Abstract

Optical properties of a nearly ferroelectric superconductor in the dielectric response are theoretically investigated based on the electrodynamics of the nearly ferroelectric superconductors. The optical reflectance and transmittance of TE and TM waves are calculated and analyzed for two model structures, a superconductor occupying the half-space and a superconducting film of finite thickness. At the oblique incidence to a free-space–superconductor interface, it is found that the Brewster angle of a TM wave is close to the grazing angle of incidence. In the transmittance spectrum for a superconducting film, a sharp comblike distribution of the resonance peaks is found. These peaks are not regularly spaced in the frequency domain. The number of peaks increases substantially with an increase in the thickness of the film. In addition, the effect of the oblique incidence on this anomalous comblike distribution in a TM wave is stronger than that of a TE wave.

© 2006 Optical Society of America

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  1. M. Golosovsky, M. Tsidlekht, and D. Davidov, "High-frequency vortex dynamics in YBa2Cu3O7," Supercond. Sci. Technol. 9, 1-15 (1996).
    [CrossRef]
  2. M. R. Trunin, "Temperature dependence of microwave surface impedance in high-Tc single crystals: experimental and theoretical aspects," J. Supercond. 11, 381-408 (1998).
  3. J. Gollop, "Microwave applications of high-temperature superconductors," Supercond. Sci. Technol. 10, 120-141 (1997).
    [CrossRef]
  4. V. M. Pan, D. A. Luzhbin, A. A. Kalenyuk, A. L. Kasatkin, V. A. Komashko, A. V. Velichko, and M. Lancaster, "Microwave impedance of YBa2Cu3O7−δ high-temperature superconductor films in a magnetic field," Low Temp. Phys. 31, 254-262 (2005), and references therein.
    [CrossRef]
  5. Y. Levi, O. Millo, A. Sharoni, Y. Tsabba, G. Leitus, and S. Reich, "Evidence for localized high-Tc superconducting regimes on the surface of Na-doped WO3," Europhys. Lett. 51, 564-570 (2000).
    [CrossRef]
  6. M. L. Cohen, "Superconductivity in many-valley semiconductors and in semimetals," Phys. Rev. 134, A511-A521 (1964).
    [CrossRef]
  7. C. S. Koonce, M. L. Cohen, J. E. Schooley, W. R. Hosler, and L. F. Pfeiffer, "Superconducting transition temperature of semiconducting SrTiO3," Phys. Rev. 163, 380-390 (1967).
    [CrossRef]
  8. E. Savaguchi, A. Kukuchi, and Y. Codera, "Dielectric constant of strontium titanate at low temperature," J. Phys. Soc. Jpn. 17, 1666-1667 (1962).
    [CrossRef]
  9. J. L. Birman and N. A. Zimbovskaya, "Electrodynamics of nearly ferroelectric superconductors," Phys. Rev. B 64, 144506 (2001).
    [CrossRef]
  10. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  11. C. H. R. Ooi and T. C. A. Yeung, "Polariton gap in a superconductor-dielectric superlattice," Phys. Lett. A 259, 413-419 (1999).
    [CrossRef]

2005 (1)

V. M. Pan, D. A. Luzhbin, A. A. Kalenyuk, A. L. Kasatkin, V. A. Komashko, A. V. Velichko, and M. Lancaster, "Microwave impedance of YBa2Cu3O7−δ high-temperature superconductor films in a magnetic field," Low Temp. Phys. 31, 254-262 (2005), and references therein.
[CrossRef]

2001 (1)

J. L. Birman and N. A. Zimbovskaya, "Electrodynamics of nearly ferroelectric superconductors," Phys. Rev. B 64, 144506 (2001).
[CrossRef]

2000 (1)

Y. Levi, O. Millo, A. Sharoni, Y. Tsabba, G. Leitus, and S. Reich, "Evidence for localized high-Tc superconducting regimes on the surface of Na-doped WO3," Europhys. Lett. 51, 564-570 (2000).
[CrossRef]

1999 (1)

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

1998 (1)

M. R. Trunin, "Temperature dependence of microwave surface impedance in high-Tc single crystals: experimental and theoretical aspects," J. Supercond. 11, 381-408 (1998).

