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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 24 — Nov. 27, 2006
  • pp: 11506–11511
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Light transmission through a high index dielectric hole in a metal film surrounded by surface corrugations

Juuso Olkkonen, Kari Kataja, and Dennis G. Howe  »View Author Affiliations


Optics Express, Vol. 14, Issue 24, pp. 11506-11511 (2006)
http://dx.doi.org/10.1364/OE.14.011506


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Abstract

We analyze transmission of a normally incident plane wave through a 100nm diameter hole in a silver film that is filled with a high index dielectric and is surrounded by 300nm wide surface grooves. Specifically, we study the dependency of the transmission efficiency on the number of grooves, groove depth, and the horizontal distance between the groove and the central hole. We observe that the investigated structure exhibits over five orders of magnitude larger transmission efficiency versus a single hole without the dielectric filling.

© 2006 Optical Society of America

1. Introduction

The exploitation of sub-wavelength apertures in opaque films for light confinement into the subwavelength domain has been limited due to the negligible transmission efficiency of very small apertures. It has been recently noted [1–5

1. D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen, “Beyond the Bethe Limit: Tunable Enhanced Light Transmission Through a Single Sub-Wavelength Aperture,” Adv. Mater. 11, 860–862 (1999). [CrossRef]

], however, that cylindrical surface corrugations around a single, central, sub-wavelength-sized hole in a metal film can greatly enhance the otherwise weak transmission through the hole. This enhanced transmission is widely attributed to the influence of surface plasmon polaritons (SPPs) excited by the surface corrugations [1

1. D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen, “Beyond the Bethe Limit: Tunable Enhanced Light Transmission Through a Single Sub-Wavelength Aperture,” Adv. Mater. 11, 860–862 (1999). [CrossRef]

,2

2. 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]

,3

3. T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata A, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: Physics and applications,” Nanotechnology 13, 429–432 (2002). [CrossRef]

,4

4. A. Degiron A and T. W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694–3700 (2004). [CrossRef] [PubMed]

,6

6. 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]

]. This effect can be explained also in terms of the diffracted evanescent wave model, proposed by Lezec et al. [5

5. 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]

], in which the surface waves excited by the surface corrugations interfere with the incident plane wave that directly impinges on the aperture. According to this latter model, the phase difference between the incident plane wave and the surface waves determines the transmission maxima and minima.

This paper is organized as follows. First, we analytically study the propagation constant (β) of guided modes that are supported by an infinitely long cylindrical, dielectric-filled hole in a silver medium. Then we study transmission properties of a sub-wavelength aperture, 50nm in radius, in a thick metal film versus the thickness of the metal film and the refractive index of the aperture. Finally, the influence of surface grooves on transmission efficiency is investigated in detail.

2. Light transmission through a single cylindrical aperture in a planar silver film

Throughout this paper, we consider a cylindrical sub-wavelength aperture, 50nm in radius, in a silver film (nAg=0.055+4.44i [9

9. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

]) that is illuminated by a normally incident, linearly polarized plane wave having free space wavelength (λ 0) of 650nm. First, we shall consider a cylindrical aperture that has infinite length along its axis (propagation direction of the incident wave). Such an aperture, which can be considered as a cylindrical waveguide having a silver cladding, can be characterized by examining the complex propagation constant (β=β re+β re i) of the hybrid HE11 waveguide mode [9

9. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

]. Figure 1 shows β of the HE11 mode for the aforementioned cylindrical waveguide as a function of the refractive index of the waveguide core (nc). Interestingly, the imaginary part of β starts to strongly decrease, while the real part exhibits a simultaneous increase, when nc>2.2. The imaginary part attains its minimum when nc=2.77, after which it starts to slowly increase. These results are obtained via standard waveguide theories with no weak guiding assumption [10

10. K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, San Diego, 2000).

,11

11. J. Takahara and T. Kobayashi, “Nano-optical waveguides breaking through diffraction limit of light,” in Optomechatronic Micro/Nano Components, Devices, and Systems, Y. Katagiri, eds., Proc. SPIE5604, 158–172 (2004). [CrossRef]

].

Figure 2 shows the transmission efficiency (η) of a normally incident plane wave through a 50nm radius cylindrical hole in a free standing silver film as a function of the Ag-film thickness (t) for three different refractive indexes (nc) of the hole: nc=1.0 (solid line), nc=2.4 (dashed line), nc=2.8 (dashed-dotted line). We consider only completely opaque silver films, i.e., t≥100nm. The transmission efficiency is computed throughout this paper as a ratio of the total power emanating from the geometrical exit (lower film surface) aperture of the hole and the incident power falling into the geometrical entrance (upper film surface) aperture of the hole. The results are obtained via the BOR-FDTD method [12

12. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Second Edition, Artech House, Boston, 2000).

