Abstract

The transmission of a normally incident wave through an array of subwavelength gold film with Z-shaped slits has been explored by using the finite-difference time-domain method. The results show that the transmission of a thinner metal film perforated with a Z-shaped slit array behaves nearly the same as that of a thicker metal film perforated with straight slit array with the same central slit length, which is useful for the miniaturization of the optical device. It is also presented that the transmission of a Z-shaped slit array sensitively depends on the slit geometrical parameters. By adjusting the width and length of each section of the Z-shaped slit, noticeable magnitude modification of the transmission, redshift, and blueshift of the resonance modes is found, which is useful for the design of frequency-selective and sensor optical devices.

© 2011 Optical Society of America

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2010 (1)

2009 (2)

2008 (1)

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

2007 (6)

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

M. H. Chowdhury, J. M. Catchmark, and J. R. Lakowicza, “Imaging three-dimensional light propagation through periodic nanohole arrays using scanning aperture microscopy,” Appl. Phys. Lett. 91, 103118 (2007).
[CrossRef]

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Transmission of microwaves through a stepped subwavelength slit,” Appl. Phys. Lett. 91, 251106 (2007).
[CrossRef]

Y. Pang, C. Genet, and T. W. Ebbesen, “Optical transmission through subwavelength slit apertures in metallic films,” Opt. Commun. 280, 10–15 (2007).
[CrossRef]

P. Ginzburg and M. Orenstein, “Plasmonic transmission lines: from micro to nano scale with λ/4 impedance matching,” Opt. Express 15, 6762–6767 (2007).
[CrossRef] [PubMed]

A. Battula, Y. L. Lu, R. J. Knize, K. Reinhardt, and S. C. Chen, “Tunable transmission at 100 THz through a metallic hole array with a varying hole channel shape,” Opt. Express 15, 14629–14635 (2007).
[CrossRef] [PubMed]

2006 (5)

M. W. Docter, I. T. Young, O. M. Piciu, A. Bossche, P. F. A. Alkemade, P. M. van den Berg, and Y. Garini, “Measuring the wavelength-dependent divergence of transmission through sub-wavelength hole-arrays by spectral imaging,” Opt. Express 14, 9477–9482 (2006).
[CrossRef] [PubMed]

Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Optical transmission at oblique incidence through a periodic array of sub-wavelength slits in a metallic host,” Opt. Express 14, 10220–10227 (2006).
[CrossRef] [PubMed]

A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry–Perot cavities,” J. Appl. Phys. 99, 124903(2006).
[CrossRef]

Z. C. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

A. Battula and S. C. Chen, “Extraordinary transmission in a narrow energy band for metallic gratings with converging–diverging channels,” Appl. Phys. Lett. 89, 131113 (2006).
[CrossRef]

2005 (4)

2004 (1)

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 subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

2003 (1)

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

2002 (1)

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

2000 (1)

H. E. Went, A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and A. P. Crick, “Selective transmission through very deep zero-order metallic gratings at microwave frequencies,” Appl. Phys. Lett. 77, 2789 (2000).
[CrossRef]

1998 (1)

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

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200(1994).
[CrossRef]

1983 (1)

1966 (1)

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

Alexander, R. W.

Alkemade, P. F. A.

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 subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Battula, A.

A. Battula, Y. L. Lu, R. J. Knize, K. Reinhardt, and S. C. Chen, “Tunable transmission at 100 THz through a metallic hole array with a varying hole channel shape,” Opt. Express 15, 14629–14635 (2007).
[CrossRef] [PubMed]

A. Battula and S. C. Chen, “Extraordinary transmission in a narrow energy band for metallic gratings with converging–diverging channels,” Appl. Phys. Lett. 89, 131113 (2006).
[CrossRef]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200(1994).
[CrossRef]

Bossche, A.

Catchmark, J. M.

