Abstract

We demonstrate that optical transmission of a normally incident, monochromatic plane wave through a single sub-wavelength aperture in an opaque metal film can be substantially enhanced by a thin, semitransparent metal film placed parallel to the opaque metal film in front of the aperture. When the semi-transparent and the opaque metal film are separated by a proper distance, a light trapping cavity is formed and the sub-wavelength aperture exhibits a transmission maximum. An enhancement factor of ~40 is demonstrated for a cylindrical 100 nm diameter hole in a silver film.

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  1. 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(6668), 667–669 (1998).
    [CrossRef]
  2. 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(10), 860–862 (1999).
    [CrossRef]
  3. 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(24), 1972–1974 (2001).
    [CrossRef] [PubMed]
  4. T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: Physics and applications,” Nanotechnology 13(3), 429–432 (2002).
    [CrossRef]
  5. 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(21), 213901–1 (2003).
    [CrossRef] [PubMed]
  6. D. A. Thomas and H. P. Hughes, “Enhanced optical transmission through a subwavelength 1D aperture,” Solid State Commun. 129(8), 519–524 (2004).
    [CrossRef]
  7. 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 Condens. Matter 58(11), 6779–6782 (1998).
    [CrossRef]
  8. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3629 .
    [CrossRef] [PubMed]
  9. F. Wu, D. Han, X. Li, X. Liu, and J. Zi, “Enhanced transmission mediated by guided resonances in metallic gratings coated with dielectric layers,” Opt. Express 16(9), 6619–6624 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6619 .
    [CrossRef] [PubMed]
  10. J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2000).
  11. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
    [CrossRef]
  12. A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Second Edition, Artech House, INC., 2000).
  13. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
    [CrossRef]
  14. M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microw. Guid. Wave Lett. 7(5), 121–123 (1997).
    [CrossRef]
  15. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev., B, Solid State 6(12), 4370–4379 (1972).
    [CrossRef]
  16. 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(18), 6980–6989 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-18-6980 .
    [CrossRef] [PubMed]

2008 (1)

2005 (1)

2004 (2)

2003 (1)

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(21), 213901–1 (2003).
[CrossRef] [PubMed]

2002 (1)

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

2001 (1)

1999 (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(10), 860–862 (1999).
[CrossRef]

1998 (2)

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 Condens. Matter 58(11), 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(6668), 667–669 (1998).
[CrossRef]

1997 (1)

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microw. Guid. Wave Lett. 7(5), 121–123 (1997).
[CrossRef]

1996 (1)

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev., B, Solid State 6(12), 4370–4379 (1972).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev., B, Solid State 6(12), 4370–4379 (1972).
[CrossRef]

Ebbesen, T. W.

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(21), 213901–1 (2003).
[CrossRef] [PubMed]

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: Physics and applications,” Nanotechnology 13(3), 429–432 (2002).
[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(24), 1972–1974 (2001).
[CrossRef] [PubMed]

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(10), 860–862 (1999).
[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 Condens. Matter 58(11), 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(6668), 667–669 (1998).
[CrossRef]

García-Vidal, F. J.

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(21), 213901–1 (2003).
[CrossRef] [PubMed]

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[CrossRef]

Ghaemi, H. F.

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(6668), 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 Condens. Matter 58(11), 6779–6782 (1998).
[CrossRef]

Grupp, D. E.

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(10), 860–862 (1999).
[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 Condens. Matter 58(11), 6779–6782 (1998).
[CrossRef]

Han, D.

Howe, D.

Hughes, H. P.

D. A. Thomas and H. P. Hughes, “Enhanced optical transmission through a subwavelength 1D aperture,” Solid State Commun. 129(8), 519–524 (2004).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev., B, Solid State 6(12), 4370–4379 (1972).
[CrossRef]

Kataja, K.

Lewen, G. D.

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

Lezec, H. J.

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3629 .
[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(21), 213901–1 (2003).
[CrossRef] [PubMed]

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: Physics and applications,” Nanotechnology 13(3), 429–432 (2002).
[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(24), 1972–1974 (2001).
[CrossRef] [PubMed]

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(10), 860–862 (1999).
[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 Condens. Matter 58(11), 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(6668), 667–669 (1998).
[CrossRef]

Li, X.

Linke, R. A.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: Physics and applications,” Nanotechnology 13(3), 429–432 (2002).
[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(24), 1972–1974 (2001).
[CrossRef] [PubMed]

Liu, X.

Martín-Moreno, L.

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(21), 213901–1 (2003).
[CrossRef] [PubMed]

Mrozowski, M.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microw. Guid. Wave Lett. 7(5), 121–123 (1997).
[CrossRef]

Nahata, A.

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

Okoniewski, M.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microw. Guid. Wave Lett. 7(5), 121–123 (1997).
[CrossRef]

Olkkonen, J.

Pellerin, K. M.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: Physics and applications,” Nanotechnology 13(3), 429–432 (2002).
[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(24), 1972–1974 (2001).
[CrossRef] [PubMed]

Stuchly, M. A.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microw. Guid. Wave Lett. 7(5), 121–123 (1997).
[CrossRef]

Thio, T.

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

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: Physics and applications,” Nanotechnology 13(3), 429–432 (2002).
[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(24), 1972–1974 (2001).
[CrossRef] [PubMed]

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(10), 860–862 (1999).
[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 Condens. Matter 58(11), 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(6668), 667–669 (1998).
[CrossRef]

Thomas, D. A.

