Abstract

A hybrid metamaterial-waveguide (HMW) system, consisting of a plasmon-induced transparency (PIT) metamaterial layer deposited on top of a slab waveguide, is investigated at mid-infrared wavelengths. The proposed hybrid system supports three quasi-guided modes. Two of them are excited through the conventional pathway, i.e. directly excited from the free-space waves via the diffractive coupling, while the theoretical analysis and numerical simulation both demonstrate that the third one undergoes a completely different excitation pathway, i.e. induced by the dark plasmon mode via near field coupling. The interactions between the three quasi-guided modes and the PIT effect further lead to the interesting multi-spectral transmission characteristics that cannot be realized in traditional HMW systems. This is the first report, to our best knowledge, describing this unconventional excitation mechanism of the quasi-guided mode as well as the interaction between the quasi-guided waveguide mode and PIT effect.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (1)

2016 (1)

2015 (2)

P. Ding, J. He, J. Wang, C. Fan, and E. Liang, “Electromagnetically induced transparency in all-dielectric metamaterial-waveguide system,” Appl. Opt. 54(12), 3708–3714 (2015).

I. Al-Naib, Y. Yang, M. M. Dignam, W. Zhang, and R. Singh, “Ultra-high Q even eigenmode resonance in terahertz metamaterials,” Appl. Phys. Lett. 106(1), 011102 (2015).

2013 (4)

J. Liu, B. Xu, J. Zhang, and G. Song, “Double plasmon-induced transparency in hybrid waveguide-plasmon system and its application for localized plasmon resonance sensing with high figure of merit,” Plasmonics 8(2), 995–1001 (2013).

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, “Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).

S. Biswas, J. Duan, D. Nepal, K. Park, R. Pachter, and R. A. Vaia, “Plasmon-induced transparency in the visible region via self-assembled gold nanorod heterodimers,” Nano Lett. 13(12), 6287–6291 (2013).
[PubMed]

X. Shi, D. Han, Y. Dai, Z. Yu, Y. Sun, H. Chen, X. Liu, and J. Zi, “Plasmonic analog of electromagnetically induced transparency in nanostructure graphene,” Opt. Express 21(23), 28438–28443 (2013).
[PubMed]

2012 (2)

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, and Z. Tian, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(13), 131101 (2012).

2011 (1)

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).

2010 (4)

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).

J. Zhang, L. Cai, W. Bai, and G. Song, “Hybrid waveguide-plasmon resonances in gold pillar arrays on top of a dielectric waveguide,” Opt. Lett. 35(20), 3408–3410 (2010).
[PubMed]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[PubMed]

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

2009 (1)

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).

2008 (2)

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[PubMed]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633 (2005).

2004 (1)

V. Yannopapas and N. Stefanou, “Optical excitation of coupled waveguide-particle plasmon modes: A theoretical analysis,” Phys. Rev. B 69(1), 012408 (2004).

2003 (1)

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[PubMed]

2002 (2)

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[PubMed]

2001 (1)

S. Linden, A. Christ, J. Kuhl, and H. Giessen, “Selective suppression of extinction within the plasmon resonance of gold nanoparticles,” Appl. Phys. B 73(4), 311–316 (2001).

1996 (1)

1993 (1)

1991 (1)

K. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[PubMed]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[PubMed]

Al-Naib, I.

I. Al-Naib, Y. Yang, M. M. Dignam, W. Zhang, and R. Singh, “Ultra-high Q even eigenmode resonance in terahertz metamaterials,” Appl. Phys. Lett. 106(1), 011102 (2015).

Aussenegg, F. R.

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

Azad, A. K.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

Bai, W.

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).

J. Zhang, L. Cai, W. Bai, and G. Song, “Hybrid waveguide-plasmon resonances in gold pillar arrays on top of a dielectric waveguide,” Opt. Lett. 35(20), 3408–3410 (2010).
[PubMed]

Biswas, S.