M. H. Chowdhury, J. M. Catchmark, and J. R. Lakowicza, “Imaging three-dimensional light propagation through periodic nanohole arrays using scanning aperture microscopy,” Appl. Phys. Lett. 91, 103118 (2007).
[CrossRef]

Chavel, P.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Chen, S. C.

Chowdhury, M. H.

M. H. Chowdhury, J. M. Catchmark, and J. R. Lakowicza, “Imaging three-dimensional light propagation through periodic nanohole arrays using scanning aperture microscopy,” Appl. Phys. Lett. 91, 103118 (2007).
[CrossRef]

Crick, A. P.

H. E. Went, A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and A. P. Crick, “Selective transmission through very deep zero-order metallic gratings at microwave frequencies,” Appl. Phys. Lett. 77, 2789 (2000).
[CrossRef]

Devaux, E.

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 subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

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 subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Docter, M. W.

Dong, X.

Du, C.

Ebbesen, T.

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

Ebbesen, T. W.

Y. Pang, C. Genet, and T. W. Ebbesen, “Optical transmission through subwavelength slit apertures in metallic films,” Opt. Commun. 280, 10–15 (2007).
[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 subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

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

Gao, H.

Garcia-Vidal, F. J.

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

Garini, Y.

Genet, C.

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

Y. Pang, C. Genet, and T. W. Ebbesen, “Optical transmission through subwavelength slit apertures in metallic films,” Opt. Commun. 280, 10–15 (2007).
[CrossRef]

Ghaemi, H. F.

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

Ginzburg, P.

Gramotnev, D. K.

Gray, S. K.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2005).

Hibbins, A. P.

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Transmission of microwaves through a stepped subwavelength slit,” Appl. Phys. Lett. 91, 251106 (2007).
[CrossRef]

A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry–Perot cavities,” J. Appl. Phys. 99, 124903(2006).
[CrossRef]

H. E. Went, A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and A. P. Crick, “Selective transmission through very deep zero-order metallic gratings at microwave frequencies,” Appl. Phys. Lett. 77, 2789 (2000).
[CrossRef]

Hugonin, J. P.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Jung, Y. S.

Y. S. Jung, Z. J. Sun, and H. K. Kim, “Blueshift of surface plasmon resonance spectra in anneal-treated silver nanoslit arrays,” Appl. Phys. Lett. 87, 263116 (2005).
[CrossRef]

Kim, H. K.

Y. S. Jung, Z. J. Sun, and H. K. Kim, “Blueshift of surface plasmon resonance spectra in anneal-treated silver nanoslit arrays,” Appl. Phys. Lett. 87, 263116 (2005).
[CrossRef]

Kim, K. S.

Knize, R. J.

Lakowicza, J. R.

M. H. Chowdhury, J. M. Catchmark, and J. R. Lakowicza, “Imaging three-dimensional light propagation through periodic nanohole arrays using scanning aperture microscopy,” Appl. Phys. Lett. 91, 103118 (2007).
[CrossRef]

Lalanne, P.

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Lawrence, C. R.

H. E. Went, A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and A. P. Crick, “Selective transmission through very deep zero-order metallic gratings at microwave frequencies,” Appl. Phys. Lett. 77, 2789 (2000).
[CrossRef]

Lee, T. W.

Liu, H. T.

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

Liu, S. T.

Lockyear, M. J.

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Transmission of microwaves through a stepped subwavelength slit,” Appl. Phys. Lett. 91, 251106 (2007).
[CrossRef]

A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry–Perot cavities,” J. Appl. Phys. 99, 124903(2006).
[CrossRef]

Long, L. L.

Lu, Y. L.

Luo, X.

Mansuripur, M.

Martin-Moreno, L.

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

Mason, D. R.

Moloney, J. V.

Munk, B. A.

B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley Interscience, 2000).
[CrossRef]

Murray, W. A.

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 subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004).
[CrossRef] [PubMed]

Ordal, M. A.