1997 (1)

J. Gollop, "Microwave applications of high-temperature superconductors," Supercond. Sci. Technol. 10, 120-141 (1997).
[CrossRef]

1996 (1)

M. Golosovsky, M. Tsidlekht, and D. Davidov, "High-frequency vortex dynamics in YBa2Cu3O7," Supercond. Sci. Technol. 9, 1-15 (1996).
[CrossRef]

1967 (1)

C. S. Koonce, M. L. Cohen, J. E. Schooley, W. R. Hosler, and L. F. Pfeiffer, "Superconducting transition temperature of semiconducting SrTiO3," Phys. Rev. 163, 380-390 (1967).
[CrossRef]

1964 (1)

M. L. Cohen, "Superconductivity in many-valley semiconductors and in semimetals," Phys. Rev. 134, A511-A521 (1964).
[CrossRef]

1962 (1)

E. Savaguchi, A. Kukuchi, and Y. Codera, "Dielectric constant of strontium titanate at low temperature," J. Phys. Soc. Jpn. 17, 1666-1667 (1962).
[CrossRef]

Birman, J. L.

J. L. Birman and N. A. Zimbovskaya, "Electrodynamics of nearly ferroelectric superconductors," Phys. Rev. B 64, 144506 (2001).
[CrossRef]

Codera, Y.

E. Savaguchi, A. Kukuchi, and Y. Codera, "Dielectric constant of strontium titanate at low temperature," J. Phys. Soc. Jpn. 17, 1666-1667 (1962).
[CrossRef]

Cohen, M. L.

C. S. Koonce, M. L. Cohen, J. E. Schooley, W. R. Hosler, and L. F. Pfeiffer, "Superconducting transition temperature of semiconducting SrTiO3," Phys. Rev. 163, 380-390 (1967).
[CrossRef]

M. L. Cohen, "Superconductivity in many-valley semiconductors and in semimetals," Phys. Rev. 134, A511-A521 (1964).
[CrossRef]

Davidov, D.

M. Golosovsky, M. Tsidlekht, and D. Davidov, "High-frequency vortex dynamics in YBa2Cu3O7," Supercond. Sci. Technol. 9, 1-15 (1996).
[CrossRef]

Gollop, J.

J. Gollop, "Microwave applications of high-temperature superconductors," Supercond. Sci. Technol. 10, 120-141 (1997).
[CrossRef]

Golosovsky, M.

M. Golosovsky, M. Tsidlekht, and D. Davidov, "High-frequency vortex dynamics in YBa2Cu3O7," Supercond. Sci. Technol. 9, 1-15 (1996).
[CrossRef]

Hosler, W. R.

C. S. Koonce, M. L. Cohen, J. E. Schooley, W. R. Hosler, and L. F. Pfeiffer, "Superconducting transition temperature of semiconducting SrTiO3," Phys. Rev. 163, 380-390 (1967).
[CrossRef]

Kalenyuk, A. A.

V. M. Pan, D. A. Luzhbin, A. A. Kalenyuk, A. L. Kasatkin, V. A. Komashko, A. V. Velichko, and M. Lancaster, "Microwave impedance of YBa2Cu3O7−δ high-temperature superconductor films in a magnetic field," Low Temp. Phys. 31, 254-262 (2005), and references therein.
[CrossRef]

Kasatkin, A. L.

V. M. Pan, D. A. Luzhbin, A. A. Kalenyuk, A. L. Kasatkin, V. A. Komashko, A. V. Velichko, and M. Lancaster, "Microwave impedance of YBa2Cu3O7−δ high-temperature superconductor films in a magnetic field," Low Temp. Phys. 31, 254-262 (2005), and references therein.
[CrossRef]

Komashko, V. A.

V. M. Pan, D. A. Luzhbin, A. A. Kalenyuk, A. L. Kasatkin, V. A. Komashko, A. V. Velichko, and M. Lancaster, "Microwave impedance of YBa2Cu3O7−δ high-temperature superconductor films in a magnetic field," Low Temp. Phys. 31, 254-262 (2005), and references therein.
[CrossRef]

Koonce, C. S.

C. S. Koonce, M. L. Cohen, J. E. Schooley, W. R. Hosler, and L. F. Pfeiffer, "Superconducting transition temperature of semiconducting SrTiO3," Phys. Rev. 163, 380-390 (1967).
[CrossRef]

Kukuchi, A.