], in which the Yee cell size is chosen to be 2.5nm both in the radial and in the longitudinal z direction. The computation domain is terminated by uniaxial perfectly matched layers (UPML) [12

12. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Second Edition, Artech House, Boston, 2000).

], which provide highly absorbing boundary conditions. We observe that by filling the hole by a high index medium, η can be enhanced over a factor of 500. It is also seen that η exhibits a clear Fabry-Pérot kind of behavior; transmission maxima and minima appear periodically with thickness period of π/βre. A similar behavior has been observed also for single slits in metal films [13

13. Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601–5603 (2001). [CrossRef] [PubMed]

,14

14. 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]

].

Fig. 1. Complex propagation constant (β=β re+β im i) of the HE11 mode as a function of the refractive index of the waveguide core (nc) for an infinitely long cylindrical waveguide having a silver cladding and a core radius of 50nm. k 0=2π/λ 0, λ 0=650nm, and nAg=0.055+4.44i.
Fig. 2. Transmission efficiency (η) of a normally incident linearly polarized plane wave through a sub-wavelength (r=50nm), cylindrical dielectric hole in a silver film as a function of the film thickness (t) for different refractive indexes of the hole: nc=1.0 (red line), nc=2.4 (blue), nc=2.8 (green). The refractive indexes of the incident and the exit medium are denoted by n0 and n1, respectively. n0=n1=1.0, nAg=0.055+4.44i, λ 0=650nm. The solid line is magnified by a factor of 500.
Fig. 3. (a) Cross-section of the modeled structure: A sub-wavelength hole (r=50nm) in a silver film (t=515nm) that is filled by a high index dielectric medium (nc=2.8) is surrounded by a single groove having depth h and width w. (b) Transmission efficiency (η) of a normally incident, linearly polarized plane wave through the sub-wavelength hole shown in (a) as a function of the groove depth (h) and the distance (s 1) between the central hole and the groove. In all cases, w=300nm, λ 0=650nm, and nAg=0.055+4.44i.

3. Light transmission through a single aperture in a corrugated silver film

We are now in a position to explore transmission properties of a single, high index, subwavelength (nc=2.8, r=50nm) hole in a thick silver film surrounded by concentric circular grooves. First, we study the influence of a single circular surface groove on transmission efficiency as a function of the groove depth (h) and distance from the central hole (s 1), see Fig. 3(a). To investigate relatively deep grooves with no light leakage through them, we consider a 515nm thick silver film. This thickness also provides resonant transmission trough the aperture according the results of Fig. 2. The groove width (w) is a fixed parameter, having value of 300nm, which is a common value used in recent experiments [4

4. A. Degiron A and T. W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694–3700 (2004). [CrossRef] [PubMed]

, 5

5. 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]

]. Figure 3(b) shows the transmission efficiency (η) for a central hole that is surrounded by a single circular groove as a function of s 1 and h. Figure 3(b) is obtained by linearly interpolating the results of simulations in which s 1 is varied from 50 to 1000nm in 50nm steps and h is varied from 20 to 400nm in 20nm steps. Clearly, transmission efficiency depends periodically both on s 1 and h. The periodic dependency on s 1 is due to the phase difference (at the entrance of the central hole) between the incident plane wave and the surface wave excited by the concentric circular groove. This result is in accordance with the predictions of the diffracted evanescent wave model [5

5. 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]

]. The periodic dependency on h is due to interference occurring within the groove. The maximum transmission efficiency also increases as a function of s 1. This is due to fact that the length of the groove’s circular contour, which excites surface waves, increases linearly with s 1. However, when the groove is far enough from the central hole, the transmission efficiency starts to decrease due to attenuation of the surface waves.

Fig. 4. Transmission efficiency (η) of a normally incident, linearly polarized plane wave through a sub-wavelength hole (r=50nm, nc=2.8) in a free standing silver film (t=180nm) when the central hole is surrounded by (a) a single groove, (b) two grooves (s 1=300nm), and (c) three grooves (s 1=s 2=300nm). (d) Transmission efficiency as a function of the number of grooves when the radial distance (sn) between the adjacent grooves is 300nm. In all cases, w=300nm, h=120nm, λ 0=650nm, and nAg=0.055+4.44i.

Figures 4(a)–(c) show results for the cases where the central hole is surrounded first by a single groove and then by two and three grooves. The metal film is now 180nm thick and groove is 120nm deep and 300nm wide. When s 1=550nm in Fig. 4(a), light transmission through the central hole is almost zero. This is due to the fact that approximately equal power, with opposite phases, couples from the incident plane wave and the surface wave into the central hole, resulting in nearly zero transmission. In Figure 4(b), the distance between the first groove and the central hole (s 1) is set to 300nm, which is the location of the first maximum in Fig. 4(a). It is seen that the transmission efficiency exhibits increased maxima and that the locations of the maxima and minima depend on the distance between the first and the second groove (s 2). This occurs due to the same physical phenomena observed in the single groove case. The first maximum appears in Fig. 4(b) at s 2=300nm, which is used as a distance between the first and the second groove in Fig. 4(c). Figure 4(d) shows how the transmission efficiency depends on the number of grooves (n) when the radial distance between the adjacent grooves is 300nm. The transmission efficiency increases until n=13 when η is about five orders of magnitude higher than η of a single aperture without the dielectric filling.

