Abstract

We have observed resonant terahertz transmission peaks in samples comprising perforated periodic hole array in a metal film, covered with a high dielectric substrate. These resonant transmissions arise from the interplay between waveguide modes in dielectric substrate and the periodic hole array in the metal film. Finite difference time domain (FDTD) simulations show good agreement with the data, in support of the proposed mechanism. Inducing additional resonant transmissions using guided modes can lead to the ease in tuning the transmission peak frequencies that are potentially useful to terahertz (THz) bio-sensing.

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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. F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
    [CrossRef]
  3. M. Liscidini and J. E. Sipe, “Enhancement of diffraction for biosensing applications via Bloch surface waves,” Appl. Phys. Lett. 91(25), 253125 (2007).
    [CrossRef]
  4. F. Miyamaru, M. W. Takeda, T. Suzuki, and C. Otani, “Highly sensitive surface plasmon terahertz imaging with planar plasmonic crystals,” Opt. Express 15(22), 14804–14809 (2007).
    [CrossRef] [PubMed]
  5. Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006).
    [CrossRef] [PubMed]
  6. W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X. C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007).
    [CrossRef] [PubMed]
  7. F. J. Garcia-Vidial, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
    [CrossRef]
  8. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
    [CrossRef] [PubMed]
  9. D. Qu and D. Grischkowsky, “Observation of a new type of THz resonance of surface plasmons propagating on metal-film hole arrays,” Phys. Rev. Lett. 93(19), 196804 (2004).
    [CrossRef] [PubMed]
  10. F. Miyamaru, Y. Sasagawa, and M. W. Takeda, “Effect of dielectric thin films on reflection properties of metal hole arrays,” Appl. Phys. Lett. 96(2), 021106 (2010).
    [CrossRef]
  11. S. A. Kuznetsov, M. Navarro-Cía, V. V. Kubarev, A. V. Gelfand, M. Beruete, I. Campillo, and M. Sorolla, “Regular and anomalous extraordinary optical transmission at the THz-gap,” Opt. Express 17(14), 11730–11738 (2009).
    [CrossRef] [PubMed]
  12. R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Multiple extraordinary optical transmission peaks from evanescent coupling in perforated metal plates surrounded by dielectrics,” Opt. Express 18(8), 7893–7898 (2010).
    [CrossRef] [PubMed]
  13. J. Han, A. Lakhtakia, Z. Tian, X. Lu, and W. Zhang, “Magnetic and magnetothermal tunabilities of subwavelength-hole arrays in a semiconductor sheet,” Opt. Lett. 34(9), 1465–1467 (2009).
    [CrossRef] [PubMed]
  14. J. Han, X. Lu, and W. Zhang, “Terahertz transmission in subwavelength holes of asymmetric metal-dielectric interfaces: The effect of a dielectric layer,” J. Appl. Phys. 103(3), 033108 (2008).
    [CrossRef]
  15. A. Yu. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced optical transmission, beaming and focusing through a subwavelength slit under excitation of dielectric waveguide modes,” J. Opt. A 11, 125702 (2009).
  16. Simulations were performed using the software CONCERTO 6.5, Vector Fields Limited, England, 2007.
  17. V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
    [CrossRef]
  18. See for example: K. Q. Zhang, and D. Li, “Electromagnetic theory for Microwaves and Optoelectronics” (2nd Edtion, Springer, Berlin, 2008).
    [PubMed]

2010 (2)

2009 (3)

2008 (1)

J. Han, X. Lu, and W. Zhang, “Terahertz transmission in subwavelength holes of asymmetric metal-dielectric interfaces: The effect of a dielectric layer,” J. Appl. Phys. 103(3), 033108 (2008).
[CrossRef]

2007 (4)

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[CrossRef]

M. Liscidini and J. E. Sipe, “Enhancement of diffraction for biosensing applications via Bloch surface waves,” Appl. Phys. Lett. 91(25), 253125 (2007).
[CrossRef]

F. Miyamaru, M. W. Takeda, T. Suzuki, and C. Otani, “Highly sensitive surface plasmon terahertz imaging with planar plasmonic crystals,” Opt. Express 15(22), 14804–14809 (2007).
[CrossRef] [PubMed]

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X. C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007).
[CrossRef] [PubMed]

2006 (1)

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006).
[CrossRef] [PubMed]

2005 (1)

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
[CrossRef]

2004 (1)

D. Qu and D. Grischkowsky, “Observation of a new type of THz resonance of surface plasmons propagating on metal-film hole arrays,” Phys. Rev. Lett. 93(19), 196804 (2004).
[CrossRef] [PubMed]

2003 (1)

F. J. Garcia-Vidial, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
[CrossRef]

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

1998 (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]

Azad, A. K.

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X. C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007).
[CrossRef] [PubMed]

Beruete, M.

Campillo, I.

Chen, J.

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X. C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007).
[CrossRef] [PubMed]

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Ebbesen, T. W.

F. J. Garcia-Vidial, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

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 de Abajo, F. J.

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[CrossRef]

García-Meca, C.

Garcia-Vidal, F. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

García-Vidal, F. J.

