Abstract

Plasmonic structures made of periodically arranged metallic rings integrated into subwavelength holes are investigated at the far-infrared terahertz frequencies. The emergence and the interplay of various resonances sustained by such plasmonic samples are elucidated. To reveal a coherent physical picture, relevant dimensions of the samples are modified and their impact on the resonance properties is analyzed. The experimental work is fully supported by numerical simulations. The understanding of the interplay of various resonances will foster applications which require plasmonic substrates to exhibit simultaneously resonances at well-defined frequencies and line widths.

© 2012 Optical Society of America

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  1. S. Enoch, R. Quidant, and G. Badenes, “Optical sensing based on plasmon coupling in nanoparticle arrays,” Opt. Express 12, 3422–3427 (2004).
    [CrossRef]
  2. M. Specht, J. D. Pedarnig, W. M. Heckl, and T. W. Hänsch, “Scanning plasmon near-field microscope,” Phys. Rev. Lett. 68, 476–479 (1992).
    [CrossRef]
  3. M. Lahav, A. Vaskevich, and I. Rubinstein, “Biological sensing using transmission surface plasmon resonance spectroscopy,” Langmuir 20, 7365–7367 (2004).
    [CrossRef]
  4. F. Capasso, N. Yu, E. Cubukcu, and E. Smythe, “Using plasmonics to shape light beams,” Opt. Photon. News 20, 22–27 (2009).
  5. H. Zhan, R. Mendis, and D. M. Mittleman, “Characterization of the terahertz near-field output of parallel-plate waveguides,” J. Opt. Soc. Am. B 28, 558–566 (2011).
    [CrossRef]
  6. F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
    [CrossRef]
  7. F. I. Baida, D. Van Labeke, and B. Guizal, “Enhanced confined lght transmission by single subwavelength apertures in metallic films,” Appl. Opt. 42, 6811–6815 (2003).
    [CrossRef]
  8. W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94, 033902 (2005).
  9. W. Fan, S. Zhang, K. J. Malloy, and S. R. J. Brueck, “Enhanced mid-infrared transmission through nanoscale metal coaxial-aperture arrays,” Opt. Express 13, 4406–4413 (2005).
    [CrossRef]
  10. X. Lu, J. Han, and W. Zhang, “Transmission field enhancement of terahertz pulses in plasmonic, rectangular coaxial geometries,” Opt. Lett. 35, 904–906 (2010).
    [CrossRef]
  11. X. Lu, J. Han, and W. Zhang, “Localized plasmonic properties of subwavelength geometries resonating at terahertz frequencies,” IEEE J. Sel. Top. Quantum Electron. 17, 119–129 (2011).
    [CrossRef]
  12. 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]
  13. C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16, 2080–2090 (2008).
    [CrossRef]
  14. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
    [CrossRef]
  15. J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91, 071122 (2007).
  16. D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
    [CrossRef]
  17. D. Grischkowsky, S. Keiding, M. van Exter, and Ch. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990).
    [CrossRef]
  18. W. Zhang, “Resonant terahertz transmission in plasmonic arrays of subwavelength holes,” Eur. Phys. J. Appl. Phys. 43, 1 (2008).
  19. X. Lu, J. Han, and W. Zhang, “Resonant terahertz reflection of periodic arrays of subwavelength metallic rectangles,” Appl. Phys. Lett. 92, 121103 (2008).
  20. C. Dahmen and G. von Plessen, “Optical effects of metallic nanoparticles,” Aust. J. Chem. 60, 447–456 (2007).
  21. X. Lu and W. Zhang, “Terahertz localized plasmonic properties of subwavelength ring and coaxial geometries,” Appl. Phys. Lett. 94, 181106 (2009).
  22. T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Arch. Elektron. Übertragungstech 31, 116–120 (1977).

2011 (2)

X. Lu, J. Han, and W. Zhang, “Localized plasmonic properties of subwavelength geometries resonating at terahertz frequencies,” IEEE J. Sel. Top. Quantum Electron. 17, 119–129 (2011).
[CrossRef]

H. Zhan, R. Mendis, and D. M. Mittleman, “Characterization of the terahertz near-field output of parallel-plate waveguides,” J. Opt. Soc. Am. B 28, 558–566 (2011).
[CrossRef]

2010 (1)

2009 (2)

F. Capasso, N. Yu, E. Cubukcu, and E. Smythe, “Using plasmonics to shape light beams,” Opt. Photon. News 20, 22–27 (2009).

X. Lu and W. Zhang, “Terahertz localized plasmonic properties of subwavelength ring and coaxial geometries,” Appl. Phys. Lett. 94, 181106 (2009).

