Abstract

This work numerically investigates optical responses (absorptance, reflectance, and transmittance) of deep slits with five nanoscale slit profile variations at the transverse magnetic wave incidence by employing the rigorous coupled-wave analysis. For slits with attached features, their optical responses can be much different due to the modified cavity geometry and dangled structures, even at wavelengths between 3 and 15 µm. The shifts of cavity resonance excitation result in higher transmittance through narrower slits at specific wavelengths and resonance modes are confirmed with the electromagnetic fields. Opposite roles possibly played by features in increasing or decreasing absorptance are determined by the feature position and demonstrated by Poynting vectors. Correlations among all responses of a representative slit array, the angle of incidence, and the slit density are also comprehensively studied. When multiple slit types coexist in an array (complex slits), a wide-band transmittance or absorptance enhancement is feasible by merging spectral peaks contributed from each type of slits distinctively. Discrepancy among infrared optical responses of four selected slit combinations is explained while effects of slit density are also discussed.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  4. S. Astilean, P. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun. 175, 265-273 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  7. J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. P. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature 416, 61-64 (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  16. Y.-B. Chen, B. J. Lee, and Z. M. Zhang, "Infrared radiative properties of submicron metallic slits," J. Heat Transf.-Trans. ASME 130, 082404 (2008).
    [CrossRef]
  17. B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Confinement of infrared radiation to nanometer scales through metallic slit arrays," J. Quant. Spectrosc. Radiat. Transfer 109, 608-619 (2008).
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    [CrossRef]
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    [CrossRef]

2008 (5)

B. Hou and W. J. Wen, "Transmission resonances of electromagnetic wave through metallic gratings: phase and field characterizations," Opt. Express 16, 17098-17106 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-17098.
[CrossRef] [PubMed]

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared," J. Comput. Theor. Nanosci. 5, 201-213 (2008).

Y.-B. Chen, B. J. Lee, and Z. M. Zhang, "Infrared radiative properties of submicron metallic slits," J. Heat Transf.-Trans. ASME 130, 082404 (2008).
[CrossRef]

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Confinement of infrared radiation to nanometer scales through metallic slit arrays," J. Quant. Spectrosc. Radiat. Transfer 109, 608-619 (2008).
[CrossRef]

P. Hewageegana and V. Apalkov, "Enhanced mid-infrared transmission through a metallic diffraction grating," J. Phys.: Condens. Matter 20, 395228 (2008).
[CrossRef]

2007 (5)

D. Crouse and P. Keshavareddy, "Polarization independent enhanced optical transmission in one-dimensional gratings and device applications," Opt. Express 15, 1415-1427 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-4-1415.
[CrossRef] [PubMed]

D. C. Skigin and R. A. Depine, "Diffraction by dual-period gratings," Appl. Opt. 46, 1385-1391 (2007).
[CrossRef] [PubMed]

A. Moreau, C. Lafarge, N. Laurent, K. Edee, and G. Granet, "Enhanced transmission of slit arrays in an extremely thin metallic film," J. Opt. A 9, 165-169 (2007).
[CrossRef]

Y.-B. Chen, Z. M. Zhang, and P. J. Timans, "Radiative properties of patterned wafers with nanoscale linewidth," J. Heat Transf.-Trans. ASME 129, 79-90 (2007).
[CrossRef]

Y.-B. Chen and Z. M. Zhang, "Design of tungsten complex gratings for thermophotovoltaic radiators," Opt. Commun. 269, 411-417 (2007).
[CrossRef]

2006 (2)

2005 (1)

2002 (4)

F. J. García-Vidal and L. Martín-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002).
[CrossRef]

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. P. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature 416, 61-64 (2002).
[CrossRef] [PubMed]

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161403 (2002).
[CrossRef]

2000 (2)

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

S. Astilean, P. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun. 175, 265-273 (2000).
[CrossRef]

1999 (1)

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

1995 (1)

1986 (1)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, "Organ pipe radiant modes of periodic micromachined silicon surfaces," Nature 324, 549-551 (1986).
[CrossRef]

1983 (1)

Alexander, R. W.

Apalkov, V.

