Role of radiation and surface plasmon polaritons in the optical interactions between a nano-slit and a nano-groove on a metal surface

Long Chen; Jacob T. Robinson; Michal Lipson

doi:10.1364/OE.14.012629

Role of radiation and surface plasmon polaritons in the optical interactions between a nano-slit and a nano-groove on a metal surface

Long Chen, Jacob T. Robinson , and Michal Lipson

Optics Express
Vol. 14,
Issue 26,
pp. 12629-12636
(2006)
•https://doi.org/10.1364/OE.14.012629

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Long Chen, Jacob T. Robinson , and Michal Lipson, "Role of radiation and surface plasmon polaritons in the optical interactions between a nano-slit and a nano-groove on a metal surface," Opt. Express 14, 12629-12636 (2006)

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Related Topics
Table of Contents Category
- Diffraction and Gratings
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Apertures (050.1220)
- Diffraction (050.1940)
- Surface plasmons (240.6680)

About this Article
History
- Original Manuscript: September 20, 2006
- Revised Manuscript: December 8, 2006
- Manuscript Accepted: December 8, 2006
- Published: December 25, 2006

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Open Access

Abstract

Through full-vectorial simulations and analytical models, we investigate the role of radiation and surface plasmon polaritons (SPP) in the optical interaction between a nano-slit and a parallel nano-groove on a metal surface. We quantitatively confirm the radiaton as the interaction mechanism in perfect electrical conductors (PEC), and verify the role of radiation and SPP in the slit-groove interaction in silver. While the contribution of SPP dominates for the nano-slit and nano-groove placed far apart, the radiation plays a significant role for the nano-slit and nano-groove with smaller separations comparable to one wavelength. We present the first quantitative of the individual contributions of the radiation and SPP on the transmission through the nano-slit.

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References

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Publication

T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]
H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[Crossref] [PubMed]
W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]
H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[Crossref]
L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[Crossref] [PubMed]
W.L. Barnes, W.A. Murray, J. Dintlinger, E. Devaux, and T.W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film”, Phys. Rev. Lett. 92, 107401 (2004).
[Crossref] [PubMed]
D.E. Grupp, H.J. Lezec, K.M. Pellerin, T.W. Ebbesen, and T. Thio, “Fundamental role of metal surface in enhanced transmission through subwavelength apertures,” Appl. Phys. Lett. 77, 1569–1571 (2000).
[Crossref]
H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-Assisted Two-Slit Transmission: Young’s Experiment Revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[Crossref] [PubMed]
F. Przybilla, A. Degiron, J.-Y. Laluet, C. Genêt, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006).
[Crossref]
H. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12, 3629–3651 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-16-3629.
[Crossref] [PubMed]
G. Gay, O. Alloschery, B. Viaris Lesegno de, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Physics 2, 262 (2006).
[Crossref]
P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nature Physics 2, 551 (2006).
[Crossref]
E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985)
Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86, 5601 (2001)
[Crossref] [PubMed]
F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit,” Phys. Rev. Lett. 90, 213901 (2003).
[Crossref] [PubMed]
P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of Surface Plasmon Generation at Nanoslit Apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[Crossref]

2006 (3)

F. Przybilla, A. Degiron, J.-Y. Laluet, C. Genêt, and T. W. Ebbesen, “Optical transmission in perforated noble and transition metal films,” J. Opt. A: Pure Appl. Opt. 8, 458–463 (2006).
[Crossref]

G. Gay, O. Alloschery, B. Viaris Lesegno de, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nature Physics 2, 262 (2006).
[Crossref]

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nature Physics 2, 551 (2006).
[Crossref]

2005 (2)

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of Surface Plasmon Generation at Nanoslit Apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[Crossref]

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-Assisted Two-Slit Transmission: Young’s Experiment Revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[Crossref] [PubMed]

2004 (2)