S. Biswas, J. Duan, D. Nepal, K. Park, R. Pachter, and R. A. Vaia, “Plasmon-induced transparency in the visible region via self-assembled gold nanorod heterodimers,” Nano Lett. 13(12), 6287–6291 (2013).
[PubMed]

Boller, K.

K. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[PubMed]

Cai, L.

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).

J. Zhang, L. Cai, W. Bai, and G. Song, “Hybrid waveguide-plasmon resonances in gold pillar arrays on top of a dielectric waveguide,” Opt. Lett. 35(20), 3408–3410 (2010).
[PubMed]

Cao, W.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, “Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).

Chen, H.

Chen, H. T.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[PubMed]

Christ, A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[PubMed]

S. Linden, A. Christ, J. Kuhl, and H. Giessen, “Selective suppression of extinction within the plasmon resonance of gold nanoparticles,” Appl. Phys. B 73(4), 311–316 (2001).

Dai, Y.

Dignam, M. M.

I. Al-Naib, Y. Yang, M. M. Dignam, W. Zhang, and R. Singh, “Ultra-high Q even eigenmode resonance in terahertz metamaterials,” Appl. Phys. Lett. 106(1), 011102 (2015).

Ding, P.

Ditlbacher, H.

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

Duan, J.

S. Biswas, J. Duan, D. Nepal, K. Park, R. Pachter, and R. A. Vaia, “Plasmon-induced transparency in the visible region via self-assembled gold nanorod heterodimers,” Nano Lett. 13(12), 6287–6291 (2013).
[PubMed]

Fan, C.

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[PubMed]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633 (2005).

Galler, N.

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

Gan, Q.

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[PubMed]

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[PubMed]

S. Linden, A. Christ, J. Kuhl, and H. Giessen, “Selective suppression of extinction within the plasmon resonance of gold nanoparticles,” Appl. Phys. B 73(4), 311–316 (2001).

Gippius, N. A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[PubMed]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).

Grigorenko, A. N.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[PubMed]

Gu, J.

M. Liu, Z. Tian, X. Zhang, J. Gu, C. Ouyang, J. Han, and W. Zhang, “Tailoring the plasmon-induced transparency resonances in terahertz metamaterials,” Opt. Express 25(17), 19844–19855 (2017).
[PubMed]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, and Z. Tian, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(13), 131101 (2012).

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[PubMed]

Ham, B. S.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[PubMed]

Han, D.

Han, J.

M. Liu, Z. Tian, X. Zhang, J. Gu, C. Ouyang, J. Han, and W. Zhang, “Tailoring the plasmon-induced transparency resonances in terahertz metamaterials,” Opt. Express 25(17), 19844–19855 (2017).
[PubMed]

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, “Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

Harris, S. E.

K. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[PubMed]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[PubMed]

He, J.

Hemmer, P. R.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[PubMed]

Hohenau, A.

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

Hohenester, U.

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

Imamogdlu, A.

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633 (2005).

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[PubMed]

Imamolu, A.

K. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[PubMed]

Ishihara, T.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).

Jang, W. H.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).

Koller, D. M.

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

Kravets, V. G.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[PubMed]

Krenn, J. R.

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

Kuhl, J.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[PubMed]

S. Linden, A. Christ, J. Kuhl, and H. Giessen, “Selective suppression of extinction within the plasmon resonance of gold nanoparticles,” Appl. Phys. B 73(4), 311–316 (2001).

Lee, Y.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).

Leitner, A.

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

Liang, E.

Linden, S.

S. Linden, A. Christ, J. Kuhl, and H. Giessen, “Selective suppression of extinction within the plasmon resonance of gold nanoparticles,” Appl. Phys. B 73(4), 311–316 (2001).

Liu, J.

J. Liu, B. Xu, J. Zhang, and G. Song, “Double plasmon-induced transparency in hybrid waveguide-plasmon system and its application for localized plasmon resonance sensing with high figure of merit,” Plasmonics 8(2), 995–1001 (2013).