Orenstein, M.

Pang, Y.

Y. Pang, C. Genet, and T. W. Ebbesen, “Optical transmission through subwavelength slit apertures in metallic films,” Opt. Commun. 280, 10–15 (2007).
[CrossRef]

Piciu, O. M.

Qiu, M.

Z. C. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

Raether, H.

H. Raether, Surface Plasmons, G.Hobler, ed. (Springer, 1988).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

Reinhardt, K.

Rodier, J. C.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Ruan, Z. C.

Z. C. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96, 233901 (2006).
[CrossRef] [PubMed]

Sambles, J. R.

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Transmission of microwaves through a stepped subwavelength slit,” Appl. Phys. Lett. 91, 251106 (2007).
[CrossRef]

A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry–Perot cavities,” J. Appl. Phys. 99, 124903(2006).
[CrossRef]

H. E. Went, A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and A. P. Crick, “Selective transmission through very deep zero-order metallic gratings at microwave frequencies,” Appl. Phys. Lett. 77, 2789 (2000).
[CrossRef]

Sauvan, C.

P. Lalanne, C. Sauvan, J. P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
[CrossRef]

Shi, H.

Sun, Z. J.

Y. S. Jung, Z. J. Sun, and H. K. Kim, “Blueshift of surface plasmon resonance spectra in anneal-treated silver nanoslit arrays,” Appl. Phys. Lett. 87, 263116 (2005).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2005).

Thio, T.

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

van den Berg, P. M.

Wang, C.

Wang, W.

Wang, Y. H.

Wang, Y. Q.

Ward, C. A.

Went, H. E.

H. E. Went, A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and A. P. Crick, “Selective transmission through very deep zero-order metallic gratings at microwave frequencies,” Appl. Phys. Lett. 77, 2789 (2000).
[CrossRef]

Wolf, P. A.

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

Xie, Y.

Yee, K. S.

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

Young, I. T.

Zakharian, A. R.

Zhang, Y.

Appl. Opt. (1)

Appl. Phys. Lett. (5)

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Transmission of microwaves through a stepped subwavelength slit,” Appl. Phys. Lett. 91, 251106 (2007).
[CrossRef]

M. H. Chowdhury, J. M. Catchmark, and J. R. Lakowicza, “Imaging three-dimensional light propagation through periodic nanohole arrays using scanning aperture microscopy,” Appl. Phys. Lett. 91, 103118 (2007).
[CrossRef]

A. Battula and S. C. Chen, “Extraordinary transmission in a narrow energy band for metallic gratings with converging–diverging channels,” Appl. Phys. Lett. 89, 131113 (2006).
[CrossRef]

Y. S. Jung, Z. J. Sun, and H. K. Kim, “Blueshift of surface plasmon resonance spectra in anneal-treated silver nanoslit arrays,” Appl. Phys. Lett. 87, 263116 (2005).
[CrossRef]

H. E. Went, A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and A. P. Crick, “Selective transmission through very deep zero-order metallic gratings at microwave frequencies,” Appl. Phys. Lett. 77, 2789 (2000).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

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

J. Appl. Phys. (1)

A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry–Perot cavities,” J. Appl. Phys. 99, 124903(2006).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200(1994).
[CrossRef]

Nature (3)

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

H. T. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

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

Opt. Commun. (1)

Y. Pang, C. Genet, and T. W. Ebbesen, “Optical transmission through subwavelength slit apertures in metallic films,” Opt. Commun. 280, 10–15 (2007).
[CrossRef]

Opt. Express (10)

Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through a periodic array of slits in a thick metallic film,” Opt. Express 13, 4485–4491 (2005).
[CrossRef] [PubMed]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13, 6815–3820 (2005).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

y z cross section of one lattice of the gold slit array with Z-shaped channel defined for FDTD simulations. Param eters are defined in the text.