W.L. Barnes, W.A. Murray, J. Dintlinger, E. Devaux, and T.W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film”, Phys. Rev. Lett. 92, 107401 (2004).
[Crossref] [PubMed]

H. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12, 3629–3651 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-16-3629.
[Crossref] [PubMed]

2003 (2)

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit,” Phys. Rev. Lett. 90, 213901 (2003).
[Crossref] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[Crossref] [PubMed]

2001 (2)

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001).
[Crossref] [PubMed]

Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86, 5601 (2001)
[Crossref] [PubMed]

2000 (1)

D.E. Grupp, H.J. Lezec, K.M. Pellerin, T.W. Ebbesen, and T. Thio, “Fundamental role of metal surface in enhanced transmission through subwavelength apertures,” Appl. Phys. Lett. 77, 1569–1571 (2000).
[Crossref]

1998 (2)

T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[Crossref]

Alkemade, P. F. A.

Alloschery, O.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Barnes, W.L.

Blok, H.

Degiron, A.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Devaux, E.

Dintlinger, J.

Dubois, G.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Ebbesen, T.W.

H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[Crossref]

Eliel, E. R.

Garcia-Vidal, F. J.

García-Vidal, F. J.

Gay, G.

Gbur, G.

Genêt, C.

Ghaemi, H.F.

H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[Crossref]

T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Grupp, D.E.

H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[Crossref]

Hooft, G. W. ’t

Hugonin, J. P.

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nature Physics 2, 551 (2006).
[Crossref]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of Surface Plasmon Generation at Nanoslit Apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[Crossref]

Kuzmin, N.

Lalanne, P.

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nature Physics 2, 551 (2006).
[Crossref]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of Surface Plasmon Generation at Nanoslit Apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[Crossref]

Laluet, J.-Y.

Lenstra, D.

Lesegno de, B. Viaris

Lezec, H.

Lezec, H. J.

Lezec, H.J.

H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[Crossref]

T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Linke, R. A.

Martin-Moreno, L.

Martín-Moreno, L.

Murray, W.A.

O’Dwyer, C.

Palik, E. D.

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

Pellerin, K. M.

Pellerin, K.M.

Pendry, J. B.

Przybilla, F.

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of Surface Plasmon Generation at Nanoslit Apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[Crossref]

Schouten, H. F.

Takakura, Y.

Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86, 5601 (2001)
[Crossref] [PubMed]

Thio, T.

T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[Crossref]

Visser, T. D.

Weiner, J.

Wolff, P.A.

T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Appl. Phys. Lett. (1)

J. Opt. A: Pure Appl. Opt. (1)

Nature (2)

T. W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Nature Physics (2)

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nature Physics 2, 551 (2006).
[Crossref]

Opt. Express (1)

Phys. Rev. B (1)

H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
[Crossref]

Phys. Rev. Lett. (6)

Y. Takakura, “Optical Resonance in a Narrow Slit in a Thick Metallic Screen,” Phys. Rev. Lett. 86, 5601 (2001)
[Crossref] [PubMed]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of Surface Plasmon Generation at Nanoslit Apertures,” Phys. Rev. Lett. 95, 263902 (2005).
[Crossref]

Science (1)

Other (1)

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

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Fig. 1.

(a) Schematic of the slit-groove configuration. (b) Schematic of an isolated groove scattering. (c) and (d) are snapshots of the scattered E_z field from a single groove in PEC and silver, respectively. Note the wave-front distortion in the box in (d) due to the wave-vector mismatch between the SPP and the radiation. (e) Decay length of SPP on silver-air interface. (f) Damping of SPP at λ=1.0 µm and the radiation (1/√x), assuming they have the same value at x=1 µm.

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Fig. 2.