Liu, M.

M. Liu, Z. Tian, X. Zhang, J. Gu, C. Ouyang, J. Han, and W. Zhang, “Tailoring the plasmon-induced transparency resonances in terahertz metamaterials,” Opt. Express 25(17), 19844–19855 (2017).
[PubMed]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

Liu, X.

X. Shi, D. Han, Y. Dai, Z. Yu, Y. Sun, H. Chen, X. Liu, and J. Zi, “Plasmonic analog of electromagnetically induced transparency in nanostructure graphene,” Opt. Express 21(23), 28438–28443 (2013).
[PubMed]

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, and Z. Tian, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(13), 131101 (2012).

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

Lu, Y.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[PubMed]

Ma, Y.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, and Z. Tian, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(13), 131101 (2012).

Magnusson, R.

Maier, S. A.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633 (2005).

Muljarov, E. A.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).

Musser, J. A.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[PubMed]

Nepal, D.

S. Biswas, J. Duan, D. Nepal, K. Park, R. Pachter, and R. A. Vaia, “Plasmon-induced transparency in the visible region via self-assembled gold nanorod heterodimers,” Nano Lett. 13(12), 6287–6291 (2013).
[PubMed]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[PubMed]

Oulton, R. F.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).

Ouyang, C.

Pachter, R.

S. Biswas, J. Duan, D. Nepal, K. Park, R. Pachter, and R. A. Vaia, “Plasmon-induced transparency in the visible region via self-assembled gold nanorod heterodimers,” Nano Lett. 13(12), 6287–6291 (2013).
[PubMed]

Park, K.

S. Biswas, J. Duan, D. Nepal, K. Park, R. Pachter, and R. A. Vaia, “Plasmon-induced transparency in the visible region via self-assembled gold nanorod heterodimers,” Nano Lett. 13(12), 6287–6291 (2013).
[PubMed]

Reil, F.

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

Rhee, J. Y.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).

Schedin, F.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[PubMed]

Schmidt, H.

Shahriar, M. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[PubMed]

Shi, X.

Singh, R.

I. Al-Naib, Y. Yang, M. M. Dignam, W. Zhang, and R. Singh, “Ultra-high Q even eigenmode resonance in terahertz metamaterials,” Appl. Phys. Lett. 106(1), 011102 (2015).

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, “Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, and Z. Tian, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(13), 131101 (2012).

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

Song, G.

J. Liu, B. Xu, J. Zhang, and G. Song, “Double plasmon-induced transparency in hybrid waveguide-plasmon system and its application for localized plasmon resonance sensing with high figure of merit,” Plasmonics 8(2), 995–1001 (2013).

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).

J. Zhang, L. Cai, W. Bai, and G. Song, “Hybrid waveguide-plasmon resonances in gold pillar arrays on top of a dielectric waveguide,” Opt. Lett. 35(20), 3408–3410 (2010).
[PubMed]

Stefanou, N.

V. Yannopapas and N. Stefanou, “Optical excitation of coupled waveguide-particle plasmon modes: A theoretical analysis,” Phys. Rev. B 69(1), 012408 (2004).

Sudarshanam, V. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[PubMed]

Sun, Y.

Taylor, A. J.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

Tian, Z.

M. Liu, Z. Tian, X. Zhang, J. Gu, C. Ouyang, J. Han, and W. Zhang, “Tailoring the plasmon-induced transparency resonances in terahertz metamaterials,” Opt. Express 25(17), 19844–19855 (2017).
[PubMed]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, and Z. Tian, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(13), 131101 (2012).

Tikhodeev, S. G.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[PubMed]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).

Tonouchi, M.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, “Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).

Trügler, A.

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

Turukhin, A. V.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[PubMed]

Vaia, R. A.

