Abstract

The angle- and thickness-dependent photonic band structures in a one-dimensional superconducting photonic crystal are theoretically investigated. The analysis is made within the framework of the Bloch theorem together with the transfer matrix method in a multilayer structure. The photonic band structures are investigated as functions of the thicknesses of the constituent superconducting and dielectric layers. Additionally, the effects coming from the oblique incident angle for both TE and TM waves are also numerically elucidated. The existence of omnidirectional gaps in this kind of photonic crystal is also found.

© 2009 Optical Society of America

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References

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  1. J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton Univ. Press, 1995).
  2. E. Yablonovitch, “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  3. C. M. Soukoulis, Photonic Band Gap Materials (Kluwer Academic, 1996).
  4. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679-1682 (1998).
    [CrossRef] [PubMed]
  5. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25-28 (1999).
    [CrossRef]
  6. E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283-295 (1993).
    [CrossRef]
  7. H. Contopanagos, E. Yablonovitch, and N. G. Alexopoulos, “Electromagnetic properties of periodic multilayers of ultrathin metallic films from dc to ultraviolet frequencies,” J. Opt. Soc. Am. A 16, 2294-2306 (1999).
    [CrossRef]
  8. C. H. Raymond Ooi and T. C. Au Yeung, “Polariton gap in a superconductor-dielectric superlattice,” Phys. Lett. A 259, 413-419 (1999).
    [CrossRef]
  9. C. H. Raymond Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920-5926 (2000).
    [CrossRef]
  10. C.-J. Wu, M.-S. Chen, and T.-J. Yang, “Photonic band structure in a superconductor-dielectric superlattice,” Physica C 432, 133-138 (2005).
    [CrossRef]
  11. C.-J. Wu, “Transmission and reflection in a periodic superconductor/dielectric film multilayer structure,” J. Electromagn. Waves Appl. 19, 1991-1996 (2005).
    [CrossRef]
  12. O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculation of the band structure,” Phys. Rev. B 74, 092505 (2006).
    [CrossRef]
  13. A. H. Aly, H.-T. Hsu, T.-J. Yang, C.-J. Wu, and C. K. Hwangbo, “Extraordinary optical properties of a superconducting periodic multilayer in near-zero-permittivity operation range,” J. Appl. Phys. 105, 083917 (2009).
    [CrossRef]
  14. P. Yeh, Optical Waves in Layered Media (Wiley, 1998).
  15. K. Fosshein, Superconducting Technology: 10 Case Studies (World Scientific, 1991).
  16. C. Kittel, Introduction to Solid State Physics (Wiley, 2005).

2009

A. H. Aly, H.-T. Hsu, T.-J. Yang, C.-J. Wu, and C. K. Hwangbo, “Extraordinary optical properties of a superconducting periodic multilayer in near-zero-permittivity operation range,” J. Appl. Phys. 105, 083917 (2009).
[CrossRef]

2006

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculation of the band structure,” Phys. Rev. B 74, 092505 (2006).
[CrossRef]

2005

C.-J. Wu, M.-S. Chen, and T.-J. Yang, “Photonic band structure in a superconductor-dielectric superlattice,” Physica C 432, 133-138 (2005).
[CrossRef]

C.-J. Wu, “Transmission and reflection in a periodic superconductor/dielectric film multilayer structure,” J. Electromagn. Waves Appl. 19, 1991-1996 (2005).
[CrossRef]

2000

C. H. Raymond Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920-5926 (2000).
[CrossRef]

1999

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

C. H. Raymond Ooi and T. C. Au Yeung, “Polariton gap in a superconductor-dielectric superlattice,” Phys. Lett. A 259, 413-419 (1999).
[CrossRef]

H. Contopanagos, E. Yablonovitch, and N. G. Alexopoulos, “Electromagnetic properties of periodic multilayers of ultrathin metallic films from dc to ultraviolet frequencies,” J. Opt. Soc. Am. A 16, 2294-2306 (1999).
[CrossRef]

1998

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

1993

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Alexopoulos, N. G.

Aly, A. H.

A. H. Aly, H.-T. Hsu, T.-J. Yang, C.-J. Wu, and C. K. Hwangbo, “Extraordinary optical properties of a superconducting periodic multilayer in near-zero-permittivity operation range,” J. Appl. Phys. 105, 083917 (2009).
[CrossRef]

Au Yeung, T. C.

C. H. Raymond Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920-5926 (2000).
[CrossRef]

C. H. Raymond Ooi and T. C. Au Yeung, “Polariton gap in a superconductor-dielectric superlattice,” Phys. Lett. A 259, 413-419 (1999).
[CrossRef]

Berman, O. L.

