Abstract

In this paper, a novel one-dimensional superconducting photonic crystal based on the quasi-periodic Thue–Morse (ThM) arrangement is theoretically investigated by the transfer matrix method, which can switch two transmission properties by controlling ambient temperature. Its transmission spectrum realizes omnidirectional photonic band gap (OBG) characteristics in low-temperature zones (about 10 K) and wide-angle broadband absorption characteristics in high-temperature zones (about 90 K) as the whole structure remains the same in the terahertz regime. The intrinsic reason for switchable functions can be ascribed to the superconducting negative permittivity that is dependent on both temperature and frequency under the superconducting state, which causes an OBG corresponding to the zero-averaged (volume) refractive index (zero-$\bar n $) and broadband absorption induced by high permittivity dissipation. From the numerical results, the OBG from the Bragg gap or absorption bandwidth can be notably tuned by manipulating the periodicity of the ThM sequence and dielectric or superconducting thicknesses. The effects of incident angle and polarization modes on the proposed structure are also considered. We report that the proposed structure has a preeminent zero-$\bar n $ OBG ranging from 0.1 to 1.7 THz at 10 K and stable broadband absorption for a wide angle (at most 70 deg) in TM mode at 90 K, which provides theoretical guidance for the design and application of the temperature-switchable mode selector.

© 2020 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (1)

2015 (1)

Z. Mehdi, “All superconducting photonic crystals with wide-band flat-top responses in visible region,” J. Supercond. Nov. Magn. 28, 3513–3518 (2015).
[Crossref]

2014 (1)

H. F. Zhang, S.-B. Liu, and H. Yang, “Omnidirectional photonic band gap in one-dimensional ternary superconductor-dielectric photonic crystals based on a new Thue-Morse aperiodic structure,” J. Supercon. Nov. Magn. 27, 41–52 (2014).
[Crossref]

2010 (1)

V. V. Grigoriev and F. Biancalana, “Bistability and stationary gap solitons in quasiperiodic photonic crystals based on Thue-Morse sequence,” Photon. Nanostr. Fundam. Applic. 8, 285–290 (2010).
[Crossref]

2009 (2)

2008 (2)

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

H. Rauh and Y. A. Genenko, “The effect of a superconducting surface layer on the optical properties of a dielectric photonic composite,” J. Phys. Condens. Matter 20, 145203 (2008).
[Crossref]

2007 (3)

Y. Xiang, X. Dai, and S. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[Crossref]

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
[Crossref]

L. Moretti and V. Mocella, “Two-dimensional photonic aperiodic crystals based on Thue-Morse sequence,” Opt. Express 15, 15314–15323 (2007).
[Crossref]

2005 (2)

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref]

M. Artoni, G. La Rocca, and F. Bassani, “Resonantly absorbing one-dimensional photonic crystals,” Phys. Rev. E 72, 046604 (2005).
[Crossref]

2004 (1)

L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. Leblanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84, 5186–5188 (2004).
[Crossref]

2003 (2)

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[Crossref]

L. Wu, S. He, and L. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B 67, 235103 (2003).
[Crossref]

2002 (3)

1998 (1)

1985 (1)

M. Suzuki, “Transfer-matrix method and Monte Carlo simulation in quantum spin systems,” Phys. Rev. B 31, 2957–2965 (1985).
[Crossref]

Alamariu, B.

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

Artoni, M.

M. Artoni, G. La Rocca, and F. Bassani, “Resonantly absorbing one-dimensional photonic crystals,” Phys. Rev. E 72, 046604 (2005).
[Crossref]

Bassani, F.

M. Artoni, G. La Rocca, and F. Bassani, “Resonantly absorbing one-dimensional photonic crystals,” Phys. Rev. E 72, 046604 (2005).
[Crossref]

Bermel, P.

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

Biancalana, F.

V. V. Grigoriev and F. Biancalana, “Bistability and stationary gap solitons in quasiperiodic photonic crystals based on Thue-Morse sequence,” Photon. Nanostr. Fundam. Applic. 8, 285–290 (2010).
[Crossref]

Birks, T. A.

Broderick, K.

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

Capolino, F.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref]

Chen, C.

Chen, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[Crossref]

Chen, S.

J. Homola, J. Dostaek, S. Chen, A. Rasooly, S. Y. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Phys. Rev. B 75, 61–69 (2002).
[Crossref]

Dai, X.

Y. Xiang, X. Dai, and S. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[Crossref]

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
[Crossref]

Della Villa, A.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref]

Dostaek, J.

J. Homola, J. Dostaek, S. Chen, A. Rasooly, S. Y. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Phys. Rev. B 75, 61–69 (2002).
[Crossref]

Drouard, E.

Duan, X.

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. Leblanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84, 5186–5188 (2004).
[Crossref]

El Daif, O.