E. Savaguchi, A. Kukuchi, and Y. Codera, "Dielectric constant of strontium titanate at low temperature," J. Phys. Soc. Jpn. 17, 1666-1667 (1962).
[CrossRef]

Lancaster, M.

V. M. Pan, D. A. Luzhbin, A. A. Kalenyuk, A. L. Kasatkin, V. A. Komashko, A. V. Velichko, and M. Lancaster, "Microwave impedance of YBa2Cu3O7−δ high-temperature superconductor films in a magnetic field," Low Temp. Phys. 31, 254-262 (2005), and references therein.
[CrossRef]

Leitus, G.

Y. Levi, O. Millo, A. Sharoni, Y. Tsabba, G. Leitus, and S. Reich, "Evidence for localized high-Tc superconducting regimes on the surface of Na-doped WO3," Europhys. Lett. 51, 564-570 (2000).
[CrossRef]

Levi, Y.

Y. Levi, O. Millo, A. Sharoni, Y. Tsabba, G. Leitus, and S. Reich, "Evidence for localized high-Tc superconducting regimes on the surface of Na-doped WO3," Europhys. Lett. 51, 564-570 (2000).
[CrossRef]

Luzhbin, D. A.

V. M. Pan, D. A. Luzhbin, A. A. Kalenyuk, A. L. Kasatkin, V. A. Komashko, A. V. Velichko, and M. Lancaster, "Microwave impedance of YBa2Cu3O7−δ high-temperature superconductor films in a magnetic field," Low Temp. Phys. 31, 254-262 (2005), and references therein.
[CrossRef]

Millo, O.

Y. Levi, O. Millo, A. Sharoni, Y. Tsabba, G. Leitus, and S. Reich, "Evidence for localized high-Tc superconducting regimes on the surface of Na-doped WO3," Europhys. Lett. 51, 564-570 (2000).
[CrossRef]

Ooi, C. H. R.

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

Pan, V. M.

V. M. Pan, D. A. Luzhbin, A. A. Kalenyuk, A. L. Kasatkin, V. A. Komashko, A. V. Velichko, and M. Lancaster, "Microwave impedance of YBa2Cu3O7−δ high-temperature superconductor films in a magnetic field," Low Temp. Phys. 31, 254-262 (2005), and references therein.
[CrossRef]

Pfeiffer, L. F.

C. S. Koonce, M. L. Cohen, J. E. Schooley, W. R. Hosler, and L. F. Pfeiffer, "Superconducting transition temperature of semiconducting SrTiO3," Phys. Rev. 163, 380-390 (1967).
[CrossRef]

Reich, S.

Y. Levi, O. Millo, A. Sharoni, Y. Tsabba, G. Leitus, and S. Reich, "Evidence for localized high-Tc superconducting regimes on the surface of Na-doped WO3," Europhys. Lett. 51, 564-570 (2000).
[CrossRef]

Savaguchi, E.

E. Savaguchi, A. Kukuchi, and Y. Codera, "Dielectric constant of strontium titanate at low temperature," J. Phys. Soc. Jpn. 17, 1666-1667 (1962).
[CrossRef]

Schooley, J. E.

C. S. Koonce, M. L. Cohen, J. E. Schooley, W. R. Hosler, and L. F. Pfeiffer, "Superconducting transition temperature of semiconducting SrTiO3," Phys. Rev. 163, 380-390 (1967).
[CrossRef]

Sharoni, A.

Y. Levi, O. Millo, A. Sharoni, Y. Tsabba, G. Leitus, and S. Reich, "Evidence for localized high-Tc superconducting regimes on the surface of Na-doped WO3," Europhys. Lett. 51, 564-570 (2000).
[CrossRef]

Trunin, M. R.

M. R. Trunin, "Temperature dependence of microwave surface impedance in high-Tc single crystals: experimental and theoretical aspects," J. Supercond. 11, 381-408 (1998).

Tsabba, Y.

Y. Levi, O. Millo, A. Sharoni, Y. Tsabba, G. Leitus, and S. Reich, "Evidence for localized high-Tc superconducting regimes on the surface of Na-doped WO3," Europhys. Lett. 51, 564-570 (2000).
[CrossRef]

Tsidlekht, M.

M. Golosovsky, M. Tsidlekht, and D. Davidov, "High-frequency vortex dynamics in YBa2Cu3O7," Supercond. Sci. Technol. 9, 1-15 (1996).
[CrossRef]

Velichko, A. V.