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculation of the band structure,” Phys. Rev. B 74, 092505 (2006).
[CrossRef]

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Chen, M.-S.

C.-J. Wu, M.-S. Chen, and T.-J. Yang, “Photonic band structure in a superconductor-dielectric superlattice,” Physica C 432, 133-138 (2005).
[CrossRef]

Chigrin, D. N.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Coalson, R. D.

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculation of the band structure,” Phys. Rev. B 74, 092505 (2006).
[CrossRef]

Contopanagos, H.

Eiderman, S. L.

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculation of the band structure,” Phys. Rev. B 74, 092505 (2006).
[CrossRef]

Fan, S.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Fink, Y.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Fosshein, K.

K. Fosshein, Superconducting Technology: 10 Case Studies (World Scientific, 1991).

Gaponenko, S. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Hsu, H.-T.

A. H. Aly, H.-T. Hsu, T.-J. Yang, C.-J. Wu, and C. K. Hwangbo, “Extraordinary optical properties of a superconducting periodic multilayer in near-zero-permittivity operation range,” J. Appl. Phys. 105, 083917 (2009).
[CrossRef]

Hwangbo, C. K.

A. H. Aly, H.-T. Hsu, T.-J. Yang, C.-J. Wu, and C. K. Hwangbo, “Extraordinary optical properties of a superconducting periodic multilayer in near-zero-permittivity operation range,” J. Appl. Phys. 105, 083917 (2009).
[CrossRef]

Joannopoulos, J. D.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton Univ. Press, 1995).

Kam, C. H.

C. H. Raymond Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920-5926 (2000).
[CrossRef]

Kittel, C.

C. Kittel, Introduction to Solid State Physics (Wiley, 2005).

Lavrinenko, A. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Lim, T. K.

C. H. Raymond Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920-5926 (2000).
[CrossRef]

Lozovik, Y. E.

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculation of the band structure,” Phys. Rev. B 74, 092505 (2006).
[CrossRef]

Meade, R.

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton Univ. Press, 1995).

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Raymond Ooi, C. H.

C. H. Raymond Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920-5926 (2000).
[CrossRef]

C. H. Raymond Ooi and T. C. Au Yeung, “Polariton gap in a superconductor-dielectric superlattice,” Phys. Lett. A 259, 413-419 (1999).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, Photonic Band Gap Materials (Kluwer Academic, 1996).

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Winn, J.

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton Univ. Press, 1995).

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Wu, C.-J.

A. H. Aly, H.-T. Hsu, T.-J. Yang, C.-J. Wu, and C. K. Hwangbo, “Extraordinary optical properties of a superconducting periodic multilayer in near-zero-permittivity operation range,” J. Appl. Phys. 105, 083917 (2009).
[CrossRef]

C.-J. Wu, M.-S. Chen, and T.-J. Yang, “Photonic band structure in a superconductor-dielectric superlattice,” Physica C 432, 133-138 (2005).
[CrossRef]

C.-J. Wu, “Transmission and reflection in a periodic superconductor/dielectric film multilayer structure,” J. Electromagn. Waves Appl. 19, 1991-1996 (2005).
[CrossRef]

Yablonovitch, E.

Yang, T.-J.

A. H. Aly, H.-T. Hsu, T.-J. Yang, C.-J. Wu, and C. K. Hwangbo, “Extraordinary optical properties of a superconducting periodic multilayer in near-zero-permittivity operation range,” J. Appl. Phys. 105, 083917 (2009).
[CrossRef]

C.-J. Wu, M.-S. Chen, and T.-J. Yang, “Photonic band structure in a superconductor-dielectric superlattice,” Physica C 432, 133-138 (2005).
[CrossRef]

Yarotsky, D. A.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1998).

Appl. Phys. A

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

J. Appl. Phys.

A. H. Aly, H.-T. Hsu, T.-J. Yang, C.-J. Wu, and C. K. Hwangbo, “Extraordinary optical properties of a superconducting periodic multilayer in near-zero-permittivity operation range,” J. Appl. Phys. 105, 083917 (2009).
[CrossRef]

J. Electromagn. Waves Appl.

C.-J. Wu, “Transmission and reflection in a periodic superconductor/dielectric film multilayer structure,” J. Electromagn. Waves Appl. 19, 1991-1996 (2005).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Phys. Lett. A

C. H. Raymond Ooi and T. C. Au Yeung, “Polariton gap in a superconductor-dielectric superlattice,” Phys. Lett. A 259, 413-419 (1999).
[CrossRef]