4. Summary and conclusion

This paper investigated for the first time transmission of a normally incident, linearly polarized plane wave through a high index dielectric-filled hole surrounded by surface corrugations. The dependency of transmission efficiency on a single 300nm wide groove was studied versus the groove depth and its distance from the central hole. It was observed that the phase difference between the incident plane wave and the surface waves determines the occurrence of transmission maxima and minima. A similar behavior was also observed with several grooves. When the central hole is surrounded by 13 grooves, the transmission efficiency is increased by five orders of magnitude compared to a single aperture without the dielectric filling.

References and links

1.

D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen, “Beyond the Bethe Limit: Tunable Enhanced Light Transmission Through a Single Sub-Wavelength Aperture,” Adv. Mater. 11, 860–862 (1999). [CrossRef]

2.

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]

3.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata A, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: Physics and applications,” Nanotechnology 13, 429–432 (2002). [CrossRef]

4.

A. Degiron A and T. W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694–3700 (2004). [CrossRef] [PubMed]

5.

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]

6.

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]

7.

A. R. Zakharian, M. Mansuripur, and J. V. Moloney, “Transmission of light through small elliptical apertures,” Opt. Express 12, 2631–2648 (2004). [CrossRef] [PubMed]

8.

J. Olkkonen, K. Kataja, and D. Howe, “Light transmission through a high index dielectric-filled sub-wavelength hole in a metal film,” Opt. Express 13, 6980–6989 (2005). [CrossRef] [PubMed]

9.

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

10.

K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, San Diego, 2000).

11.

J. Takahara and T. Kobayashi, “Nano-optical waveguides breaking through diffraction limit of light,” in Optomechatronic Micro/Nano Components, Devices, and Systems, Y. Katagiri, eds., Proc. SPIE5604, 158–172 (2004). [CrossRef]

12.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Second Edition, Artech House, Boston, 2000).

13.

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 86, 5601–5603 (2001). [CrossRef] [PubMed]

14.

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]

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction

ToC Category:
Diffraction and Gratings

History
Original Manuscript: September 28, 2006
Revised Manuscript: November 1, 2006
Manuscript Accepted: November 1, 2006
Published: November 27, 2006

Citation
Juuso Olkkonen, Kari Kataja, and Dennis G. Howe, "Light transmission through a high index dielectric hole in a metal film surrounded by surface corrugations," Opt. Express 14, 11506-11511 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-24-11506


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References

  1. D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen, "Beyond the Bethe Limit: Tunable Enhanced Light Transmission Through a Single Sub-Wavelength Aperture," Adv. Mater. 11, 860-862 (1999). [CrossRef]
  2. 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, 1972-4 (2001). [CrossRef]
  3. T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata A, and R. A. Linke, "Giant optical transmission of sub-wavelength apertures: Physics and applications," Nanotechnology 13, 429-432 (2002). [CrossRef]
  4. A. Degiron A and T. W. Ebbesen, "Analysis of the transmission process through single apertures surrounded by periodic corrugations," Opt. Express 12, 3694-3700 (2004). [CrossRef] [PubMed]
  5. 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]
  6. 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, 6779-82 (1998). [CrossRef]
  7. A. R. Zakharian, M. Mansuripur, J. V. Moloney, "Transmission of light through small elliptical apertures," Opt. Express 12, 2631-2648 (2004). [CrossRef] [PubMed]
  8. J. Olkkonen, K. Kataja, and D. Howe, "Light transmission through a high index dielectric-filled sub-wavelength hole in a metal film," Opt. Express 13, 6980-6989 (2005). [CrossRef] [PubMed]
  9. P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972). [CrossRef]
  10. K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, San Diego, 2000).
  11. J. Takahara, and T. Kobayashi, "Nano-optical waveguides breaking through diffraction limit of light," in Optomechatronic Micro/Nano Components, Devices, and Systems, Y. Katagiri, eds., Proc. SPIE 5604, 158-172 (2004). [CrossRef]
  12. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Second Edition, Artech House, Boston, 2000).
  13. Y. Takakura, "Optical resonance in a narrow slit in a thick metallic screen," Phys. Rev. Lett. 86, 5601-5603 (2001). [CrossRef] [PubMed]
  14. 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]

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