S. Biswas, J. Duan, D. Nepal, K. Park, R. Pachter, and R. A. Vaia, “Plasmon-induced transparency in the visible region via self-assembled gold nanorod heterodimers,” Nano Lett. 13(12), 6287–6291 (2013).
[PubMed]

Wang, J.

Wang, S. S.

Wang, Y.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

Xu, B.

J. Liu, B. Xu, J. Zhang, and G. Song, “Double plasmon-induced transparency in hybrid waveguide-plasmon system and its application for localized plasmon resonance sensing with high figure of merit,” Plasmonics 8(2), 995–1001 (2013).

Xu, H.

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).

Xu, Y.

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).

Yablonskii, A. L.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).

Yang, Y.

I. Al-Naib, Y. Yang, M. M. Dignam, W. Zhang, and R. Singh, “Ultra-high Q even eigenmode resonance in terahertz metamaterials,” Appl. Phys. Lett. 106(1), 011102 (2015).

Yannopapas, V.

V. Yannopapas and N. Stefanou, “Optical excitation of coupled waveguide-particle plasmon modes: A theoretical analysis,” Phys. Rev. B 69(1), 012408 (2004).

Yao, J.

Yu, Z.

Yuan, C.

Zentgraf, T.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).

Zhang, C.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, “Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).

Zhang, J.

J. Liu, B. Xu, J. Zhang, and G. Song, “Double plasmon-induced transparency in hybrid waveguide-plasmon system and its application for localized plasmon resonance sensing with high figure of merit,” Plasmonics 8(2), 995–1001 (2013).

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).

J. Zhang, L. Cai, W. Bai, and G. Song, “Hybrid waveguide-plasmon resonances in gold pillar arrays on top of a dielectric waveguide,” Opt. Lett. 35(20), 3408–3410 (2010).
[PubMed]

Zhang, S.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

Zhang, W.

M. Liu, Z. Tian, X. Zhang, J. Gu, C. Ouyang, J. Han, and W. Zhang, “Tailoring the plasmon-induced transparency resonances in terahertz metamaterials,” Opt. Express 25(17), 19844–19855 (2017).
[PubMed]

I. Al-Naib, Y. Yang, M. M. Dignam, W. Zhang, and R. Singh, “Ultra-high Q even eigenmode resonance in terahertz metamaterials,” Appl. Phys. Lett. 106(1), 011102 (2015).

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, “Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

Zhang, X.

M. Liu, Z. Tian, X. Zhang, J. Gu, C. Ouyang, J. Han, and W. Zhang, “Tailoring the plasmon-induced transparency resonances in terahertz metamaterials,” Opt. Express 25(17), 19844–19855 (2017).
[PubMed]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

Zhao, X.

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[PubMed]

Zhu, J.

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, and Z. Tian, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(13), 131101 (2012).

Zhu, L.

Zi, J.

Appl. Opt. (2)

Appl. Phys. B (1)

S. Linden, A. Christ, J. Kuhl, and H. Giessen, “Selective suppression of extinction within the plasmon resonance of gold nanoparticles,” Appl. Phys. B 73(4), 311–316 (2001).

Appl. Phys. Lett. (4)

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, and Z. Tian, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(13), 131101 (2012).

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, “Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).

I. Al-Naib, Y. Yang, M. M. Dignam, W. Zhang, and R. Singh, “Ultra-high Q even eigenmode resonance in terahertz metamaterials,” Appl. Phys. Lett. 106(1), 011102 (2015).

J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparency based on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett. 99(18), 181120 (2011).

Nano Lett. (1)

S. Biswas, J. Duan, D. Nepal, K. Park, R. Pachter, and R. A. Vaia, “Plasmon-induced transparency in the visible region via self-assembled gold nanorod heterodimers,” Nano Lett. 13(12), 6287–6291 (2013).
[PubMed]

Nat. Commun. (1)

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3, 1151 (2012).
[PubMed]

Nat. Mater. (1)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[PubMed]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B (4)

Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B 82(19), 195112 (2010).

