Abstract

We present a systematic study of light transmission through individual nanoscale apertures (rectangular slits and circular holes) etched in a 300-nm-thick silver film. Transmission spectra were obtained as functions of aperture shape and size, as well as the wavelength and polarization state of the normally incident light beam. By varying the wavelength of the incident light in the 550–750 nm range and the characteristic dimensions of the apertures from 100nm to 10 μm, a universal behavior of light transmission is revealed. The role of incident polarization and aperture dimensions is investigated in detail, and a clear transition from the geometric regime of light transmission (large apertures) to the subwavelength regime is demonstrated experimentally. A quantitative analysis of the extinction coefficient is reported for rectangular slits, demonstrating that they can act as efficient linear polarizers with extinction ratios >1001. Finally, a method to convert far-field to near-field data is developed for circular apertures, revealing the contribution of surface plasmon polaritons to the decrease in light transmission for apertures below the cutoff condition.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  48. D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, “Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: role of surface wave interference and local coupling between adjacent slits,” Phys. Rev. B 77, 115411 (2008).
    [CrossRef]

2012

F. van Beijnum, C. Retif, C. B. Smiet, H. Liu, P. Lalanne, and M. P. van Exter, “Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission,” Nature 492, 411–414 (2012).
[CrossRef]

T. Søndergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission with tapered slits: effect of higher diffraction and slit resonance orders,” J. Opt. Soc. Am. B 29, 130–137 (2012).
[CrossRef]

J.-M. Yi, A. Cuche, F. de León-Pérez, A. Degiron, E. Laux, E. Devaux, C. Genet, J. Alegret, L. Martín-Moreno, and T. W. Ebbesen, “Diffraction regimes of single holes,” Phys. Rev. Lett. 109, 023901 (2012).
[CrossRef]

2010

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

2009

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009).
[CrossRef]

J. W. Lee, T. H. Park, P. Nordlander, and D. M. Mittleman, “Terahertz transmission properties of an individual slit in a thin metallic plate,” Opt. Express 17, 12660–12667 (2009).
[CrossRef]

2008

2007

F. J. García de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267 (2007).
[CrossRef]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[CrossRef]

2006

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

H. Gao, J. Henzie, and T. W. Odom, “Direct evidence for surface plasmon-mediated enhanced light transmission through metallic nanohole arrays,” Nano Lett. 6, 2104–2108 (2006).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411 (2006).
[CrossRef]

2005

R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13, 1933–1938 (2005).
[CrossRef]

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef]

S.-H. Chang, S. Gray, and G. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,” Opt. Express 13, 3150–3165 (2005).
[CrossRef]

A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. 7, S90–S96 (2005).

K. L. van der Molen, K. J. Klein-Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory,” Phys. Rev. B 72, 045421 (2005).
[CrossRef]

2004

K. J. Klein-Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef]

A. Degiron, H. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

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

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92, 037401 (2004).
[CrossRef]

2003

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

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]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef]

2002

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]

F. J. Garcia de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10, 1475–1484 (2002).
[CrossRef]

2001

R. Wannemacher, “Plasmon-supported transmission of light through nanometric holes in metallic thin films,” Opt. Commun. 195, 107–118 (2001).
[CrossRef]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001).
[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]

2000

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100 (2000).
[CrossRef]

C. Soennichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000).
[CrossRef]

1998

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

1994

1987

A. Roberts, “Electromagnetic theory of diffraction by a circular aperture in a thick, perfectly conducting screen,” J. Opt. Soc. Am. 4, 1970–1983 (1987).
[CrossRef]

1984

A. Lewis, M. Isaacson, A. Harootunian, and A. Murray, “Development of a 500  Å spatial resolution light microscope: I. Light is efficiently transmitted through λ/16 diameter apertures,” Ultramicroscopy 13, 227–231 (1984).
[CrossRef]

1972

E. A. Ash and G. Nicholls, “Super-resolution aperture scanning microscope,” Nature 237, 510–512 (1972).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1954

C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[CrossRef]

1950

C. J. Bouwkamp, “On the diffraction of electromagnetic waves by small circular disks and holes,” Philips Res. Rep. 5, 401–422 (1950).

1944

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

1897

J. W. Strutt (Lord Rayleigh), “On the passage of electric waves through tubes,” J. Phil. Mag. 43(261), 125–132 (1897).

Ahn, Y. H.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef]

Alegret, J.

