Abstract

The possibility of constructing an optical sensor for temperature monitoring based on the Goos–Hänchen (GH) effect is explored using a theoretical model. This model considers the lateral shift of the incident beam upon reflection from a metal–dielectric interface, with the shift becoming a function of temperature due mainly to the temperature dependence of the optical properties of the metal. It is found that such a sensor can be most effective by using long wavelength p-polarized incident light at almost grazing incidence onto the metal, where significant variation of negative GH shifts can be observed as a function of the temperature.

© 2007 Optical Society of America

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References

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  1. See, e.g. K. Ujihahr, "Reflectivity of metals at high temperatures," J. App. Phys. 43, 2376-2383 (1972).
    [CrossRef]
  2. See, e.g., Y. Liu, M. Choy, A. Mandelis, J. Batista, and B. Li, "Laser thermoreflectance temperature measurements of metal coating alloys on a rotating platform," J. Phys. IV 125, 601-604 (2005), and references therein.
  3. See, e.g., F. Lang and P. Leiderer, "Liquid-vapour phase transitions at interfaces: sub-nanosecond investigations by monitoring the ejection of thin liquid films," New J. Phys. 8, 14 (2006), and references therein.
    [CrossRef]
  4. H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse, "A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance," Opt. Commun. 188, 283 (2001).
    [CrossRef]
  5. H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse," Surface plasmon resonance monitoring of temperature via phase measurement," Opt. Commun. 241, 409-418 (2004).
    [CrossRef]
  6. S. K. Ozdemir and G. Turhan-Sayan, "Temperature effects on surface plasmon resonance: design considerations for an optical temperature sensor," J. Lightwave Tech. 21, 805-814 (2003).
    [CrossRef]
  7. A. K. Sharma and B. D. Gupta, "Theoretical model of a fiber optic remote sensor based on surface plasmon resonance for temperature detection," Opt. Fiber Tech. 12, 87-100 (2006).
    [CrossRef]
  8. X. Yin and L. Hesselink, "Goos-Hänchen shift surface plasmon resonance sensor," Appl. Phys. Lett. 89, 261108 (2006).
    [CrossRef]
  9. F. Goos and H. Hänchen, "Ein neue und fundamentaler Versuch zur total reflection," Ann. Phys. 1, 333-346 (1947).
    [CrossRef]
  10. F. Goos and H. Hänchen, "Neumessung des strahlversetzungseffektes bei totalreflexion," Ann. Phys. 5, 251-252 (1949).
    [CrossRef]
  11. For an earlier comprehensive review, see H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 116-137 (1970).
  12. H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 299-319 (1971).
  13. H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 553-569 (1971).
  14. W. J. Wild and C. L. Giles, "Goos-Hänchen shifts from absorbing media," Phys. Rev. A 25, 2099-2101 (1982).
    [CrossRef]
  15. H. M. Lai and S. W. Chan, "Large and negative Goos-Hänchen shift near Brewster dip on reflection from weakly absorbing media," Opt. Lett. 27, 680-682 (2002).
    [CrossRef]
  16. P. T. Leung, C.-W. Chen, and H.-P. Chiang, "Large negative Goos-Hänchen shift at metal surfaces," Opt. Commun. 276, 206-208 (2007).
    [CrossRef]
  17. Most of the details for the temperature model can be found in H.-P. Chiang, P. T. Leung, and Wan-Sun Tse, "Optical properties of composite materials at high temperatures," Solid State Commun. 101, 45-50 (1997).
    [CrossRef]
  18. Strictly speaking the effective mass does have a minor dependence on temperature, the theoretical modeling of such dependence will be extremely complicated. This was discussed, e.g., in a recent article by M. Rashidi-Huyeh and B. Palpant, "Counterintuitive thermo-optical response of metal-dielectric nanocomposite materials as a result of local electromagnetic field enhancement," Phys. Rev. B 74, 075405 (2006).
    [CrossRef]
  19. D. Z. Han, F. Q. Wu, X. Li, X. H. Liu, and J. Zi, "Enhanced transmission of optically thick metallic films at infrared wavelengths," Appl. Phys. Lett. 88, 161110 (2006).
    [CrossRef]

2007 (1)

P. T. Leung, C.-W. Chen, and H.-P. Chiang, "Large negative Goos-Hänchen shift at metal surfaces," Opt. Commun. 276, 206-208 (2007).
[CrossRef]

2006 (5)

Strictly speaking the effective mass does have a minor dependence on temperature, the theoretical modeling of such dependence will be extremely complicated. This was discussed, e.g., in a recent article by M. Rashidi-Huyeh and B. Palpant, "Counterintuitive thermo-optical response of metal-dielectric nanocomposite materials as a result of local electromagnetic field enhancement," Phys. Rev. B 74, 075405 (2006).
[CrossRef]

D. Z. Han, F. Q. Wu, X. Li, X. H. Liu, and J. Zi, "Enhanced transmission of optically thick metallic films at infrared wavelengths," Appl. Phys. Lett. 88, 161110 (2006).
[CrossRef]

