Abstract

We have found that a relatively unknown and little understood type of standing-wave surface-plasmon resonance may be excited in strongly blazed overhanging zero-order metallic gratings. A modeling code based on an oblique coordinate transformation has been implemented to evaluate the optical response of these structures. For certain dimensions of surface topography, very strong resonant absorption of light is found that is insensitive to the angle of incidence yet is sharply wavelength selective. These resonances are not the well-known geometrical cavity resonances but have smaller periodicities determined by the self-coupling of surface-plasmon modes on the overhanging surfaces.

© 1998 Optical Society of America

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  1. J. P. Plumey, B. Guizal, J. Chandezon, “Coordinate transformation methods as applied to asymmetric gratings with vertical facets,” J. Opt. Soc. Am. A 14, 610–617 (1997).
    [CrossRef]
  2. T. W. Preist, J. B. Harris, N. P. Wanstall, J. R. Sambles, “Optical response of blazed and overhanging gratings using oblique Chandezon transformations,” J. Mod. Opt. 44, 1073–1080 (1997).
  3. J. Chandezon, M. T. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72, 839–846 (1982).
    [CrossRef]
  4. S. J. Elston, G. P. Bryan-Brown, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
    [CrossRef]
  5. L. Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited,” J. Opt. Soc. Am. A 11, 2816–2828 (1994).
    [CrossRef]
  6. N. P. K. Cotter, T. W. Preist, J. R. Sambles, “Scattering-matrix approach to multilayer diffraction,” J. Opt. Soc. Am. A 12, 1097–1103 (1995).
    [CrossRef]
  7. M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, J. R. Sambles, “Stationary surface plasmons on a zero order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
    [CrossRef]
  8. A. Wirgin, T. Lopez-Rios, “Can surface-enhanced Raman scattering be caused by waveguide resonances?” Opt. Commun. 48, 416–420 (1984).
    [CrossRef]
  9. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–552 (1969).
    [CrossRef]
  10. E. V. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, N. Garcia, “Nature of surface-enhanced-Raman-scattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314–2317 (1983).
    [CrossRef]
  11. J. L. Martinez, Y. Gao, T. Lopez-Rios, A. Wirgin, “Anisotropic surface-enhanced Raman scattering at obliquely evaporated Ag films,” Phys. Rev. B 35, 9481–9488 (1987).
    [CrossRef]
  12. F. J. Garcia-Vidal, J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166 (1996).
    [CrossRef] [PubMed]
  13. B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large-amplitude gratings,” Phys. Rev. B 23, 4965–4976 (1981).
    [CrossRef]
  14. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, London, 1988).
  15. A. Wirgin, “On the behaviour of the lamellar staircase grating,” Opt. Commun. 2, 349–351 (1970).
    [CrossRef]

1998 (1)

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, J. R. Sambles, “Stationary surface plasmons on a zero order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[CrossRef]

1997 (2)

J. P. Plumey, B. Guizal, J. Chandezon, “Coordinate transformation methods as applied to asymmetric gratings with vertical facets,” J. Opt. Soc. Am. A 14, 610–617 (1997).
[CrossRef]

T. W. Preist, J. B. Harris, N. P. Wanstall, J. R. Sambles, “Optical response of blazed and overhanging gratings using oblique Chandezon transformations,” J. Mod. Opt. 44, 1073–1080 (1997).

1996 (1)

F. J. Garcia-Vidal, J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

1991 (1)

S. J. Elston, G. P. Bryan-Brown, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

1987 (1)

J. L. Martinez, Y. Gao, T. Lopez-Rios, A. Wirgin, “Anisotropic surface-enhanced Raman scattering at obliquely evaporated Ag films,” Phys. Rev. B 35, 9481–9488 (1987).
[CrossRef]

1984 (1)

A. Wirgin, T. Lopez-Rios, “Can surface-enhanced Raman scattering be caused by waveguide resonances?” Opt. Commun. 48, 416–420 (1984).
[CrossRef]

1983 (1)

E. V. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, N. Garcia, “Nature of surface-enhanced-Raman-scattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314–2317 (1983).
[CrossRef]

1982 (1)

1981 (1)

B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large-amplitude gratings,” Phys. Rev. B 23, 4965–4976 (1981).
[CrossRef]

1970 (1)

A. Wirgin, “On the behaviour of the lamellar staircase grating,” Opt. Commun. 2, 349–351 (1970).
[CrossRef]

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–552 (1969).
[CrossRef]

Albano, E. V.