P. Hewageegana and V. Apalkov, "Enhanced mid-infrared transmission through a metallic diffraction grating," J. Phys.: Condens. Matter 20, 395228 (2008).
[CrossRef]

Astilean, S.

S. Astilean, P. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun. 175, 265-273 (2000).
[CrossRef]

Barbara, A.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Benabbas, A.

Bigot, J. Y.

Bustarret, E.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Cao, Q.

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

Carminati, R.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. P. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature 416, 61-64 (2002).
[CrossRef] [PubMed]

Chen, Y.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. P. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature 416, 61-64 (2002).
[CrossRef] [PubMed]

Chen, Y.-B.

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared," J. Comput. Theor. Nanosci. 5, 201-213 (2008).

Y.-B. Chen, B. J. Lee, and Z. M. Zhang, "Infrared radiative properties of submicron metallic slits," J. Heat Transf.-Trans. ASME 130, 082404 (2008).
[CrossRef]

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Confinement of infrared radiation to nanometer scales through metallic slit arrays," J. Quant. Spectrosc. Radiat. Transfer 109, 608-619 (2008).
[CrossRef]

Y.-B. Chen and Z. M. Zhang, "Design of tungsten complex gratings for thermophotovoltaic radiators," Opt. Commun. 269, 411-417 (2007).
[CrossRef]

Y.-B. Chen, Z. M. Zhang, and P. J. Timans, "Radiative properties of patterned wafers with nanoscale linewidth," J. Heat Transf.-Trans. ASME 129, 79-90 (2007).
[CrossRef]

Collin, S.

Crouse, D.

Depine, R. A.

Edee, K.

A. Moreau, C. Lafarge, N. Laurent, K. Edee, and G. Granet, "Enhanced transmission of slit arrays in an extremely thin metallic film," J. Opt. A 9, 165-169 (2007).
[CrossRef]

Enoch, S.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

García-Vidal, F. J.

F. J. García-Vidal and L. Martín-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002).
[CrossRef]

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Gaylord, T. K.

Gebhart, B.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, "Organ pipe radiant modes of periodic micromachined silicon surfaces," Nature 324, 549-551 (1986).
[CrossRef]

Granet, G.

A. Moreau, C. Lafarge, N. Laurent, K. Edee, and G. Granet, "Enhanced transmission of slit arrays in an extremely thin metallic film," J. Opt. A 9, 165-169 (2007).
[CrossRef]

Grann, E. B.

Greffet, J. J.

Halté, V.

Hesketh, P. J.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, "Organ pipe radiant modes of periodic micromachined silicon surfaces," Nature 324, 549-551 (1986).
[CrossRef]

Hewageegana, P.

P. Hewageegana and V. Apalkov, "Enhanced mid-infrared transmission through a metallic diffraction grating," J. Phys.: Condens. Matter 20, 395228 (2008).
[CrossRef]

Hou, B.

Jiao, X. J.

Joulain, K.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. P. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature 416, 61-64 (2002).
[CrossRef] [PubMed]

Keshavareddy, P.

Lafarge, C.

A. Moreau, C. Lafarge, N. Laurent, K. Edee, and G. Granet, "Enhanced transmission of slit arrays in an extremely thin metallic film," J. Opt. A 9, 165-169 (2007).
[CrossRef]

Lalanne, P.

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

S. Astilean, P. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun. 175, 265-273 (2000).
[CrossRef]

Laurent, N.

A. Moreau, C. Lafarge, N. Laurent, K. Edee, and G. Granet, "Enhanced transmission of slit arrays in an extremely thin metallic film," J. Opt. A 9, 165-169 (2007).
[CrossRef]

Lee, B. J.

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared," J. Comput. Theor. Nanosci. 5, 201-213 (2008).

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Confinement of infrared radiation to nanometer scales through metallic slit arrays," J. Quant. Spectrosc. Radiat. Transfer 109, 608-619 (2008).
[CrossRef]

Y.-B. Chen, B. J. Lee, and Z. M. Zhang, "Infrared radiative properties of submicron metallic slits," J. Heat Transf.-Trans. ASME 130, 082404 (2008).
[CrossRef]

Long, L. L.