V. M. Pan, D. A. Luzhbin, A. A. Kalenyuk, A. L. Kasatkin, V. A. Komashko, A. V. Velichko, and M. Lancaster, "Microwave impedance of YBa2Cu3O7−δ high-temperature superconductor films in a magnetic field," Low Temp. Phys. 31, 254-262 (2005), and references therein.
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Yeung, T. C. A.

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

Zimbovskaya, N. A.

J. L. Birman and N. A. Zimbovskaya, "Electrodynamics of nearly ferroelectric superconductors," Phys. Rev. B 64, 144506 (2001).
[CrossRef]

Europhys. Lett. (1)

Y. Levi, O. Millo, A. Sharoni, Y. Tsabba, G. Leitus, and S. Reich, "Evidence for localized high-Tc superconducting regimes on the surface of Na-doped WO3," Europhys. Lett. 51, 564-570 (2000).
[CrossRef]

J. Phys. Soc. Jpn. (1)

E. Savaguchi, A. Kukuchi, and Y. Codera, "Dielectric constant of strontium titanate at low temperature," J. Phys. Soc. Jpn. 17, 1666-1667 (1962).
[CrossRef]

J. Supercond. (1)

M. R. Trunin, "Temperature dependence of microwave surface impedance in high-Tc single crystals: experimental and theoretical aspects," J. Supercond. 11, 381-408 (1998).

Low Temp. Phys. (1)

V. M. Pan, D. A. Luzhbin, A. A. Kalenyuk, A. L. Kasatkin, V. A. Komashko, A. V. Velichko, and M. Lancaster, "Microwave impedance of YBa2Cu3O7−δ high-temperature superconductor films in a magnetic field," Low Temp. Phys. 31, 254-262 (2005), and references therein.
[CrossRef]

Phys. Lett. A (1)

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

Phys. Rev. (2)

M. L. Cohen, "Superconductivity in many-valley semiconductors and in semimetals," Phys. Rev. 134, A511-A521 (1964).
[CrossRef]

C. S. Koonce, M. L. Cohen, J. E. Schooley, W. R. Hosler, and L. F. Pfeiffer, "Superconducting transition temperature of semiconducting SrTiO3," Phys. Rev. 163, 380-390 (1967).
[CrossRef]

Phys. Rev. B (1)

J. L. Birman and N. A. Zimbovskaya, "Electrodynamics of nearly ferroelectric superconductors," Phys. Rev. B 64, 144506 (2001).
[CrossRef]

Supercond. Sci. Technol. (2)

M. Golosovsky, M. Tsidlekht, and D. Davidov, "High-frequency vortex dynamics in YBa2Cu3O7," Supercond. Sci. Technol. 9, 1-15 (1996).
[CrossRef]

J. Gollop, "Microwave applications of high-temperature superconductors," Supercond. Sci. Technol. 10, 120-141 (1997).
[CrossRef]

Other (1)

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

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Figures (9)

Fig. 1
Fig. 1

Geometry of a SC occupying the half-space z 0 . An optical wave is obliquely incident on the plane boundary z = 0 . The angle of incidence is θ and the angle of refraction is θ s .

Fig. 2
Fig. 2

Geometry of a SC slab occupying the space 0 z L . An optical wave is obliquely incident on the left plane boundary with an angle of incidence of θ. The angle in the slab is θ 2 , which can be obtained by the law of refraction.

Fig. 3
Fig. 3

Calculated index of refraction as a function of frequency for n-STO.

Fig. 4
Fig. 4

Calculated reflectance R TE , R TM from ω c to ω T O at six different angles of incidence: (a) θ = 0 ° , (b) 15°, (c) 30°, (d) 60°, (e) 75°, (f) 85°.

Fig. 5
Fig. 5

Calculated reflectance R TE , R TM versus angle of incidence at three different frequencies: (a) 15, (b) 20, (c) 25 GHz . For the TM wave, the calculated Brewster angle is θ B = 89.12209 ° at 15 GHz , θ B = 89.72702 ° at 20 GHz , and θ B = 89.92876 ° at 25 GHz .

Fig. 6
Fig. 6

Calculated TM reflectance versus angle of incidence around the Brewster angle. Here A, B, and C denote the Brewster angles for 15, 20, and 25 GHz , respectively.