A. Yu. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced optical transmission, beaming and focusing through a subwavelength slit under excitation of dielectric waveguide modes,” J. Opt. A 11, 125702 (2009).

Garcia-Vidial, F. J.

F. J. Garcia-Vidial, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
[CrossRef]

Gelfand, A. V.

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]

Grischkowsky, D.

D. Qu and D. Grischkowsky, “Observation of a new type of THz resonance of surface plasmons propagating on metal-film hole arrays,” Phys. Rev. Lett. 93(19), 196804 (2004).
[CrossRef] [PubMed]

Han, J.

J. Han, A. Lakhtakia, Z. Tian, X. Lu, and W. Zhang, “Magnetic and magnetothermal tunabilities of subwavelength-hole arrays in a semiconductor sheet,” Opt. Lett. 34(9), 1465–1467 (2009).
[CrossRef] [PubMed]

J. Han, X. Lu, and W. Zhang, “Terahertz transmission in subwavelength holes of asymmetric metal-dielectric interfaces: The effect of a dielectric layer,” J. Appl. Phys. 103(3), 033108 (2008).
[CrossRef]

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X. C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007).
[CrossRef] [PubMed]

Kubarev, V. V.

Kuznetsov, S. A.

Lakhtakia, A.

Lezec, H. J.

F. J. Garcia-Vidial, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

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]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Liscidini, M.

M. Liscidini and J. E. Sipe, “Enhancement of diffraction for biosensing applications via Bloch surface waves,” Appl. Phys. Lett. 91(25), 253125 (2007).
[CrossRef]

Lomakin, V.

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
[CrossRef]

Lu, X.

J. Han, A. Lakhtakia, Z. Tian, X. Lu, and W. Zhang, “Magnetic and magnetothermal tunabilities of subwavelength-hole arrays in a semiconductor sheet,” Opt. Lett. 34(9), 1465–1467 (2009).
[CrossRef] [PubMed]

J. Han, X. Lu, and W. Zhang, “Terahertz transmission in subwavelength holes of asymmetric metal-dielectric interfaces: The effect of a dielectric layer,” J. Appl. Phys. 103(3), 033108 (2008).
[CrossRef]

Martí, J.

Martínez, A.

Martin-Moreno, L.

F. J. Garcia-Vidial, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Martín-Moreno, L.

A. Yu. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced optical transmission, beaming and focusing through a subwavelength slit under excitation of dielectric waveguide modes,” J. Opt. A 11, 125702 (2009).

Michielssen, E.

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
[CrossRef]

Miyamaru, F.

F. Miyamaru, Y. Sasagawa, and M. W. Takeda, “Effect of dielectric thin films on reflection properties of metal hole arrays,” Appl. Phys. Lett. 96(2), 021106 (2010).
[CrossRef]

F. Miyamaru, M. W. Takeda, T. Suzuki, and C. Otani, “Highly sensitive surface plasmon terahertz imaging with planar plasmonic crystals,” Opt. Express 15(22), 14804–14809 (2007).
[CrossRef] [PubMed]

Navarro-Cía, M.

Nikitin, A. Yu.

A. Yu. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced optical transmission, beaming and focusing through a subwavelength slit under excitation of dielectric waveguide modes,” J. Opt. A 11, 125702 (2009).

Ortuño, R.

Otani, C.

Qiu, M.

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006).
[CrossRef] [PubMed]

Qu, D.

D. Qu and D. Grischkowsky, “Observation of a new type of THz resonance of surface plasmons propagating on metal-film hole arrays,” Phys. Rev. Lett. 93(19), 196804 (2004).
[CrossRef] [PubMed]

Rodríguez-Fortuño, F. J.

Ruan, Z.

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006).
[CrossRef] [PubMed]

Sasagawa, Y.

F. Miyamaru, Y. Sasagawa, and M. W. Takeda, “Effect of dielectric thin films on reflection properties of metal hole arrays,” Appl. Phys. Lett. 96(2), 021106 (2010).
[CrossRef]

Sipe, J. E.

M. Liscidini and J. E. Sipe, “Enhancement of diffraction for biosensing applications via Bloch surface waves,” Appl. Phys. Lett. 91(25), 253125 (2007).
[CrossRef]

Sorolla, M.

Suzuki, T.

Takeda, M. W.

F. Miyamaru, Y. Sasagawa, and M. W. Takeda, “Effect of dielectric thin films on reflection properties of metal hole arrays,” Appl. Phys. Lett. 96(2), 021106 (2010).
[CrossRef]

F. Miyamaru, M. W. Takeda, T. Suzuki, and C. Otani, “Highly sensitive surface plasmon terahertz imaging with planar plasmonic crystals,” Opt. Express 15(22), 14804–14809 (2007).
[CrossRef] [PubMed]

Thio, T.

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]

Tian, Z.

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]

Xu, J.

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X. C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007).
[CrossRef] [PubMed]

Zhang, W.