J.-M. Yi, A. Cuche, F. de León-Pérez, A. Degiron, E. Laux, E. Devaux, C. Genet, J. Alegret, L. Martín-Moreno, and T. W. Ebbesen, “Diffraction regimes of single holes,” Phys. Rev. Lett. 109, 023901 (2012).
[CrossRef]

Ash, E. A.

E. A. Ash and G. Nicholls, “Super-resolution aperture scanning microscope,” Nature 237, 510–512 (1972).
[CrossRef]

Atwater, H. A.

D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express 16, 9222–9238 (2008).
[CrossRef]

D. Pacifici, H. J. Lezec, H. A. Atwater, and J. Weiner, “Quantitative determination of optical transmission through subwavelength slit arrays in Ag films: role of surface wave interference and local coupling between adjacent slits,” Phys. Rev. B 77, 115411 (2008).
[CrossRef]

Barnard, E.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009).
[CrossRef]

Barnes, W. L.

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

Beermann, J.

Bethe, H. A.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
[CrossRef]

Bouwkamp, C. J.

C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[CrossRef]

C. J. Bouwkamp, “On the diffraction of electromagnetic waves by small circular disks and holes,” Philips Res. Rep. 5, 401–422 (1950).

Bozhevolnyi, S. I.

Bravo-Abad, J.

Brolo, A. G.

R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13, 1933–1938 (2005).
[CrossRef]

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92, 037401 (2004).
[CrossRef]

Brongersma, M. L.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009).
[CrossRef]

Chang, S.-H.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Cuche, A.

J.-M. Yi, A. Cuche, F. de León-Pérez, A. Degiron, E. Laux, E. Devaux, C. Genet, J. Alegret, L. Martín-Moreno, and T. W. Ebbesen, “Diffraction regimes of single holes,” Phys. Rev. Lett. 109, 023901 (2012).
[CrossRef]

de Leon-Perez, F.

de León-Pérez, F.

J.-M. Yi, A. Cuche, F. de León-Pérez, A. Degiron, E. Laux, E. Devaux, C. Genet, J. Alegret, L. Martín-Moreno, and T. W. Ebbesen, “Diffraction regimes of single holes,” Phys. Rev. Lett. 109, 023901 (2012).
[CrossRef]

Degiron, A.

J.-M. Yi, A. Cuche, F. de León-Pérez, A. Degiron, E. Laux, E. Devaux, C. Genet, J. Alegret, L. Martín-Moreno, and T. W. Ebbesen, “Diffraction regimes of single holes,” Phys. Rev. Lett. 109, 023901 (2012).
[CrossRef]

F. Przybilla, A. Degiron, C. Genet, T. W. Ebbesen, F. de Leon-Perez, J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Efficiency and finite size effects in enhanced transmission through subwavelength apertures,” Opt. Express 16, 9571–9579 (2008).
[CrossRef]

A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. 7, S90–S96 (2005).

A. Degiron, H. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401 (2003).
[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]

Devaux, E.

T. Søndergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, “Extraordinary optical transmission with tapered slits: effect of higher diffraction and slit resonance orders,” J. Opt. Soc. Am. B 29, 130–137 (2012).
[CrossRef]

J.-M. Yi, A. Cuche, F. de León-Pérez, A. Degiron, E. Laux, E. Devaux, C. Genet, J. Alegret, L. Martín-Moreno, and T. W. Ebbesen, “Diffraction regimes of single holes,” Phys. Rev. Lett. 109, 023901 (2012).
[CrossRef]

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

Dintinger, J.

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

Duch, A. C.

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Figures (6)

Fig. 1.
Fig. 1.

Sample SEM images of the nanoapertures studied in this paper. The apertures are sorted into three groups, each corresponding to a different column in the figure. The first group contains rectangular apertures of fixed length (l=10μm) and variable width (w=50, 500, and 1750 nm shown here). The second group contains rectangular apertures of fixed width (w=100nm) and variable length (l=50, 500, and 1750 nm shown here). The third group contains circular apertures of variable diameter (2a=50, 500, and 1750 nm shown here).

Fig. 2.
Fig. 2.