E. V. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, N. Garcia, “Nature of surface-enhanced-Raman-scattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314–2317 (1983).
[CrossRef]

Bryan-Brown, G. P.

S. J. Elston, G. P. Bryan-Brown, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

Chandezon, J.

Cornet, G.

Cotter, N. P. K.

Daiser, S.

E. V. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, N. Garcia, “Nature of surface-enhanced-Raman-scattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314–2317 (1983).
[CrossRef]

Dupuis, M. T.

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–552 (1969).
[CrossRef]

Elston, S. J.

S. J. Elston, G. P. Bryan-Brown, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

Ertl, G.

E. V. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, N. Garcia, “Nature of surface-enhanced-Raman-scattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314–2317 (1983).
[CrossRef]

Gao, Y.

J. L. Martinez, Y. Gao, T. Lopez-Rios, A. Wirgin, “Anisotropic surface-enhanced Raman scattering at obliquely evaporated Ag films,” Phys. Rev. B 35, 9481–9488 (1987).
[CrossRef]

Garcia, N.

E. V. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, N. Garcia, “Nature of surface-enhanced-Raman-scattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314–2317 (1983).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166 (1996).
[CrossRef] [PubMed]

Guizal, B.

Harris, J. B.

T. W. Preist, J. B. Harris, N. P. Wanstall, J. R. Sambles, “Optical response of blazed and overhanging gratings using oblique Chandezon transformations,” J. Mod. Opt. 44, 1073–1080 (1997).

Laks, B.

B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large-amplitude gratings,” Phys. Rev. B 23, 4965–4976 (1981).
[CrossRef]

Li, L.

Lopez-Rios, T.

J. L. Martinez, Y. Gao, T. Lopez-Rios, A. Wirgin, “Anisotropic surface-enhanced Raman scattering at obliquely evaporated Ag films,” Phys. Rev. B 35, 9481–9488 (1987).
[CrossRef]

A. Wirgin, T. Lopez-Rios, “Can surface-enhanced Raman scattering be caused by waveguide resonances?” Opt. Commun. 48, 416–420 (1984).
[CrossRef]

Maradudin, A. A.

B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large-amplitude gratings,” Phys. Rev. B 23, 4965–4976 (1981).
[CrossRef]

Martinez, J. L.

J. L. Martinez, Y. Gao, T. Lopez-Rios, A. Wirgin, “Anisotropic surface-enhanced Raman scattering at obliquely evaporated Ag films,” Phys. Rev. B 35, 9481–9488 (1987).
[CrossRef]

Maystre, D.

Mills, D. L.

B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large-amplitude gratings,” Phys. Rev. B 23, 4965–4976 (1981).
[CrossRef]

Miranda, R.

E. V. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, N. Garcia, “Nature of surface-enhanced-Raman-scattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314–2317 (1983).
[CrossRef]

Pendry, J. B.

F. J. Garcia-Vidal, J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166 (1996).
[CrossRef] [PubMed]

Plumey, J. P.

Preist, T. W.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, J. R. Sambles, “Stationary surface plasmons on a zero order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[CrossRef]

T. W. Preist, J. B. Harris, N. P. Wanstall, J. R. Sambles, “Optical response of blazed and overhanging gratings using oblique Chandezon transformations,” J. Mod. Opt. 44, 1073–1080 (1997).

N. P. K. Cotter, T. W. Preist, J. R. Sambles, “Scattering-matrix approach to multilayer diffraction,” J. Opt. Soc. Am. A 12, 1097–1103 (1995).
[CrossRef]

Raether, H.

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

Sambles, J. R.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, J. R. Sambles, “Stationary surface plasmons on a zero order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[CrossRef]

T. W. Preist, J. B. Harris, N. P. Wanstall, J. R. Sambles, “Optical response of blazed and overhanging gratings using oblique Chandezon transformations,” J. Mod. Opt. 44, 1073–1080 (1997).