Fig. 7
Fig. 7

Calculated transmittance spectra for the normal incidence to a NFE SC slab at three different thicknesses of the superconducting film: L = 10 λ L , 5 λ L , and 2 λ L . A comblike transmittance spectrum is seen in such a material. The resonance peaks are not regularly spaced.

Fig. 8
Fig. 8

Calculated transmittance spectra for TE and TM polarizations at an oblique incidence of θ = 75 ° for a superconducting film of thickness 2 λ L .

Fig. 9
Fig. 9

Calculated transmittance spectra for TE and TM polarizations at an oblique incidence of θ = 85 ° for a superconducting film of thickness 2 λ L . The resonance peak is broadened in the TM polarization.

Equations (34)

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× × E = μ 0 ϵ ( ω ) 2 t 2 E μ 0 Λ E ,
Λ = m * N s e 2 = μ 0 λ L 2 ,
ϵ ( ω ) = ϵ ω L O 2 ω 2 ω T O 2 ω 2 ,
2 E + [ ω 2 μ 0 ϵ ( ω ) μ 0 Λ ] E = 0 .
k s 2 = ω 2 μ 0 ϵ ( ω ) μ 0 Λ = ω 2 μ 0 ϵ ( ω ) 1 λ L 2 .
ω c 1 , c 2 = ω T O ω L O 2 2 ω T O 2 ( 1 + 1 a 2 ) ± ω L O 2 ω T O ( 1 + 1 a 2 ) 2 ω L O 2 ω T O 2 4 a 2 ,
n s = k s k 0 = 1 k 0 ω 2 μ 0 ϵ ( ω ) 1 λ L 2 ,
r TE = cos θ ( n s n ) 2 sin θ cos θ + ( n s n ) 2 sin θ ,
r TM = ( n s n ) 2 sin θ ( n s n ) 2 cos θ ( n s n ) 2 sin θ + ( n s n ) 2 cos θ ,
R TE = r TE 2 ,
R TM = r TM 2 .
r = 1 n s 1 + n s .
r = Z s Z 0 Z s + Z 0 = 1 Z 0 Z s 1 + Z 0 Z s ,
r = r 12 + r 23 e 2 j ϕ 1 + r 12 r 23 e 2 j ϕ ,
t = t 12 t 23 e j ϕ 1 + r 12 r 23 e j 2 ϕ ,
ϕ = k s L cos θ 2 .
r 12 = n 1 cos θ 1 n 2 cos θ 2 n 1 cos θ 1 + n 2 cos θ 2 ,
r 23 = r 12 ,
t 12 = 2 n 1 cos θ 1 n 1 cos θ 1 + n 2 cos θ 2 ,
t 23 = 2 n 2 cos θ 2 n 1 cos θ 1 + n 2 cos θ 2 .
r 12 = n 1 cos θ 2 n 2 cos θ 1 n 1 cos θ 2 + n 2 cos θ 1 ,
r 23 = r 12 ,
t 12 = 2 n 1 cos θ 1 n 1 cos θ 2 + n 2 cos θ 1 ,
t 23 = 2 n 2 cos θ 2 n 1 cos θ 2 + n 2 cos θ 1 .
r = ( k 0 4 k s 4 ) + 2 j k 0 k s ( k 0 2 k s 2 ) cot ( k s L ) ( k 0 2 + k s 2 ) 2 + 4 k 0 2 k s 2 cot 2 ( k s L ) ,
t = e j k 0 L k s [ ( 1 + r ) k s cos ( k s L ) j ( 1 r ) k 0 sin ( k s L ) ] .
R = sin 2 ( k s L ) ρ 2 + sin 2 ( k s L ) ,
T = ρ 2 ρ 2 + sin 2 ( k s L ) ,
ρ = 2 k 0 k s k 0 2 k s 2 .
sin ( k s L ) = 0 k s L = N π , N = 1 , 2 , 3 .
ω peak , N = 1 2 μ 0 ϵ ( K N + ω L O 2 μ 0 ϵ ) ( K N + ω L O 2 μ 0 ϵ ) 2 4 K N ω T O 2 μ 0 ϵ ,
K N = N 2 π 2 L 2 + 1 λ L 2 , N = 1 , 2 , 3 .
r = r 12 ( 1 e 2 j ϕ ) 1 r 12 2 e 2 j ϕ .
k s L cos θ 2 = N π .

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