Phys. Rev. B

C. H. Raymond Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920-5926 (2000).
[CrossRef]

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculation of the band structure,” Phys. Rev. B 74, 092505 (2006).
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Physica C

C.-J. Wu, M.-S. Chen, and T.-J. Yang, “Photonic band structure in a superconductor-dielectric superlattice,” Physica C 432, 133-138 (2005).
[CrossRef]

Science

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Other

C. M. Soukoulis, Photonic Band Gap Materials (Kluwer Academic, 1996).

P. Yeh, Optical Waves in Layered Media (Wiley, 1998).

K. Fosshein, Superconducting Technology: 10 Case Studies (World Scientific, 1991).

C. Kittel, Introduction to Solid State Physics (Wiley, 2005).

J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton Univ. Press, 1995).

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Figures (8)

Fig. 1
Fig. 1

One-dimensional superconductor–dielectric superlattice, where layer 2 is the superconductor with refractive index n 2 and thickness d 2 , layer 3 is the dielectric with refractive index n 3 and thickness d 3 , and the spatial periodicity is Λ = d 2 + d 3 .

Fig. 2
Fig. 2

Calculated frequency-dependent transmittance (top) and band structure (bottom) at normal incidence. Here the solid curve is plotted for d 2 = 50 nm and d 3 = 50 nm , the dotted curve is for the bulk superconductor, i.e., d 2 = 100 nm and d 3 = 0 , and the straight gray line is for the bulk dielectric, i.e., d 2 = 0 and d 3 = 100 nm .

Fig. 3
Fig. 3

Calculated band structures for three different thickness ratios, ρ = d 2 d 3 = 1 3 , 1 , 3 . Here Λ = d 2 + d 3 is fixed at 100 nm .

Fig. 4
Fig. 4

Calculated equal-thickness ( d 2 = d 3 ) band structures for three different spatial periodicities Λ, 100 nm (solid), 150 nm (dotted), and 200 nm (dashed).

Fig. 5
Fig. 5

Calculated TE wave band structures at 0°, 45°, and 85° for d 2 = d 3 = 50 nm .

Fig. 6
Fig. 6

Calculated TM wave photonic band structure at d 2 = d 3 = 50 nm , where the the second band of normal incidence (gray dashed curve) is split into two bands at 15°.

Fig. 7
Fig. 7

Calculated TM wave photonic band structure at three distinct ρ = 1 3 , 2 3 , 1 . Here Λ = d 2 + d 3 = 100 nm , and the incident angle is 15°. The shaded strips represent the SPGs.

Fig. 8
Fig. 8

Calculated angle-dependent band structures for both TM and TE waves at d 2 = d 3 = 50 nm . There are two omnidirectional gaps. One is in the low-frequency gap, and the other is in the second PBG.

Equations (17)

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2 ψ + k s 2 ψ = 0 ,
k s = ω 2 μ 0 ϵ 0 λ L 2 ,
λ L ( T ) = λ L ( 0 ) 1 ( T T c ) 4 .
ϵ 2 r = ( k s k 0 ) 2 = 1 1 ω 2 μ 0 ϵ 0 λ L 2 ,
ω λ = 1 λ L μ 0 ϵ 0 .
t = 1 M 11 ,
M = ( M 11 M 12 M 21 M 22 ) = D 1 1 M Λ N D 1
M Λ = D 2 P 2 D 2 1 D 3 P 3 D 3 1 .
P l = ( e i ϕ l 0 0 e i ϕ l ) ,
ϕ l = k l x d l = 2 π d l λ n l cos θ l ( l = 2 , 3 ) .
D l = ( 1 1 n l cos θ l n l cos θ l ) ,
D l = ( cos θ l cos θ l n l n l ) ,
n 1 sin θ 1 = n 2 sin θ 2 = n 3 sin θ 3 .
cos ( K Λ ) = cos ( k 2 x d 2 ) cos ( k 3 x d 3 ) 1 2 ( p q + q p ) sin ( k 2 x d 2 ) sin ( k 3 x d 3 ) ,
k 2 x 2 = ω 2 μ 0 ϵ 0 cos 2 θ 1 λ L 2 , k 3 x 2 = ω 2 μ 0 ϵ 0 ( ϵ 3 r sin 2 θ ) ,
p q k 3 x k 2 x = ϵ r sin 2 θ cos 2 θ 1 ω 2 μ 0 ϵ 0 λ L 2
p q = ϵ r sin 2 θ cos 2 θ 1 ω 2 μ 0 ϵ 0 λ L 2 1 ( 1 ω 2 μ 0 ϵ 0 λ L 2 ) ϵ 3 r ,

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