Lopez-Rios, T.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Mainguy, S. P.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. P. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature 416, 61-64 (2002).
[CrossRef] [PubMed]

Marquier, F.

Martín-Moreno, L.

F. J. García-Vidal and L. Martín-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002).
[CrossRef]

Min, C. J.

Ming, H.

Moharam, M. G.

Moreau, A.

A. Moreau, C. Lafarge, N. Laurent, K. Edee, and G. Granet, "Enhanced transmission of slit arrays in an extremely thin metallic film," J. Opt. A 9, 165-169 (2007).
[CrossRef]

Mulet, J. P.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. P. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature 416, 61-64 (2002).
[CrossRef] [PubMed]

Neviere, M.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

Ordal, M. A.

Palamaru, M.

S. Astilean, P. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun. 175, 265-273 (2000).
[CrossRef]

Pardo, F.

Pelouard, J. L.

Pendry, J. B.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Pommet, D. A.

Popov, E.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

Porto, J. A.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Quemerais, P.

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161403 (2002).
[CrossRef]

Reinisch, R.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

Skigin, D. C.

Timans, P. J.

Y.-B. Chen, Z. M. Zhang, and P. J. Timans, "Radiative properties of patterned wafers with nanoscale linewidth," J. Heat Transf.-Trans. ASME 129, 79-90 (2007).
[CrossRef]

Wang, P.

Ward, C. A.

Wen, W. J.

Zemel, J. N.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, "Organ pipe radiant modes of periodic micromachined silicon surfaces," Nature 324, 549-551 (1986).
[CrossRef]

Zhang, Z. M.

Y.-B. Chen, B. J. Lee, and Z. M. Zhang, "Infrared radiative properties of submicron metallic slits," J. Heat Transf.-Trans. ASME 130, 082404 (2008).
[CrossRef]

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared," J. Comput. Theor. Nanosci. 5, 201-213 (2008).

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Confinement of infrared radiation to nanometer scales through metallic slit arrays," J. Quant. Spectrosc. Radiat. Transfer 109, 608-619 (2008).
[CrossRef]

Y.-B. Chen and Z. M. Zhang, "Design of tungsten complex gratings for thermophotovoltaic radiators," Opt. Commun. 269, 411-417 (2007).
[CrossRef]

Y.-B. Chen, Z. M. Zhang, and P. J. Timans, "Radiative properties of patterned wafers with nanoscale linewidth," J. Heat Transf.-Trans. ASME 129, 79-90 (2007).
[CrossRef]

Appl. Opt. (2)

J. Comput. Theor. Nanosci. (1)

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared," J. Comput. Theor. Nanosci. 5, 201-213 (2008).

J. Opt. A (1)

A. Moreau, C. Lafarge, N. Laurent, K. Edee, and G. Granet, "Enhanced transmission of slit arrays in an extremely thin metallic film," J. Opt. A 9, 165-169 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys.: Condens. Matter (1)

P. Hewageegana and V. Apalkov, "Enhanced mid-infrared transmission through a metallic diffraction grating," J. Phys.: Condens. Matter 20, 395228 (2008).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Confinement of infrared radiation to nanometer scales through metallic slit arrays," J. Quant. Spectrosc. Radiat. Transfer 109, 608-619 (2008).
[CrossRef]

Nature (2)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, "Organ pipe radiant modes of periodic micromachined silicon surfaces," Nature 324, 549-551 (1986).
[CrossRef]

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. P. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature 416, 61-64 (2002).
[CrossRef] [PubMed]

Opt. Commun. (2)

S. Astilean, P. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun. 175, 265-273 (2000).
[CrossRef]

Y.-B. Chen and Z. M. Zhang, "Design of tungsten complex gratings for thermophotovoltaic radiators," Opt. Commun. 269, 411-417 (2007).
[CrossRef]

Opt. Express (5)

Phys. Rev. B (3)

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

A. Barbara, P. Quemerais, E. Bustarret, and T. Lopez-Rios, "Optical transmission through subwavelength metallic gratings," Phys. Rev. B 66, 161403 (2002).
[CrossRef]

