Abstract

Using a periodic array of split ring resonator holes within a terahertz range, we numerically and experimentally confirmed a zero refractive index at localized waveguide resonant frequency of aluminum film. The effective index was directly calculated from the phase difference of electromagnetic waves passing through film and air. Thickness-independent resonant frequency, as well as spatially static hole resonant modes, clearly verified a zero refractive index. For experimentation, we fabricated samples by means of a femtosecond laser machining system and employed a terahertz time domain spectroscopy system to measure transmitted terahertz pulses. Further, the effective index of refraction extracted from phases and amplitude of measured transmitted pulses confirmed a zero refraction index at resonant frequency.

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    [CrossRef]
  4. F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
  6. Y.-J. Bao, R.-W. Peng, D.-J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N.-B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  20. L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996).
    [CrossRef]

2010

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

S.-H. Lee, S. Gee, C. Kang, and C.-S. Kee, “Terahertz Wave Transmission Properties of Metallic Periodic Structures Printed on a Photo-paper,” J. Opt. Soc. Korea 14(3), 282–285 (2010).
[CrossRef]

2009

I.-B. Sohn, M.-J. Ko, Y.-S. Kim, and Y.-C. Noh, “Direct femtosecond laser lithography for photoresist patterning,” Opt. Eng. 48(2), 024301 (2009).
[CrossRef]

2008

J.-K. Yang, I.-K. Hwang, M.-K. Seo, S.-H. Kim, and Y.-H. Lee, “Plasmon-suppressed vertically-standing nanometal structures,” Opt. Express 16(3), 1951–1957 (2008).
[CrossRef] [PubMed]

Y.-J. Bao, R.-W. Peng, D.-J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N.-B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
[CrossRef] [PubMed]

2007

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet's principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[CrossRef]

H.-T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
[CrossRef] [PubMed]

2006

J. Lee, M. Seo, D. Park, D. Kim, S. Jeoung, Ch. Lienau, Q. H. Park, and P. Planken, “Shape resonance omni-directional terahertz filters with near-unity transmittance,” Opt. Express 14(3), 1253–1259 (2006).
[CrossRef] [PubMed]

J. W. Lee, M. A. Seo, D. J. Park, S. C. Jeoung, Q. H. Park, Ch. Lienau, and D. S. Kim, “Terahertz transparency at Fabry-Perot resonances of periodic slit arrays in a metal plate: experiment and theory,” Opt. Express 14(26), 12637–12643 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

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

2004

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[CrossRef] [PubMed]

2002

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

1996

L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996).
[CrossRef]

Ahn, Y. H.

Averitt, R. D.

Bao, Y.-J.

Y.-J. Bao, R.-W. Peng, D.-J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N.-B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
[CrossRef] [PubMed]

Catrysse, P. B.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[CrossRef] [PubMed]

Chen, H.-T.

Coutaz, J.-L.

L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996).
[CrossRef]

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Duvillaret, L.

L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996).
[CrossRef]

Ebbesen, T. W.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Fan, S.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

García-Vidal, F. J.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

Garet, F.

L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996).
[CrossRef]

Gee, S.

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Giessen, H.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet's principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[CrossRef]

Highstrete, C.

Hwang, I.-K.

Jeoung, S.

Jeoung, S. C.

Kaiser, S.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet's principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[CrossRef]

Kang, C.

Kee, C.-S.

Kim, D.

Kim, D. S.

Kim, S.-H.

Kim, Y.-S.

I.-B. Sohn, M.-J. Ko, Y.-S. Kim, and Y.-C. Noh, “Direct femtosecond laser lithography for photoresist patterning,” Opt. Eng. 48(2), 024301 (2009).
[CrossRef]

Ko, M.-J.

I.-B. Sohn, M.-J. Ko, Y.-S. Kim, and Y.-C. Noh, “Direct femtosecond laser lithography for photoresist patterning,” Opt. Eng. 48(2), 024301 (2009).
[CrossRef]

Kuipers, L.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

Lederer, F.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet's principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[CrossRef]

Lee, J.

Lee, J. W.

Lee, M.

Lee, S.-H.

Lee, Y.-H.

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Lienau, Ch.

Linden, S.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Lu, W.

Y.-J. Bao, R.-W. Peng, D.-J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N.-B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
[CrossRef] [PubMed]

Lu, X.

Y.-J. Bao, R.-W. Peng, D.-J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N.-B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
[CrossRef] [PubMed]

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Martín-Moreno, L.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Meyrath, T. P.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet's principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[CrossRef]

Ming, N.-B.

Y.-J. Bao, R.-W. Peng, D.-J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N.-B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
[CrossRef] [PubMed]

Noh, Y.-C.

I.-B. Sohn, M.-J. Ko, Y.-S. Kim, and Y.-C. Noh, “Direct femtosecond laser lithography for photoresist patterning,” Opt. Eng. 48(2), 024301 (2009).
[CrossRef]

O’Hara, J. F.

Padilla, W. J.

Park, D.