N. P. K. Cotter, T. W. Preist, J. R. Sambles, “Scattering-matrix approach to multilayer diffraction,” J. Opt. Soc. Am. A 12, 1097–1103 (1995).
[CrossRef]

S. J. Elston, G. P. Bryan-Brown, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

Sobnack, M. B.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, J. R. Sambles, “Stationary surface plasmons on a zero order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[CrossRef]

Tan, W. C.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, J. R. Sambles, “Stationary surface plasmons on a zero order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[CrossRef]

Wandelt, K.

E. V. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, N. Garcia, “Nature of surface-enhanced-Raman-scattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314–2317 (1983).
[CrossRef]

Wanstall, N. P.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, J. R. Sambles, “Stationary surface plasmons on a zero order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[CrossRef]

T. W. Preist, J. B. Harris, N. P. Wanstall, J. R. Sambles, “Optical response of blazed and overhanging gratings using oblique Chandezon transformations,” J. Mod. Opt. 44, 1073–1080 (1997).

Wirgin, A.

J. L. Martinez, Y. Gao, T. Lopez-Rios, A. Wirgin, “Anisotropic surface-enhanced Raman scattering at obliquely evaporated Ag films,” Phys. Rev. B 35, 9481–9488 (1987).
[CrossRef]

A. Wirgin, T. Lopez-Rios, “Can surface-enhanced Raman scattering be caused by waveguide resonances?” Opt. Commun. 48, 416–420 (1984).
[CrossRef]

A. Wirgin, “On the behaviour of the lamellar staircase grating,” Opt. Commun. 2, 349–351 (1970).
[CrossRef]

J. Mod. Opt. (1)

T. W. Preist, J. B. Harris, N. P. Wanstall, J. R. Sambles, “Optical response of blazed and overhanging gratings using oblique Chandezon transformations,” J. Mod. Opt. 44, 1073–1080 (1997).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Commun. (2)

A. Wirgin, “On the behaviour of the lamellar staircase grating,” Opt. Commun. 2, 349–351 (1970).
[CrossRef]

A. Wirgin, T. Lopez-Rios, “Can surface-enhanced Raman scattering be caused by waveguide resonances?” Opt. Commun. 48, 416–420 (1984).
[CrossRef]

Phys. Rev. (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–552 (1969).
[CrossRef]

Phys. Rev. B (3)

J. L. Martinez, Y. Gao, T. Lopez-Rios, A. Wirgin, “Anisotropic surface-enhanced Raman scattering at obliquely evaporated Ag films,” Phys. Rev. B 35, 9481–9488 (1987).
[CrossRef]

S. J. Elston, G. P. Bryan-Brown, J. R. Sambles, “Polarization conversion from diffraction gratings,” Phys. Rev. B 44, 6393–6400 (1991).
[CrossRef]

B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large-amplitude gratings,” Phys. Rev. B 23, 4965–4976 (1981).
[CrossRef]

Phys. Rev. Lett. (3)

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, J. R. Sambles, “Stationary surface plasmons on a zero order metal grating,” Phys. Rev. Lett. 80, 5667–5670 (1998).
[CrossRef]

F. J. Garcia-Vidal, J. B. Pendry, “Collective theory for surface enhanced Raman scattering,” Phys. Rev. Lett. 77, 1163–1166 (1996).
[CrossRef] [PubMed]

E. V. Albano, S. Daiser, G. Ertl, R. Miranda, K. Wandelt, N. Garcia, “Nature of surface-enhanced-Raman-scattering active sites on coldly condensed Ag films,” Phys. Rev. Lett. 51, 2314–2317 (1983).
[CrossRef]

Other (1)

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

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Figures (10)

Fig. 1
Fig. 1

Definition of the oblique coordinate system, with angle of obliquity α.

Fig. 2
Fig. 2

Three grating surfaces generated by a sine function in the oblique coordinate system, with angle of obliquity (a) α=90°, (b) α=30°, and (c) α=10°.