Enoch, S.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref]

Fan, D.

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
[Crossref]

Fave, A.

Galdi, V.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref]

Gaspar-Armenta, J.

Genenko, Y. A.

H. Rauh and Y. A. Genenko, “The effect of a superconducting surface layer on the optical properties of a dielectric photonic composite,” J. Phys. Condens. Matter 20, 145203 (2008).
[Crossref]

Grigoriev, V. V.

V. V. Grigoriev and F. Biancalana, “Bistability and stationary gap solitons in quasiperiodic photonic crystals based on Thue-Morse sequence,” Photon. Nanostr. Fundam. Applic. 8, 285–290 (2010).
[Crossref]

Haavisto, J.

L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. Leblanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84, 5186–5188 (2004).
[Crossref]

He, S.

L. Wu, S. He, and L. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B 67, 235103 (2003).
[Crossref]

Homola, J.

J. Homola, J. Dostaek, S. Chen, A. Rasooly, S. Y. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Phys. Rev. B 75, 61–69 (2002).
[Crossref]

Hong, C.

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

Hu, C.

Jiang, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[Crossref]

Jiang, S. Y.

J. Homola, J. Dostaek, S. Chen, A. Rasooly, S. Y. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Phys. Rev. B 75, 61–69 (2002).
[Crossref]

Joannopoulos, J.

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

Kaminski, A.

Kimerling, L.

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

Kimerling, L. C.

L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. Leblanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84, 5186–5188 (2004).
[Crossref]

Knight, J. C.

La Rocca, G.

M. Artoni, G. La Rocca, and F. Bassani, “Resonantly absorbing one-dimensional photonic crystals,” Phys. Rev. E 72, 046604 (2005).
[Crossref]

Leblanc, J.

L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. Leblanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84, 5186–5188 (2004).
[Crossref]

Lemiti, M.

Letartre, X.

Li, H.

C. Chen, X. Li, H. Li, K. Xu, J. Wu, and J. Lin, “Bandpass filters based on phase-shifted photonic crystal waveguide gratings,” Opt. Express 15, 11278–11284 (2009).
[Crossref]

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[Crossref]

Li, X.

Lin, J.

Liu, G.

Liu, J.

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

Liu, S.-B.

H. F. Zhang, S.-B. Liu, and H. Yang, “Omnidirectional photonic band gap in one-dimensional ternary superconductor-dielectric photonic crystals based on a new Thue-Morse aperiodic structure,” J. Supercon. Nov. Magn. 27, 41–52 (2014).
[Crossref]

Lopez-Ríos, T.

Mehdi, Z.

Z. Mehdi, “All superconducting photonic crystals with wide-band flat-top responses in visible region,” J. Supercond. Nov. Magn. 28, 3513–3518 (2015).
[Crossref]

Michel, J.

L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. Leblanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84, 5186–5188 (2004).
[Crossref]

Mocella, V.

Moretti, L.

Negro, L. D.

L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. Leblanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84, 5186–5188 (2004).
[Crossref]

Park, Y.

Pierro, V.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref]

Ramos-Mendieta, F.

Rarity, J. G.

Rasooly, A.

J. Homola, J. Dostaek, S. Chen, A. Rasooly, S. Y. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Phys. Rev. B 75, 61–69 (2002).
[Crossref]

Rauh, H.

H. Rauh and Y. A. Genenko, “The effect of a superconducting surface layer on the optical properties of a dielectric photonic composite,” J. Phys. Condens. Matter 20, 145203 (2008).
[Crossref]

Regalado, L.

Russell, P. S. J.

Seassal, C.

Shen, L.

L. Wu, S. He, and L. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B 67, 235103 (2003).
[Crossref]

Stolfi, M.

L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. Leblanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84, 5186–5188 (2004).
[Crossref]

Suzuki, M.

M. Suzuki, “Transfer-matrix method and Monte Carlo simulation in quantum spin systems,” Phys. Rev. B 31, 2957–2965 (1985).
[Crossref]

Tayeb, G.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref]

Viktorovitch, P.

Villa, F.

Wen, S.

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
[Crossref]

Y. Xiang, X. Dai, and S. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[Crossref]

Wu, J.

Wu, L.

L. Wu, S. He, and L. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B 67, 235103 (2003).
[Crossref]

Xiang, Y.

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
[Crossref]

Y. Xiang, X. Dai, and S. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[Crossref]

Xu, K.

Yang, H.

H. F. Zhang, S.-B. Liu, and H. Yang, “Omnidirectional photonic band gap in one-dimensional ternary superconductor-dielectric photonic crystals based on a new Thue-Morse aperiodic structure,” J. Supercon. Nov. Magn. 27, 41–52 (2014).
[Crossref]

Yee, S. S.