Fig. 2
Fig. 2

Transmission spectra through a lattice of periodic gold film perforated with straight slits and Z-shaped slits with width equaling 150 nm for different central slit lengths. (a) Parameters of the straight slit are l = 650 nm , h = 650 nm , w = 150 nm ; those of the Z-shaped slit are l = 650 nm , h = 500 nm , w 1 = w 2 = w 3 = 150 nm , s 1 = s 3 = 325 nm , s 2 = 300 nm . (b) Parameters of the straight slit are l = 800 nm , h = 800 nm , w = 150 nm ; those of the Z-shaped slit are l = 800 nm , h = 500 nm , w 1 = w 2 = w 3 = 150 nm , s 1 = s 3 = 325 nm , s 2 = 450 nm .

Fig. 3
Fig. 3

Modulus distributions of the complex electric field of the surface plasmon resonance and the localized waveguide resonance modes (a) at 924.4 nm and (b)  1757.7 nm for the structure with straight slit arrays with h = 650 nm , l = 650 nm ; (c) at 862.6 nm and (d)  1757.6 nm for the structure with Z-shaped slit arrays with h = 500 nm , l = 650 nm ; and (e) at 1075.8 nm and (f)  2068.4 nm for the structure with Z-shaped slit arrays with h = 500 nm , l = 800 nm , corresponding to the transmission spectra in Fig. 2.

Fig. 4
Fig. 4

(a) Transmission spectra of the metallic straight slit array with film thickness h = 650 nm and central slit length l = 650 nm for different slit widths: w = 25 , 50, 100, and 150 nm , film thickness h = 650 nm . (b) Transmission spectra of the metallic Z-shaped slit array with film thickness h = 500 nm and central slit length l = 650 nm for different slit widths: w 1 = w 2 = w 3 = 25 , 50, 100, and 150 nm . The slit length of each section is s 1 = s 3 = 325 nm and s 2 = 300 nm , respectively.

Fig. 5
Fig. 5

Transmission spectra through a lattice of periodic gold film perforated with Z-shaped slits with slit width (a)  w 1 = 25 , 50, 100, 150 nm while w 2 = w 3 = 150 nm is fixed; and (b)  w 1 = w 3 = 25 , 50, 100, 150 nm while w 2 = 150 nm is fixed. h = 500 nm , s 1 = 325 nm , s 2 = 450 nm , s 3 = 325 nm .

Fig. 6
Fig. 6

Transmission spectra through a lattice of periodic gold film perforated with Z-shaped slits with slit widths w 2 = 25 , 50, 100, 150 nm . h = 500 nm , l = 800 nm , s 2 = 450 nm , w 1 = w 3 = 150 nm .

Fig. 7
Fig. 7

Transmission spectra through a lattice of periodic gold film perforated with Z-shaped slits with slit length s 2 = 150 , 300, and 450 nm . h = 500 nm , s 1 = 325 nm , s 2 = 325 nm , w 1 = w 2 = w 3 = 150 nm .

Fig. 8
Fig. 8

Transmission spectra through a lattice of periodic gold film perforated with Z-shaped slits with slit length s 1 = 325 , 275, 225, and 175 nm ; s 3 = 325 , 375, 425, 475 nm , respectively, while central slit length l = 800 nm is unchanged. h = 500 nm , s 2 = 450 nm , w 1 = w 2 = w 3 = 150 nm .

Equations (6)

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ε = 1 ω p 2 ω 2 + γ 2 + i ω p 2 γ 2 ω ( ω 2 + γ 2 ) ,
t 0 = τ 12 exp i k 0 l τ 23 1 R 2 exp i ϕ T ,
λ = ( p / m ) Re ( ε d ε m / ( ε d + ε m ) ) 1 / 2 ,
k 0 Re ( n eff ) l + arg ( ρ ) = n π ,
2 k L FP + θ = 2 n π ,
L eff = L FP + δ J δ Q .

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