See, e.g., F. Lang and P. Leiderer, "Liquid-vapour phase transitions at interfaces: sub-nanosecond investigations by monitoring the ejection of thin liquid films," New J. Phys. 8, 14 (2006), and references therein.
[CrossRef]

A. K. Sharma and B. D. Gupta, "Theoretical model of a fiber optic remote sensor based on surface plasmon resonance for temperature detection," Opt. Fiber Tech. 12, 87-100 (2006).
[CrossRef]

X. Yin and L. Hesselink, "Goos-Hänchen shift surface plasmon resonance sensor," Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

2005 (1)

See, e.g., Y. Liu, M. Choy, A. Mandelis, J. Batista, and B. Li, "Laser thermoreflectance temperature measurements of metal coating alloys on a rotating platform," J. Phys. IV 125, 601-604 (2005), and references therein.

2004 (1)

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse," Surface plasmon resonance monitoring of temperature via phase measurement," Opt. Commun. 241, 409-418 (2004).
[CrossRef]

2003 (1)

S. K. Ozdemir and G. Turhan-Sayan, "Temperature effects on surface plasmon resonance: design considerations for an optical temperature sensor," J. Lightwave Tech. 21, 805-814 (2003).
[CrossRef]

2002 (1)

2001 (1)

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse, "A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance," Opt. Commun. 188, 283 (2001).
[CrossRef]

1997 (1)

Most of the details for the temperature model can be found in H.-P. Chiang, P. T. Leung, and Wan-Sun Tse, "Optical properties of composite materials at high temperatures," Solid State Commun. 101, 45-50 (1997).
[CrossRef]

1982 (1)

W. J. Wild and C. L. Giles, "Goos-Hänchen shifts from absorbing media," Phys. Rev. A 25, 2099-2101 (1982).
[CrossRef]

1972 (1)

See, e.g. K. Ujihahr, "Reflectivity of metals at high temperatures," J. App. Phys. 43, 2376-2383 (1972).
[CrossRef]

1971 (2)

H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 299-319 (1971).

H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 553-569 (1971).

1970 (1)

For an earlier comprehensive review, see H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 116-137 (1970).

1949 (1)

F. Goos and H. Hänchen, "Neumessung des strahlversetzungseffektes bei totalreflexion," Ann. Phys. 5, 251-252 (1949).
[CrossRef]

1947 (1)

F. Goos and H. Hänchen, "Ein neue und fundamentaler Versuch zur total reflection," Ann. Phys. 1, 333-346 (1947).
[CrossRef]

Batista, J.

See, e.g., Y. Liu, M. Choy, A. Mandelis, J. Batista, and B. Li, "Laser thermoreflectance temperature measurements of metal coating alloys on a rotating platform," J. Phys. IV 125, 601-604 (2005), and references therein.

Chan, S. W.

Chen, C.-W.

P. T. Leung, C.-W. Chen, and H.-P. Chiang, "Large negative Goos-Hänchen shift at metal surfaces," Opt. Commun. 276, 206-208 (2007).
[CrossRef]

Chiang, H.-P.

P. T. Leung, C.-W. Chen, and H.-P. Chiang, "Large negative Goos-Hänchen shift at metal surfaces," Opt. Commun. 276, 206-208 (2007).
[CrossRef]

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse," Surface plasmon resonance monitoring of temperature via phase measurement," Opt. Commun. 241, 409-418 (2004).
[CrossRef]

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse, "A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance," Opt. Commun. 188, 283 (2001).
[CrossRef]

Most of the details for the temperature model can be found in H.-P. Chiang, P. T. Leung, and Wan-Sun Tse, "Optical properties of composite materials at high temperatures," Solid State Commun. 101, 45-50 (1997).
[CrossRef]

Choy, M.

See, e.g., Y. Liu, M. Choy, A. Mandelis, J. Batista, and B. Li, "Laser thermoreflectance temperature measurements of metal coating alloys on a rotating platform," J. Phys. IV 125, 601-604 (2005), and references therein.

Giles, C. L.

W. J. Wild and C. L. Giles, "Goos-Hänchen shifts from absorbing media," Phys. Rev. A 25, 2099-2101 (1982).
[CrossRef]

Goos, F.

F. Goos and H. Hänchen, "Neumessung des strahlversetzungseffektes bei totalreflexion," Ann. Phys. 5, 251-252 (1949).
[CrossRef]

F. Goos and H. Hänchen, "Ein neue und fundamentaler Versuch zur total reflection," Ann. Phys. 1, 333-346 (1947).
[CrossRef]

Gupta, B. D.

A. K. Sharma and B. D. Gupta, "Theoretical model of a fiber optic remote sensor based on surface plasmon resonance for temperature detection," Opt. Fiber Tech. 12, 87-100 (2006).
[CrossRef]

Han, D. Z.