Park, D. J.

Park, Q. H.

Park, Q.-H.

Pendry, J. B.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Peng, R.-W.

Y.-J. Bao, R.-W. Peng, D.-J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N.-B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
[CrossRef] [PubMed]

Planken, P.

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]

Rockstuhl, C.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet's principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[CrossRef]

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]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Seidel, A.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet's principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[CrossRef]

Seo, M.

Seo, M. A.

Seo, M.-K.

Shao, J.

Y.-J. Bao, R.-W. Peng, D.-J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N.-B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
[CrossRef] [PubMed]

Shen, J. T.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[CrossRef] [PubMed]

Shu, D.-J.

Y.-J. Bao, R.-W. Peng, D.-J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N.-B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
[CrossRef] [PubMed]

Smith, D. R.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Sohn, I.-B.

I.-B. Sohn, M.-J. Ko, Y.-S. Kim, and Y.-C. Noh, “Direct femtosecond laser lithography for photoresist patterning,” Opt. Eng. 48(2), 024301 (2009).
[CrossRef]

Sohn, J. Y.

Soukoulis, C. M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Taylor, A. J.

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Wang, M.

Y.-J. Bao, R.-W. Peng, D.-J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N.-B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
[CrossRef] [PubMed]

Wegener, M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Yang, J.-K.

Zentgraf, T.

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet's principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron.

L. Duvillaret, F. Garet, and J.-L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2(3), 739–746 (1996).
[CrossRef]

J. Opt. Soc. Korea

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Opt. Eng.

I.-B. Sohn, M.-J. Ko, Y.-S. Kim, and Y.-C. Noh, “Direct femtosecond laser lithography for photoresist patterning,” Opt. Eng. 48(2), 024301 (2009).
[CrossRef]

Opt. Express

Phys. Rev. B

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet's principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76(3), 033407 (2007).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[CrossRef] [PubMed]

Phys. Rev. Lett.

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]

Y.-J. Bao, R.-W. Peng, D.-J. Shu, M. Wang, X. Lu, J. Shao, W. Lu, and N.-B. Ming, “Role of interference between localized and propagating surface waves on the extraordinary optical transmission through a subwavelength-aperture array,” Phys. Rev. Lett. 101(8), 087401 (2008).
[CrossRef] [PubMed]

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[CrossRef] [PubMed]

Rev. Mod. Phys.

F. J. García-Vidal, L. Martín-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010).
[CrossRef]

Science

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

Other

P. Yeh, Optical Waves in Layered Media (Jhon Wesley & Sons, New Jersey, 1998).

D. Y. Smith, E. Shiles, and M. Inokuti, “Aluminum (Al)” in Handbook of Optical Constant of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985).

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Figures (8)

Fig. 1
Fig. 1

Simulated transmission spectra for y-polarized wave (solid line) and x-polarized wave (dashed line) normal incident on Al film with an array of split ring resonator holes when a = 250 μm, w = 10 μm, l = 110 μm, g = 20 μm, and d = 17.5 μm. The inset depicts dimensions of a split ring resonator hole and the polarization directions of incident light for the hole.

Fig. 2
Fig. 2

Simulated distributions of currents, J, induced by the resonant modes at 0.3571 (a) and 0.7477 THz (b). Arrows indicate both magnitude and directions of the currents. The distributions were drawn in a log-scale.

Fig. 3
Fig. 3

(a) Transmitted electric fields of y-polarized plane waves with the first resonant frequency as a function of time during film presence (solid line) and absence (dashed line). The inverse of one oscillation period, 2.803 ps, corresponded to resonant frequency 0.3571 THz. The difference in film and air refractive indices gave rise to negative time delay −55.55 fs = (neff - 1) d / c, resulting in neff = 0.038. (b) The real and imaginary parts of effective refractive indices, neff (soild circles) and κ eff (open circles), as a function of frequency around 0.3571 THz.

Fig. 4
Fig. 4

Dependence of resonant frequencies for x- and the y-polarized waves on film thickness normalized to d 0 = 17.5 μm. The dashed lines denote the positions of resonant frequencies when d = d 0

Fig. 5
Fig. 5

Electric field evolution in time of an x-polarized wave resonant mode propagated along the z direction in a yz plane and intersecting at the hole center. Film thickness was 100 μm, while the resonant frequency of the x-polarized wave was 0.7276 THz. The different colors represent different times. The dotted lines denote the end faces of the metal film centered on the origin. The ripples on the left side are due to incident interference and reflected waves.

Fig. 6
Fig. 6

(a) Partial microscopic image of the fabricated sample. Geometrical parameters were represented. (b) Schematic view of the THz-TDS experimental setup.

Fig. 7
Fig. 7

Normalized transmission spectra of Al films having arrays of split ring resonator holes with a period of 150 μm (red line) and 260 μm (black line). Dashed arrows denote resonant frequencies.

Fig. 8
Fig. 8

Extracted effective refractive index of Al films with a = 260 μm (a) and a = 150 μm (b).

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