Fig. 3
Fig. 3

Reflection coefficient Rpp at normal incidence (θ=0) as a function of angle of obliquity α for metal gratings with surfaces generated by a sine function in the oblique coordinate system showing the set of reflectivity minima at low α. All gratings have a pitch of 300 nm, a selvedge region thickness of 60 nm, and a permittivity of -17.5+0.6i. Radiation of wavelength 632.8 nm is incident normal to the gratings’ surface; thus the gratings are zero order.

Fig. 4
Fig. 4

Reflection coefficient Rpp (in the classical mount) as a function of both angle of obliquity α and angle of incidence θ for metal gratings; parameters are the same as for Fig. 3.

Fig. 5
Fig. 5

Contour maps of the enhancement at normal incidence in the magnitude of the magnetic field within the grooves for the first three resonant modes shown in Fig. 3. (a) Angle of obliquity α=18.77°; map scaled to its maximum magnetic field enhancement of 12.6; (b) α=10.96°; map scaled to its maximum magnetic field enhancement of 16.5; (c) α=8.31°; map scaled to its maximum magnetic field enhancement of 11.6.

Fig. 6
Fig. 6

Surface-charge density (in arbitrary units) for the first six resonant modes of Fig. 3 showing the increasing number of charge oscillations within a grating period (0V300 nm). Angles of obliquity α are (a) 18.77°, (b) 10.96°, (c) 8.31°, (d) 7.01°, (e) 6.22°, and (f) 5.66°, and radiation is incident at θ=0. Each distribution has a node near the cavity bottom (V225 nm) and an (off-scale) maximum near the tip (V75 nm).

Fig. 7
Fig. 7

Two periods of the grating surface shape that gives rise to the first six resonant modes of Fig. 3. The circles denote the position of nodes of the standing-wave surface-charge oscillation. Locally the surface sections AB are approximately triple-interface systems.

Fig. 8
Fig. 8

Curve showing the high parallel-wave-vector solution of the triple-interface system (shown in inset) as a function of layer thickness d contrasted with the wave vector of a single flat interface SPP (independent of d). As d, the wavevector of the triple-interface system approaches that of the single interface.

Fig. 9
Fig. 9

Contour maps of the enhancement in magnitude of the electric field in the xy plane for the first three resonant modes of Fig. 3. (a) Angle of obliquity α=18.77°; map scaled to its maximum electric field enhancement of 25.9 (at the cavity tip). (b) α=10.96°; map scaled to its local maximum electric field enhancement of 21.0 (at the cavity bottom); (c) α=8.31°; map scaled to its local maximum electric field enhancement of 21.9 (at the cavity bottom).

Fig. 10
Fig. 10

Dispersion curve of the surface-plasmon resonance as a contour map of the reflection coefficient Rpp, as a function of both the angular frequency ω of the incident radiation and ckx (where kx is the component of the wave vector of the incident radiation in the x direction) for a metal grating, as for Fig. 3, with angle of obliquity α=8.31°. The permittivity is given by the Drude model with plasma frequency and relaxation time ωp=1.32×1016 rad s-1 and τ=1.45×10-14 s, respectively.

Tables (1)

Tables Icon

Table 1 Semianalytical Calculationa of the Number of Standing-Wave SPP Wavelengths Mn between Two Nodes (A and B in Fig. 7) in Good Agreement with the Modeling Code

Equations (14)

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y=R sin α,x=V+R cos α.
dydx=f(V)sin α1+f(V)cos α,
v=k0V=k0(x-R cos α)=k0(x-y cot a),
u=k0[R-f(V)]=k0[y cosec-αf(x-y cot α)],
w=k0z,
Fu=Dˆ Fv+i sin α CˆG,
Gu=vDˆG+i sin αCˆ Fv+i(μ-γ2)sin α F,
F=HzandG=(μ-γ2/)E
F=EzandG=-(-γ2/μ)H,
Cˆ=(1+f2+2 f cos α)-1
Dˆ=(f+cos α)Cˆ.
f(V)=h2cosec α sin2πVλg.
Mn=12πBAkspp(l)dl
F(kspp)=(Δ+1)tT(Δ2-Δ+1)+Δ(T+t+1)=0,

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