D. A. Thomas and H. P. Hughes, “Enhanced optical transmission through a subwavelength 1D aperture,” Solid State Commun. 129(8), 519–524 (2004).
[CrossRef]

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(6668), 667–669 (1998).
[CrossRef]

Wu, F.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Zi, J.

Adv. Mater. (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(10), 860–862 (1999).
[CrossRef]

IEEE Microw. Guid. Wave Lett. (1)

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microw. Guid. Wave Lett. 7(5), 121–123 (1997).
[CrossRef]

IEEE Trans. Antenn. Propag. (2)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[CrossRef]

Nanotechnology (1)

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

Nature (1)

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(6668), 667–669 (1998).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B Condens. Matter (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 Condens. Matter 58(11), 6779–6782 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

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(21), 213901–1 (2003).
[CrossRef] [PubMed]

Phys. Rev., B, Solid State (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev., B, Solid State 6(12), 4370–4379 (1972).
[CrossRef]

Solid State Commun. (1)

D. A. Thomas and H. P. Hughes, “Enhanced optical transmission through a subwavelength 1D aperture,” Solid State Commun. 129(8), 519–524 (2004).
[CrossRef]

Other (2)

J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2000).

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

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Figures (6)

Fig. 1
Fig. 1

Illustration of the modeled structures. (a) A sub-wavelength slit in an opaque metal film is illuminated by a normally incident TE or TM polarized plane wave through a semitransparent metal film. The thickness of the semitransparent metal film (t) and the gap between the opaque and the semitransparent film (g) are selected so that the films form a light trapping cavity. When the incident light is TE polarized (electric field perpendicular to the plane of incidence), the slit is filled with a high index dielectric medium. In the TM case, the slit is always empty. The both metal films in the x- and y-directions extend to infinity. The yellow plane illustrates the plane of incidence. (b) The same as (a) but now the slit is replaced by a sub-wavelength cylindrical hole filled with a high index dielectric medium.

Fig. 2
Fig. 2

(a) Reflectance of a normally incident plane wave (Ex, Ez ≡ 0, Hy) having wavelength of 650 nm from the multilayer structure shown in the inset (d) as a function of t and g. The uppermost silver film is semitransparent (t = 0-100 nm) while the second is opaque (h = 200 nm), i.e., the transmittance through the entire structure is zero for all values of g and t. n 0 = 1.0. (b) Cross profiles of the reflectance map shown in (a) for t = 20, 30, 40, and 50 nm. (c) Electric field amplitude in the multilayer structure shown in (d) (g = 277.5 nm, h = 200 nm) without (t = 0 nm) and with the semitransparent metal film (t = 40 nm).

Fig. 3
Fig. 3

(a) Reflectance of an obliquely incident, TM polarized plane wave having free space wavelength of 650 nm from the multilayer structure (t = 40 nm, h = 200 nm, n 0 = 1) shown in the inset (c) as a function of the incident angle (θ) and the thickness of the air gap (g). (b) Cross profiles of the reflectance map shown in (a) for g = 277.5, 300, and 400 nm.

Fig. 4
Fig. 4

(a) Normalized transmission (η + ) and back-scattering (η-) efficiency as a function of the silver film thickness (h) for a 100 nm wide (w) slit under normally incident TM polarized plane wave illumination (ns = 1.0, n0 = 1.0, λ0 = 650 nm). (b) The same as (a) but now the slit is illuminated by a TE polarized plane wave and the slit is filled by a dielectric medium having refractive index (ns) of 3.8. (c) The dependency of the phase difference between the illuminating plane wave and the scattered field on the slit length in the middle of the slit entrance (point p shown in the inset). In the TM case, the phase difference is calculated from the magnetic field and from the electric field in the TE case.

Fig. 5
Fig. 5

(a) Transmission efficiency of the 100 nm wide slit with a light trapping cavity as a function of the distance between the semitransparent metal film (t = 40 nm) and the opaque metal film (g = 277.5 nm + mλ 0/2, m = 1, 2,…, 10). TM polarization: ns = 1.0, h = 165 nm. TE polarization: ns = 3.8, h = 130 nm. The red solid line depicts the transmission efficiency in the TM case when the g is varied from 10 to 600 nm in 10 nm steps. (b) Transmission efficiency as a function of the opaque metal film thickness with the fixed gap thickness of 277.5 nm. Other parameters are the same as in (a). n 0 = 1.0, and λ 0 = 650 nm.

Fig. 6
Fig. 6

(a) Transmission efficiency of a normally incident plane wave (λ 0 = 650 nm) through a cylindrical hole in a free standing silver film as a function the film thickness (h). The hole radius (r) is 50 nm and it is filled with a dielectric medium having the refractive index of n a. The red line is magnified by a factor of 500. (b) Transmission efficiency of a cylindrical hole (r = 50 nm, n a = 2.8, h = 180 nm) with a light trapping cavity as a function of the distance between the semitransparent metal film (t = 40 nm) and the opaque metal film (g = 277.5 nm + mλ 0/2, m = 1, 2,…, 8). (c) Transmission efficiency as a function of the opaque metal film thickness with the fixed gap thickness of 277.5 nm. Other parameters are the same as in (b).

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