2008 (3)

W. Zhang, “Resonant terahertz transmission in plasmonic arrays of subwavelength holes,” Eur. Phys. J. Appl. Phys. 43, 1 (2008).

X. Lu, J. Han, and W. Zhang, “Resonant terahertz reflection of periodic arrays of subwavelength metallic rectangles,” Appl. Phys. Lett. 92, 121103 (2008).

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16, 2080–2090 (2008).
[CrossRef]

2007 (2)

C. Dahmen and G. von Plessen, “Optical effects of metallic nanoparticles,” Aust. J. Chem. 60, 447–456 (2007).

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91, 071122 (2007).

2005 (3)

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94, 033902 (2005).

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]

W. Fan, S. Zhang, K. J. Malloy, and S. R. J. Brueck, “Enhanced mid-infrared transmission through nanoscale metal coaxial-aperture arrays,” Opt. Express 13, 4406–4413 (2005).
[CrossRef]

2004 (3)

2003 (1)

2002 (1)

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
[CrossRef]

1992 (1)

M. Specht, J. D. Pedarnig, W. M. Heckl, and T. W. Hänsch, “Scanning plasmon near-field microscope,” Phys. Rev. Lett. 68, 476–479 (1992).
[CrossRef]

1990 (1)

1977 (1)

T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Arch. Elektron. Übertragungstech 31, 116–120 (1977).

1944 (1)

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

Azad, A. K.

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91, 071122 (2007).

Badenes, G.

Baida, F. I.

F. I. Baida, D. Van Labeke, and B. Guizal, “Enhanced confined lght transmission by single subwavelength apertures in metallic films,” Appl. Opt. 42, 6811–6815 (2003).
[CrossRef]

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
[CrossRef]

Bethe, H. A.

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

Brueck, S. R. J.

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94, 033902 (2005).

W. Fan, S. Zhang, K. J. Malloy, and S. R. J. Brueck, “Enhanced mid-infrared transmission through nanoscale metal coaxial-aperture arrays,” Opt. Express 13, 4406–4413 (2005).
[CrossRef]

Capasso, F.

F. Capasso, N. Yu, E. Cubukcu, and E. Smythe, “Using plasmonics to shape light beams,” Opt. Photon. News 20, 22–27 (2009).

Cubukcu, E.

F. Capasso, N. Yu, E. Cubukcu, and E. Smythe, “Using plasmonics to shape light beams,” Opt. Photon. News 20, 22–27 (2009).

Dahmen, C.

C. Dahmen and G. von Plessen, “Optical effects of metallic nanoparticles,” Aust. J. Chem. 60, 447–456 (2007).

Enoch, S.

Fan, W.

W. Fan, S. Zhang, K. J. Malloy, and S. R. J. Brueck, “Enhanced mid-infrared transmission through nanoscale metal coaxial-aperture arrays,” Opt. Express 13, 4406–4413 (2005).
[CrossRef]

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94, 033902 (2005).

Fattinger, Ch.

García-Vidal, F. J.

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]

Giessen, H.

Gong, M.

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91, 071122 (2007).

Grischkowsky, D.

Guizal, B.

Han, J.

X. Lu, J. Han, and W. Zhang, “Localized plasmonic properties of subwavelength geometries resonating at terahertz frequencies,” IEEE J. Sel. Top. Quantum Electron. 17, 119–129 (2011).
[CrossRef]

X. Lu, J. Han, and W. Zhang, “Transmission field enhancement of terahertz pulses in plasmonic, rectangular coaxial geometries,” Opt. Lett. 35, 904–906 (2010).
[CrossRef]

X. Lu, J. Han, and W. Zhang, “Resonant terahertz reflection of periodic arrays of subwavelength metallic rectangles,” Appl. Phys. Lett. 92, 121103 (2008).

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91, 071122 (2007).

Hänsch, T. W.

M. Specht, J. D. Pedarnig, W. M. Heckl, and T. W. Hänsch, “Scanning plasmon near-field microscope,” Phys. Rev. Lett. 68, 476–479 (1992).
[CrossRef]

Heckl, W. M.

M. Specht, J. D. Pedarnig, W. M. Heckl, and T. W. Hänsch, “Scanning plasmon near-field microscope,” Phys. Rev. Lett. 68, 476–479 (1992).
[CrossRef]

Keiding, S.

Lahav, M.

M. Lahav, A. Vaskevich, and I. Rubinstein, “Biological sensing using transmission surface plasmon resonance spectroscopy,” Langmuir 20, 7365–7367 (2004).
[CrossRef]

Lederer, F.