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66(4), 045102 (2002).

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).

V. Yannopapas and N. Stefanou, “Optical excitation of coupled waveguide-particle plasmon modes: A theoretical analysis,” Phys. Rev. B 69(1), 012408 (2004).

Phys. Rev. Lett. (7)

D. M. Koller, U. Hohenester, A. Hohenau, H. Ditlbacher, F. Reil, N. Galler, F. R. Aussenegg, A. Leitner, A. Trügler, and J. R. Krenn, “Superresolution Moiré mapping of particle plasmon modes,” Phys. Rev. Lett. 104(14), 143901 (2010).
[PubMed]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[PubMed]

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, “Waveguide-plasmon polaritons: strong coupling of photonic and electronic resonances in a metallic photonic crystal slab,” Phys. Rev. Lett. 91(18), 183901 (2003).
[PubMed]

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[PubMed]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[PubMed]

S. E. Harris, J. E. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[PubMed]

K. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[PubMed]

Plasmonics (1)

J. Liu, B. Xu, J. Zhang, and G. Song, “Double plasmon-induced transparency in hybrid waveguide-plasmon system and its application for localized plasmon resonance sensing with high figure of merit,” Plasmonics 8(2), 995–1001 (2013).

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633 (2005).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the hybrid PITMW system and the normally incident excitation. The top view (b) and the cross-section view (c) of the unit cell.

Fig. 2
Fig. 2

(a) Transmission spectra of the hybrid PITMW system (black solid line) and the PIT metamaterial (red dashed line). The geometrical parameters of the PIT unit cell: Px = 6.6 μm, Py = 6 μm, L = 3.6 μm, W = 1.4 μm, l = 3.1 μm, w = 0.9 μm, s = 1.6 μm, d = 0.4 μm. (b)-(d) Electromagnetic field distributions near the waveguide layer of the PITMW system at Peak 1 to 3: (b) distributions of |E|, Ey, |H|, Hx on the yOz cross section at 9.626 µm; (c) distributions of |E|, Ex, |H|, Hy on the yOz cross section at 9.980 µm; (d) distributions of |E|, Ey, |H|, Hx on the xOz cross section at 10.936 µm.

Fig. 3
Fig. 3

Interaction between the dark plasmon mode and the TE0,y mode. (a-c) Transmission spectra of the hybrid PITMW system (solid lines) for various values of nw from 1.92 to 2.00. The other geometrical parameters are same as before. The insets represent |E| distributions on the yOz plane at the wavelengths indicated by the pink dots. (d) and (e) respectively represent |E| distributions on the xOy plane of the PIT metamaterial and the PITMW system with nw = 2.00 at 10.515 µm indicated by the blue vertical line.

Fig. 4
Fig. 4

Interaction between the PIT window and the TE0,x mode. (a-e) Transmission spectra of the hybrid PITMW system (solid lines) for various values of nw. The geometrical parameters of the PIT unit cell are Px = 6.6 μm, Py = 6 μm, L = 3.8 μm, W = 1.4 μm, l = 3.2 μm, w = 0.9 μm, s = 2 μm, d = 0.4 μm. The insets represent |E| distributions on the xOz plane at the wavelengths indicated by the pink dots. (f-g) represent |E| distributions on the xOy plane of the PIT metamaterial and the PITMW system (nw = 1.85) at 10.699 µm indicated by the green triangle. (h-i) represent |E| distributions on the xOy plane of the PIT metamaterial and the PITMW system (nw = 1.85) at 10.723 µm indicated by the blue triangle.

Equations (3)

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tan(κ t w )= κ( γ c + γ s ) κ 2 γ c γ s , ( TE mode )
tan(κ t w )= n w 2 κ( n s 2 γ c + n c 2 γ s ) n c 2 n s 2 κ 2 n w 4 γ c γ s , ( TM mode )
β= k xy +i 2π P x x+j 2π P y y