(a) Simulated transmission modulation for slit-groove configuration in PEC as a function of wavelength and slit-groove separation. (b) Simulated and fitted transmission modulation for λ=1.0 µm (corresponding to the dotted line in (a)): symbol is the simulated data and solid curve is the fit using the radiation model in Eq. (2b). (c) Fitted amplitude A(λ) (solid line) and simulated scattering spectrum of an isolated groove (dashed line). Inset: the evolution of the simulated scattering spectra of an isolated groove with depth=100 nm but different widths.

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Fig. 3.

(a) Simulated transmission modulation for slit-groove configuration in silver as a function of wavelength and slit-groove separation. (b) Simulated and fitted transmission modulation for λ=1.0 µm (corresponding to the dotted line in (a)): symbol is the simulated data; dashed curve is the fit using the SPP model in Eq. (3b); solid curve is the fit using the full model in Eq. (4b) incorporating contributions from both SPP and the radiation. The difference marked by the arrow indicates that radiation plays a significant role in slit-groove interaction at small separations. (d) Fitted amplitudes A(λ) and B(λ). Inset: the ratio of SPP to the radiation B/A.

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Equations (8)

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k_{sp} = k_{0} \sqrt{\frac{ε_{m} ε_{0}}{(ε_{m} + ε_{0})}},

E ~ 1 + \frac{A}{\sqrt{d}} \exp (i k_{0} d + i ϕ),

T_{modulation} ~ {∣ E ∣}^{2} ~ 1 + \frac{A^{2}}{d} + \frac{2 A}{\sqrt{d}} \cos (k_{0} d + ϕ) .

E ~ 1 + B \exp (i k_{sp} d + i ϕ_{sp}),

T_{modulation} ~ {∣ E ∣}^{2} ~ 1 + B^{2} + 2 B \cos (k_{sp} d + ϕ_{sp}) .

E ~ 1 + \frac{A}{\sqrt{d}} \cdot \exp (i k_{0} d + i ϕ_{0}) + B \cdot \exp (i k_{sp} d + i ϕ_{sp}),

T_{modulation} ~ {∣ E ∣}^{2} ~ 1 + \frac{A^{2}}{d} + B^{2} + \frac{2 A}{\sqrt{d}} \cos (k_{0} d + ϕ_{0}) + 2 B \cos (k_{sp} d + ϕ_{sp})

+ \frac{2 AB}{\sqrt{d}} \cos [(k_{sp} - k_{0}) d + (ϕ_{sp} - ϕ_{0})] .

Abstract

References

2006 (3)

2005 (2)

2004 (2)

2003 (2)

2002 (1)

2001 (2)

2000 (1)

1998 (2)

Alkemade, P. F. A.

Alloschery, O.

Barnes, W. L.

Barnes, W.L.

Blok, H.

Degiron, A.

Dereux, A.

Devaux, E.

Dintlinger, J.

Dubois, G.

Ebbesen, T. W.

Ebbesen, T.W.

Eliel, E. R.

Garcia-Vidal, F. J.

García-Vidal, F. J.

Gay, G.

Gbur, G.

Genêt, C.

Ghaemi, H.F.

Grupp, D.E.

Hooft, G. W. ’t

Hugonin, J. P.

Kuzmin, N.

Lalanne, P.

Laluet, J.-Y.

Lenstra, D.

Lesegno de, B. Viaris

Lezec, H.

Lezec, H. J.

Lezec, H.J.

Linke, R. A.

Martin-Moreno, L.

Martín-Moreno, L.

Murray, W.A.

O’Dwyer, C.

Palik, E. D.

Pellerin, K. M.

Pellerin, K.M.

Pendry, J. B.

Przybilla, F.

Rodier, J. C.

Schouten, H. F.

Takakura, Y.

Thio, T.

Visser, T. D.

Weiner, J.

Wolff, P.A.

Appl. Phys. Lett. (1)

J. Opt. A: Pure Appl. Opt. (1)

Nature (2)

Nature Physics (2)

Opt. Express (1)

Phys. Rev. B (1)

Phys. Rev. Lett. (6)

Science (1)

Other (1)

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