Lu, X.

X. Lu, J. Han, and W. Zhang, “Localized plasmonic properties of subwavelength geometries resonating at terahertz frequencies,” IEEE J. Sel. Top. Quantum Electron. 17, 119–129 (2011).
[CrossRef]

X. Lu, J. Han, and W. Zhang, “Transmission field enhancement of terahertz pulses in plasmonic, rectangular coaxial geometries,” Opt. Lett. 35, 904–906 (2010).
[CrossRef]

X. Lu and W. Zhang, “Terahertz localized plasmonic properties of subwavelength ring and coaxial geometries,” Appl. Phys. Lett. 94, 181106 (2009).

X. Lu, J. Han, and W. Zhang, “Resonant terahertz reflection of periodic arrays of subwavelength metallic rectangles,” Appl. Phys. Lett. 92, 121103 (2008).

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91, 071122 (2007).

Malloy, K. J.

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94, 033902 (2005).

W. Fan, S. Zhang, K. J. Malloy, and S. R. J. Brueck, “Enhanced mid-infrared transmission through nanoscale metal coaxial-aperture arrays,” Opt. Express 13, 4406–4413 (2005).
[CrossRef]

Martín-Moreno, L.

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]

Mendis, R.

Meyrath, T. P.

Minhas, B.

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94, 033902 (2005).

Mittleman, D. M.

Moreno, E.

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]

Pedarnig, J. D.

M. Specht, J. D. Pedarnig, W. M. Heckl, and T. W. Hänsch, “Scanning plasmon near-field microscope,” Phys. Rev. Lett. 68, 476–479 (1992).
[CrossRef]

Porto, J. A.

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]

Qu, D.

Quidant, R.

Rockstuhl, C.

Rubinstein, I.

M. Lahav, A. Vaskevich, and I. Rubinstein, “Biological sensing using transmission surface plasmon resonance spectroscopy,” Langmuir 20, 7365–7367 (2004).
[CrossRef]

Smythe, E.

F. Capasso, N. Yu, E. Cubukcu, and E. Smythe, “Using plasmonics to shape light beams,” Opt. Photon. News 20, 22–27 (2009).

Specht, M.

M. Specht, J. D. Pedarnig, W. M. Heckl, and T. W. Hänsch, “Scanning plasmon near-field microscope,” Phys. Rev. Lett. 68, 476–479 (1992).
[CrossRef]

van Exter, M.

Van Labeke, D.

F. I. Baida, D. Van Labeke, and B. Guizal, “Enhanced confined lght transmission by single subwavelength apertures in metallic films,” Appl. Opt. 42, 6811–6815 (2003).
[CrossRef]

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
[CrossRef]

Vaskevich, A.

M. Lahav, A. Vaskevich, and I. Rubinstein, “Biological sensing using transmission surface plasmon resonance spectroscopy,” Langmuir 20, 7365–7367 (2004).
[CrossRef]

von Plessen, G.

C. Dahmen and G. von Plessen, “Optical effects of metallic nanoparticles,” Aust. J. Chem. 60, 447–456 (2007).

Weiland, T.

T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Arch. Elektron. Übertragungstech 31, 116–120 (1977).

Yu, N.

F. Capasso, N. Yu, E. Cubukcu, and E. Smythe, “Using plasmonics to shape light beams,” Opt. Photon. News 20, 22–27 (2009).

Zentgraf, T.

Zhan, H.

Zhang, S.

W. Fan, S. Zhang, K. J. Malloy, and S. R. J. Brueck, “Enhanced mid-infrared transmission through nanoscale metal coaxial-aperture arrays,” Opt. Express 13, 4406–4413 (2005).
[CrossRef]

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94, 033902 (2005).

Zhang, W.

X. Lu, J. Han, and W. Zhang, “Localized plasmonic properties of subwavelength geometries resonating at terahertz frequencies,” IEEE J. Sel. Top. Quantum Electron. 17, 119–129 (2011).
[CrossRef]

X. Lu, J. Han, and W. Zhang, “Transmission field enhancement of terahertz pulses in plasmonic, rectangular coaxial geometries,” Opt. Lett. 35, 904–906 (2010).
[CrossRef]

X. Lu and W. Zhang, “Terahertz localized plasmonic properties of subwavelength ring and coaxial geometries,” Appl. Phys. Lett. 94, 181106 (2009).

X. Lu, J. Han, and W. Zhang, “Resonant terahertz reflection of periodic arrays of subwavelength metallic rectangles,” Appl. Phys. Lett. 92, 121103 (2008).