J. Han, A. Lakhtakia, Z. Tian, X. Lu, and W. Zhang, “Magnetic and magnetothermal tunabilities of subwavelength-hole arrays in a semiconductor sheet,” Opt. Lett. 34(9), 1465–1467 (2009).
[CrossRef] [PubMed]

J. Han, X. Lu, and W. Zhang, “Terahertz transmission in subwavelength holes of asymmetric metal-dielectric interfaces: The effect of a dielectric layer,” J. Appl. Phys. 103(3), 033108 (2008).
[CrossRef]

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X. C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007).
[CrossRef] [PubMed]

Zhang, X. C.

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X. C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

M. Liscidini and J. E. Sipe, “Enhancement of diffraction for biosensing applications via Bloch surface waves,” Appl. Phys. Lett. 91(25), 253125 (2007).
[CrossRef]

F. J. Garcia-Vidial, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83, 4500 (2003).
[CrossRef]

F. Miyamaru, Y. Sasagawa, and M. W. Takeda, “Effect of dielectric thin films on reflection properties of metal hole arrays,” Appl. Phys. Lett. 96(2), 021106 (2010).
[CrossRef]

J. Appl. Phys. (1)

J. Han, X. Lu, and W. Zhang, “Terahertz transmission in subwavelength holes of asymmetric metal-dielectric interfaces: The effect of a dielectric layer,” J. Appl. Phys. 103(3), 033108 (2008).
[CrossRef]

J. Opt. A (1)

A. Yu. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced optical transmission, beaming and focusing through a subwavelength slit under excitation of dielectric waveguide modes,” J. Opt. A 11, 125702 (2009).

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 (1)

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006).
[CrossRef] [PubMed]

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X. C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007).
[CrossRef] [PubMed]

D. Qu and D. Grischkowsky, “Observation of a new type of THz resonance of surface plasmons propagating on metal-film hole arrays,” Phys. Rev. Lett. 93(19), 196804 (2004).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[CrossRef]

Science (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Other (2)

See for example: K. Q. Zhang, and D. Li, “Electromagnetic theory for Microwaves and Optoelectronics” (2nd Edtion, Springer, Berlin, 2008).
[PubMed]

Simulations were performed using the software CONCERTO 6.5, Vector Fields Limited, England, 2007.

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Figures (5)

Fig. 1
Fig. 1

(a) A microscopic optical image of the sample. (b) Top view of the sample, showing the hole array in the Cu metallic film. (c) Side view of the sample together with the coordinate system defined relative to the sample geometry, showing the thick silicon overlayer (bottom) bonded to the metallic layer with the hole array. (d) The transmission spectrum of the sample. The Wood’s anomaly (W-N) frequencies are delineated by the black dashed lines, denoted by the (1,0) and (1,1) gratings of the square lattice. The extra transmission peaks are associated with the guided modes in the silicon overlayer. Inset: Fabry-Perot transmission characteristic of the silicon substrate. From the interference pattern a dielectric constant of 12 is deduced.

Fig. 2
Fig. 2

(a) Upper panel: the measured transmission spectrum. Lower panel: FDTD simulated transmission spectrum. Clear correspondence is seen. (b) Distribution of the Ez component on the x-y interfacial plane between the metal film and the dielectric substrate at resonant transmission frequencies. The positions of the holes in the metal film are delineated by the dashed lines. The upper panel is for the field distributions at the first 6 resonant frequencies, which have the same pattern except for the differences in magnitudes; the lower panel is for the field distribution at the 7th resonant frequency. The waveguiding mode characters are clearly seen from the patterns shown.

Fig. 3
Fig. 3

(a) Dispersion relation for the m = 2 waveguide mode in dielectric layer plotted together with both the light lines in air (for θ = 90 mode) and in silicon. Here θ is the angle between the incident wave vector and the z axis. (b) Folded dispersion of the waveguide mode (and light lines for θ = 90 mode) in the first BZ; the red circle denotes the intersection of the dispersion of the guided mode and the normally propagating light line in air ( θ = 0 ).

Fig. 4
Fig. 4

(a) Simulated field distributions of the Ez component of the electric field at resonant frequencies 0.296 THz and 0.311 THz on the x-z plane passing through two origins of circular holes. (b) Simulated total electric field on the same x-z plane. Concentration of the field intensity in the vicinity of the holes is clearly seen.

Fig. 5
Fig. 5

(a) The transmission spectra of samples with different substrate thicknesses (Red line: 430μm, blue line: 330μm, green line: 380μm and black line: 500μm). (b) The relation between thickness and peak frequency for different modes: solid lines and square dots are calculated and measured transmission peaks for different substrate thicknesses, respectively. For these modes, black color line and square dots are for m = 1 mode, red color line and dots are for m = 2 mode, blue color line and dots are for m = 3 mode, olive color line and dots are for m = 4 mode, and pink color line and dots are for m = 5 modes.

Equations (2)

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k t 2 ω 2 c a 2 = ε a ε s i ω 2 c s i 2 k t 2 tan ( 2 ω 2 c s i 2 k t 2 h m π ) , m = 1 , 2 , ...
( 2 π d ) 2 + ( m π 2 h ) 2 = ε s i ω 2 c 2 , m = 1 , 2 , ...

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