(a) Schematic of the inverted optical microscope configuration used to collect transmittance data from the nanoscale apertures. The optical path and main optical components are shown. (b) Diagram of the system under study, along with the notation convention used in this paper. For rectangular apertures, the length is given by l (dimension of the long side) and the width is given by w (dimension of the short side). When the aperture is a circle, the characteristic size is given by the diameter (2a). The angle of polarization (ϕP) is defined as the angle between the long axis of the slit and the incident electric field vector. When considering oblique incidence along the xz plane, ϕP=0° (90°) corresponds to TM (TE) illumination conditions. The collection geometry is also shown.

Fig. 3.
Fig. 3.

Using orthogonal polarization states to recreate transmittance spectra at intermediate ϕP values (0°<ϕP<90°). (a) Experimental transmission spectra for a rectangular slit (length l=10μm, width w=150nm), normalized against the spectrum of a wider slit (w=2μm). Each curve corresponds to a different angle of polarization, from 0° to 90° in steps of 1°. (b) Using Eq. (2) and the two experimentally found basis curves (ϕP=0° and 90°), the transmission spectrum can be recreated for any intermediate angle.

Fig. 4.
Fig. 4.

Relationship between the normalized transmittance-to-area ratio (τ) and the width-to-wavelength ratio for aperture group 1 (rectangular slit, constant length l=10μm) when (a) ϕP=90° (TE) or (b) ϕP=0° (TM). In the insets, the vertical axis is the same as the main panels, but now the horizontal axis is wavelength. The dashed black curve in panel (a) is the predicted collection efficiency of the microscope, assuming Fraunhofer diffraction behavior. (c) Experimental extinction ratio, demonstrating the strong polarization dependence in the subwavelength regime. In all three panels, each individual curve corresponds to a specific value of w (ranging from 100 to 2000 nm in steps of 50 nm); each curve is obtained by taking the transmittance spectrum for 550nm<λ<750nm, with a spectral resolution of 0.3 nm.

Fig. 5.
Fig. 5.

Relationship between the normalized transmittance-to-area ratio (τ) and the width-to-wavelength ratio for aperture group 2 (rectangular slit, constant width l=100nm) when (a) ϕP=90° (TE) or (b) ϕP=0° (TM). (c) Experimental extinction ratio. In all three panels each individual curve corresponds to a specific value of l (ranging from 150 to 2000 nm, in steps of 50 nm); each curve is obtained by taking the transmittance spectrum for 550nm<λ<750nm, with a spectral resolution of 0.3 nm.

Fig. 6.
Fig. 6.

(a) Relationship between the normalized transmittance-to-area ratio (τ) and the diameter-to-wavelength ratio for the circular apertures (color), along with a theoretical curve based on the work of Yi et al. (solid black) [43]. The transmission spectra for both orthogonal polarization states were recorded; the individual curves represent the average value. In the inset, the vertical axis is the same as the main panel, but now the horizontal axis is wavelength. (b) Using the Yi et al. model to correct the experimental data. The experimental (color) curves in this panel were obtained by dividing the color curves from panel (a) by the model curve. Gray: simulated normalized τ curves obtained using 3D FDTD simulations. In both panels, each individual curve corresponds to a specific value of 2a (ranging from 250 to 1950 nm in steps of 50 nm); each curve is obtained by taking the transmittance spectrum for 550nm<λ<750nm, with a spectral resolution of 0.3 nm.

Equations (9)

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

τ2a(λ,ϕP)=T2a(λ,ϕP)/A2a,
τw,l(λ,ϕP)=Tw,l(λ,ϕP)/Aw,l,
Tw,l(λ,ϕp)=Tw,l(λ,0°)cos2ϕp+Tw,l(λ,90°)sin2ϕp.
τ2a(λ)τ2a=1.95μm(λ)=lensσ2a(θ,ϕ,λ)dΩlensσ2a=1.95μm(θ,ϕ,λ)dΩ=0θcσ2a(θ,λ)(sinθ)dθ0θcσ2a=1.95μm(θ,λ)(sinθ)dθ,
η(w,λ,θc)=(0θc|U(w,λ,θ)|2dθ)/(0π/2|U(w,λ,θ)|2dθ),
UR(w,λ,θ)=sin[uR(w,λ,θ)]uR(w,λ,θ),
UC(a,λ,θ)=2πJ1[uC(a,λ,θ)]uC(a,λ,θ),
Ip(θ)=|1+zs|2cos2(θ)|cos(θ)+zs|24J12(Φ)Φ2,
Is(θ)=|1+zs|2cos2(θ)|1+zscos(θ)|24J12(Φ)(1Φ2/u2)2,

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