J. Homola, J. Dostaek, S. Chen, A. Rasooly, S. Y. Jiang, and S. S. Yee, “Spectral surface plasmon resonance biosensor for detection of staphylococcal enterotoxin B in milk,” Phys. Rev. B 75, 61–69 (2002).
[Crossref]

Yi, Y.

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

L. D. Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. Leblanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals,” Appl. Phys. Lett. 84, 5186–5188 (2004).
[Crossref]

Zeng, L.

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

Zhang, H.

Zhang, H. F.

H. F. Zhang, S.-B. Liu, and H. Yang, “Omnidirectional photonic band gap in one-dimensional ternary superconductor-dielectric photonic crystals based on a new Thue-Morse aperiodic structure,” J. Supercon. Nov. Magn. 27, 41–52 (2014).
[Crossref]

Zhang, Y.

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[Crossref]

Zhu, S.

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

H. Jiang, H. Chen, H. Li, Y. Zhang, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[Crossref]

L. Zeng, P. Bermel, Y. Yi, B. Alamariu, K. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Appl. Phys. Lett. 93, 221105 (2008).
[Crossref]

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[Crossref]

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[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Diagrams of the (${{\rm ThM}_6}$)M structure in the 1D SPCs. Specific substitutions for lattices A and B.
Fig. 2.
Fig. 2. [(a) and (d)] Dispersion curves, [(b) or (c)] reflection curves at 10 K, and [(e) or (f)] absorption curves at 90 K versus sequence orders or effective refractive indices for the (${{\rm ThM}_6}$)M structure at 0° in the 1D SPCs. The gray rectangle in (a) represents the PBG regions at 10 K, and the brown stripe frame in (f) signifies the absorption area at 90 K in (f).
Fig. 3.
Fig. 3. (a) Calculated reflection spectra at 10 K and (b) absorption spectra at 90 K versus different incident angles for both TE and TM polarizations in the (${{\rm ThM}_6}$)M structure. The black dashed line in both (a) and (b) represents the boundary of the polarization modes. The white dashed frame in (a) indicates the existence of OBG regions.
Fig. 4.
Fig. 4. Absolute value of ${\cos}(\kappa z)$ versus different temperatures as the incident angle is 0°, 20°, 40°, 60°, and 80° at 1.6 THz for the (a) TM polarization and (b) TE polarizations in the (${{\rm ThM}_6}$)M structure.
Fig. 5.
Fig. 5. Calculated reflection spectra at 10 K versus four different incident angles for the (${{\rm ThM}_6}$)M structure as (the thicknesses of B1) ${d_1}$ varies from 1 to 5 µm in the 1D SPCs. The black solid and grey dotted lines represent TM- and TE-polarization modes.
Fig. 6.
Fig. 6. Broken line graph of the maximum continuous absorption zones $\Delta\alpha $ at 90 K as the superconducting thickness $h$ varies from 0.1 to 2 nm and its interval of 0.1 nm for five different incident angles in the (${{\rm ThM}_6}$)M structure.

Equations (13)

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σ B ( ω , T ) = σ B ( ω , T ) j σ B ( ω , T ) = ε 0 ω p 2 τ 1 + j ω τ x n + j 1 ω μ 0 λ L 2 x s = ε 0 ω p 2 τ 1 + ω 2 τ 2 x n + j ( ε 0 ω p 2 τ 2 ω 1 + ω 2 τ 2 x n + 1 ω μ 0 λ L 2 x s ) ,
ε B ( ω , T ) = j σ B ( ω , T ) ω ε 0 .
n B = n B j n B = ε B .
λ L ( T ) = λ 0 1 ( T / T C ) p
x s = 1 ( T / T C ) 4 ;
M i = [ cos δ i j η i sin δ i j n i sin δ i cos δ i ] ,
M = Π i = 1 N M i = [ m 11 m 12 m 21 m 22 ] .
cos κ z = cos ( n ¯ ω a cos θ c ) ( η 1 z 2 η 2 z + η 2 z 2 η 1 z 1 ) × sin ( δ 1 z ) sin ( δ 2 z ) ,
| cos κ z | = 1 + ( η 1 z 2 η 2 z + η 2 z 2 η 1 z 1 ) × | sin ( δ 1 z ) sin ( δ 2 z ) | 1.
ϕ t = κ ( ω ) L = ω c n e f f ( ω ) L ,
r = ( m 11 + m 12 η N + 1 ) η 0 ( m 21 + m 22 η N + 1 ) m 11 η 0 + m 22 η N + 1 + m 21 + m 12 η N + 1 η 0 ,
t = 2 η 0 m 11 η 0 + m 22 η N + 1 + m 21 + m 12 η N + 1 η 0 .
A ( ω ) = 1 R ( ω ) T ( ω ) ,

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