructured surfaces and the composite diffracted evanescent wave model," Nat. Phys. 2, 262-267 (2006).
[CrossRef]

P. Lalanne and J. P. Hugonin, "Interaction between optical nano-objects at metallo-dielectric interfaces," Nat. Phys. 2, 551-556 (2006).
[CrossRef]

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, Comment on "The Response of Nanostructured Surfaces in the Near Field,"Nat. Phys. 2, 792 (2006).
[CrossRef]

Opt. Express

Phys. Rev. B

P. Johnson and R. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Other

Present experimental results. Value of nsurf determined from data in the far-zone

Present FDTD simulations. Value of nsurf determined from FDTD simulations in the far-zone

Measurements from Ref. [2] predominantly in the transient near-zone.

Measurements from Ref. [3] predominantly in the transient near-zone.

Value ofnsurf determined from FDTD simulations of Refs. [7, 6] in the far-zone.

G. Gay, O. Alloschery, J. Weiner, H. J. Lezec, C. O’Dwyer, M. Sukharev, and T. Seideman, "Surface quality and surface waves on subwavelength-structured silver films," Phys. Rev. E 75, 016612-1-4 (2007).
[CrossRef]

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

Permanent address: Physikalisches Institut, Universit¨at Bonn, Wegelerstrasse 8, 53115 Bonn, Germany.

G. Gay, O. Alloschery, B. Viaris de Lesegno, J. Weiner, and H. Lezec, "Surface wave generation and propagation on metallic subwavelength structures measured by Far-Field Interferometry," Phys. Rev. Lett. 96, 213901-1-4 (2006).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Diagram showing interfering wavefronts, optical path difference between Et and Eg , and far-field detection. Slit dimensions are 100 nm width, 20 μm length. Groove dimensions are 100 nm width, 100 nm nominal depth, 20 μm length. The evaporated gold layer deposited on a 1 mm fused silica substrate has a 400 nm nominal thickness.

Fig. 2.
Fig. 2.

Goniometer setup for measuring far-field light intensity and angular distributions. See text for description. Stabilized laser source is tuned to 852 nm.

Fig. 3.
Fig. 3.

Left panel: Points are the measured fringe phase φ(x sg) as a function of slit-groove distance x sg. The straight-line fit is φ0 = k surf x sg + φint with constant slope k surf and intercept φint. Gap in the data in left and right panels of this figure and in the left and right panels of Fig. 4 is due to defective structures in this interval. Right panel: Fringe amplitude η0 ≃ 1/2C as a function of x sg where C is the interference fringe contrast.

Fig. 4.
Fig. 4.

Left panel: Fringe phase difference φ(x sg)—φ0 as a function of slit groove distance x sg. Deviation in the near-zone from φ0 indicates that early, transient fringe oscillation is slightly greater and approaches φ0 asymptotically in the far-zone beyond ~ 2 μm slit-groove distance. Right panel: Same data as shown in left panel but on an expanded scale of slit-groove distances to emphasize the curvature in φ(x sg)—φ0 in the near-zone.

Fig. 5.
Fig. 5.

FDTD simulations for slit-groove center-to-center distance of 3.18 μm, slit and groove widths 100 nm, groove depth 100 nm and gold film thickness 400 nm. Map shows |Ez|, z-components (perpendicular to input and output facets) of the electric field amplitude in the vicinity of the input and output surfaces.

Fig. 6.
Fig. 6.

FDTD simulations for slit-groove center-to-center distance of 3.18 μm, slit and groove widths 100 nm, groove depth 100 nm and gold film thickness 400 nm. Map shows |Hy|, y-components (parallel to the slit and groove long axis) of the magnetic field amplitude in the vicinity of the input and output surfaces.

Fig. 7.
Fig. 7.

FDTD calculations of the transmission efficiency T = Sout z /Sin z as a function of x sg. Red curve traces T, and the blue curve traces a cos (2k fdtd surfx sg + φ fdtd int) fit to the oscillation in the asymptotic region. Note the decreasing transmission amplitude in the near-zone close to the slit edge and the higher oscillation frequency compared to the asymptotic harmonic wave. Best-fit values for λ fdtd surf = 2π/k fdtd surf = 839 nm and intrinsic phase φ fdtd int d = 0.55π rad.

Fig. 8.
Fig. 8.

Phase difference φ(x sg) —φ0 as a function of x sg, analogous to the right panel of Fig. 4 but derived from the FDTD simulation data. Residual “high frequency” oscillations in the phase difference, believed to be due to numeric artifacts in the FDTD results, have been smoothed.

Tables (1)

Tables Icon

Table 1. Summary of λsurf, n surf and n spp determined from far-field interferometric studies and FDTD simulations in gold and silver

Equations (7)

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I I 0 1 + η o 2 + 2 η o cos ( k x x sg + φ int )
C = 2 η o 1 + η o 2
n surf = λ 0 λ surf = 1.016 ± 0.004 and φ int = 0.35 π± 0.01 π
η 0 = 1 1 C 2 C 1 2 C , C 1
T = S z out S z in 2 [ 1 + cos 2 ( k surf fdtd x sg + φ int fdtd ) ] = 2 { 1 + cos 2 [ φ ( x sg ) ] }
n spp = ε m ε d ε m + ε d
ε ( ω ) = ε 0 ( ε ω p 2 ω 2 + i Γ ω )

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