F. J. García-Vidal and L. Martín-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Phys. Rev. B 66, 155412 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

Q. Cao and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Trans. ASME (2)

Y.-B. Chen, B. J. Lee, and Z. M. Zhang, "Infrared radiative properties of submicron metallic slits," J. Heat Transf.-Trans. ASME 130, 082404 (2008).
[CrossRef]

Y.-B. Chen, Z. M. Zhang, and P. J. Timans, "Radiative properties of patterned wafers with nanoscale linewidth," J. Heat Transf.-Trans. ASME 129, 79-90 (2007).
[CrossRef]

Other (3)

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

M. J. Madou, Fundamentals of Microfabrication: The Science of Miniaturization (CRC Press, 2002).

Z. M. Zhang, Nano/Microscale Heat Transfer (McGraw-Hill, 2007).

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Figures (8)

Fig. 1.
Fig. 1.

Cross-sections of five slit cases with nanoscale geometry modification, where a=20 nm, d=3600 nm, l=750 nm, w=50 nm, and Λ=800 nm represent the square feature size, slit depth, lamella width, slit width, and slit period, respectively. E and H are the electric and magnetic field vector of the incident transverse magnetic wave while k is its wavevector and θ is the angle of incidence or the polar angle. The incidence is marked with red arrowheads and its wavelength ranges from 3 to 15 µm.

Fig. 2.
Fig. 2.

Optical responses of gold slits at normal incidence: (a) Transmittance; (b) Absorptance. The arrowhead type illustrates the order of optical responses among five slit geometric modification cases at peaks in a spectrum with wavelengths specified by numbers above arrowheads in the unit of micrometer. The relative heights among arrowheads also tell the relative difference of optical responses.

Fig. 3.
Fig. 3.

Optical responses of silver slits at normal incidence: (a) Transmittance; (b) Absorptance. The geometry of four slit cases is the same as that of gold slits in Fig. 1, except the incidence of Case B and B’ is on opposite sides of slits. Insets of two contour plots are duplications of Fig. 1 in Ref. 9 as a validation of codes employed in this work.

Fig. 4.
Fig. 4.

Poynting vectors and the magnitude square of complex magnetic field in the logarithmic scale for gold slits of Case D at θ=0° and λ=3.58 µm: (a) Poynting vectors; (b) the magnitude square of complex magnetic field. The transmittance (T) and absorptance (A) in this case are listed in the figure as T=0.383 and A=0.477, respectively. Lamellae boundary in Fig. 4(b) is marked with grey lines.

Fig. 5.
Fig. 5.

Contour plots of optical responses for gold slits of Case D at various angles of incidence and wavelengths: (a) Transmittance; (b) Absorptance.

Fig. 6.
Fig. 6.

Optical responses for gold slits of Case D with selected slit densities (w/Λ=0.031, 0.042, 0.063, and 0.125) at normal incidence: (a) Transmittance; (b) Absorptance; (c) Reflectance. The legend in Fig. 6(a) specifies the slit period, lamellae width, and slit density of structures discussed here while the inset in Fig. 6(b) correlates the transmittance/absorptance with slit density at different spectral regions. In the regions marked with lines with arrowheads, both the transmittance and absorptance decrease with reducing w/Λ ratio. In contrast, the transmittance decreases but the absorptance increases with reducing w/Λ ratio in the spectral region marked with green line sections without arrowheads.

Fig. 7.
Fig. 7.

Optical responses of gold complex slits at normal incidence while two slits in a period have different profiles: (a) Transmittance; (b) Absorptance. The inset in Fig. 7(a) serves as the legend showing all dimensions of discussed complex slits.

Fig. 8.
Fig. 8.

Optical responses of gold complex slits at normal incidence: (a) Transmittance; (b) Absorptance. The two slit profile in a period come from those of Case A and D while the slit period and lamella width are different for each spectrum. The inset in Fig. 8b is the solid line of absorptance spectrum redrawn in wavenumber ν (cm-1), but every number above arrowheads is the peak wavelength λ marked in micrometer.

Equations (2)

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ε (ω)=εωp2ω2+iωγ
S=0.5 Re (E×H*)

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