W. Zhang, “Resonant terahertz transmission in plasmonic arrays of subwavelength holes,” Eur. Phys. J. Appl. Phys. 43, 1 (2008).

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91, 071122 (2007).

D. Qu, D. Grischkowsky, and W. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

X. Lu and W. Zhang, “Terahertz localized plasmonic properties of subwavelength ring and coaxial geometries,” Appl. Phys. Lett. 94, 181106 (2009).

J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91, 071122 (2007).

X. Lu, J. Han, and W. Zhang, “Resonant terahertz reflection of periodic arrays of subwavelength metallic rectangles,” Appl. Phys. Lett. 92, 121103 (2008).

Arch. Elektron. Übertragungstech (1)

T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Arch. Elektron. Übertragungstech 31, 116–120 (1977).

Aust. J. Chem. (1)

C. Dahmen and G. von Plessen, “Optical effects of metallic nanoparticles,” Aust. J. Chem. 60, 447–456 (2007).

Eur. Phys. J. Appl. Phys. (1)

W. Zhang, “Resonant terahertz transmission in plasmonic arrays of subwavelength holes,” Eur. Phys. J. Appl. Phys. 43, 1 (2008).

IEEE J. Sel. Top. Quantum Electron. (1)

X. Lu, J. Han, and W. Zhang, “Localized plasmonic properties of subwavelength geometries resonating at terahertz frequencies,” IEEE J. Sel. Top. Quantum Electron. 17, 119–129 (2011).
[CrossRef]

J. Opt. Soc. Am. B (2)

Langmuir (1)

M. Lahav, A. Vaskevich, and I. Rubinstein, “Biological sensing using transmission surface plasmon resonance spectroscopy,” Langmuir 20, 7365–7367 (2004).
[CrossRef]

Opt. Commun. (1)

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Opt. Photon. News (1)

F. Capasso, N. Yu, E. Cubukcu, and E. Smythe, “Using plasmonics to shape light beams,” Opt. Photon. News 20, 22–27 (2009).

Phys. Rev. (1)

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

Phys. Rev. Lett. (3)

M. Specht, J. D. Pedarnig, W. M. Heckl, and T. W. Hänsch, “Scanning plasmon near-field microscope,” Phys. Rev. Lett. 68, 476–479 (1992).
[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]

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94, 033902 (2005).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Microscopic image of an array of the hole-ring coaxials. (b) Schematic of the hybrid hole-ring unit cell. (c) Measured frequency-dependent spectra of the hybrid structures with 80×60μm2 solid particles (dotted curve) and 80×60/60×40μm2 rings (dashed curve) and the hole-only counterpart (solid curve), with a periodicity 160 μm and Ey, the holes are fixed as 100×80μm2.

Fig. 2.
Fig. 2.

(a) Amplitude transmissions of the hole-ring structures with various dimensions of the rings. The holes are fixed as 100×80μm2 with a periodicity 160 μm. L1=80μm, s1=60μm, and L2=60μm are fixed with s2=20 (solid curve) and 40 μm (dotted curve), respectively, with Ey. Inset: peak amplitude transmissions of the ring-only array. (b) With fixed inner dimensions: L2=40μm, s2=20μm, and various outer dimensions: 60×40 (solid curve), 80×40 (dotted curve), and 80×60 (dashed curve) μm2, respectively, with Ey. (c) With a fixed ring width w=10μm, the dimensions of rings are 80×60/60×40μm2 (dotted curve), 70×50/50×30μm2 (dashed curve), and 60×40/40×20μm2 (solid curve), which correspond to g=10, 15, and 20 μm, respectively, with Ey. (d) Resonance frequency (circle) and normalized transmissions (square) of the hybrid structures with various gaps, g=10, 15, and 20 μm, respectively.

Fig. 3.
Fig. 3.

Calculated coupling coefficient as a function of the ring dimensions, Ey.

Fig. 4.
Fig. 4.

Simulated electric field distributions of the hybrid structures with various gaps between the ring and hole. The holes are fixed as 100×80μm2 with a periodicity 160 μm, Ey with the ring dimensions: (a) 60×40/40×20μm2, g=20μm, resonating at 0.54 THz and (b) 80×60/60×40μm2, g=10μm, resonating at 0.45 THz.

Tables (1)

Tables Icon

Table 1. Calculated Coupling Coefficients and Normalized Transmittance for the Hybrid Structures with Various Dimensions of the Inner Ring but Fixed Hole-Ring Gap g=10μm along Both x and y Direction

Equations (1)

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(Ea00Eb)=diag(E1κ12κ12*E2),

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