D. Z. Han, F. Q. Wu, X. Li, X. H. Liu, and J. Zi, "Enhanced transmission of optically thick metallic films at infrared wavelengths," Appl. Phys. Lett. 88, 161110 (2006).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, "Neumessung des strahlversetzungseffektes bei totalreflexion," Ann. Phys. 5, 251-252 (1949).
[CrossRef]

F. Goos and H. Hänchen, "Ein neue und fundamentaler Versuch zur total reflection," Ann. Phys. 1, 333-346 (1947).
[CrossRef]

Hesselink, L.

X. Yin and L. Hesselink, "Goos-Hänchen shift surface plasmon resonance sensor," Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Lai, H. M.

Lang, F.

See, e.g., F. Lang and P. Leiderer, "Liquid-vapour phase transitions at interfaces: sub-nanosecond investigations by monitoring the ejection of thin liquid films," New J. Phys. 8, 14 (2006), and references therein.
[CrossRef]

Leiderer, P.

See, e.g., F. Lang and P. Leiderer, "Liquid-vapour phase transitions at interfaces: sub-nanosecond investigations by monitoring the ejection of thin liquid films," New J. Phys. 8, 14 (2006), and references therein.
[CrossRef]

Leung, P. T.

P. T. Leung, C.-W. Chen, and H.-P. Chiang, "Large negative Goos-Hänchen shift at metal surfaces," Opt. Commun. 276, 206-208 (2007).
[CrossRef]

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse," Surface plasmon resonance monitoring of temperature via phase measurement," Opt. Commun. 241, 409-418 (2004).
[CrossRef]

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse, "A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance," Opt. Commun. 188, 283 (2001).
[CrossRef]

Most of the details for the temperature model can be found in H.-P. Chiang, P. T. Leung, and Wan-Sun Tse, "Optical properties of composite materials at high temperatures," Solid State Commun. 101, 45-50 (1997).
[CrossRef]

Li, B.

See, e.g., Y. Liu, M. Choy, A. Mandelis, J. Batista, and B. Li, "Laser thermoreflectance temperature measurements of metal coating alloys on a rotating platform," J. Phys. IV 125, 601-604 (2005), and references therein.

Li, X.

D. Z. Han, F. Q. Wu, X. Li, X. H. Liu, and J. Zi, "Enhanced transmission of optically thick metallic films at infrared wavelengths," Appl. Phys. Lett. 88, 161110 (2006).
[CrossRef]

Liu, X. H.

D. Z. Han, F. Q. Wu, X. Li, X. H. Liu, and J. Zi, "Enhanced transmission of optically thick metallic films at infrared wavelengths," Appl. Phys. Lett. 88, 161110 (2006).
[CrossRef]

Liu, Y.

See, e.g., Y. Liu, M. Choy, A. Mandelis, J. Batista, and B. Li, "Laser thermoreflectance temperature measurements of metal coating alloys on a rotating platform," J. Phys. IV 125, 601-604 (2005), and references therein.

Lotsch, H.

H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 299-319 (1971).

H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 553-569 (1971).

For an earlier comprehensive review, see H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 116-137 (1970).

Mandelis, A.

See, e.g., Y. Liu, M. Choy, A. Mandelis, J. Batista, and B. Li, "Laser thermoreflectance temperature measurements of metal coating alloys on a rotating platform," J. Phys. IV 125, 601-604 (2005), and references therein.

Ozdemir, S. K.

S. K. Ozdemir and G. Turhan-Sayan, "Temperature effects on surface plasmon resonance: design considerations for an optical temperature sensor," J. Lightwave Tech. 21, 805-814 (2003).
[CrossRef]

Palpant, B.

Strictly speaking the effective mass does have a minor dependence on temperature, the theoretical modeling of such dependence will be extremely complicated. This was discussed, e.g., in a recent article by M. Rashidi-Huyeh and B. Palpant, "Counterintuitive thermo-optical response of metal-dielectric nanocomposite materials as a result of local electromagnetic field enhancement," Phys. Rev. B 74, 075405 (2006).
[CrossRef]

Rashidi-Huyeh, M.

Strictly speaking the effective mass does have a minor dependence on temperature, the theoretical modeling of such dependence will be extremely complicated. This was discussed, e.g., in a recent article by M. Rashidi-Huyeh and B. Palpant, "Counterintuitive thermo-optical response of metal-dielectric nanocomposite materials as a result of local electromagnetic field enhancement," Phys. Rev. B 74, 075405 (2006).
[CrossRef]

Sharma, A. K.

A. K. Sharma and B. D. Gupta, "Theoretical model of a fiber optic remote sensor based on surface plasmon resonance for temperature detection," Opt. Fiber Tech. 12, 87-100 (2006).
[CrossRef]

Tse, Wan-Sun

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse," Surface plasmon resonance monitoring of temperature via phase measurement," Opt. Commun. 241, 409-418 (2004).
[CrossRef]

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse, "A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance," Opt. Commun. 188, 283 (2001).
[CrossRef]

Most of the details for the temperature model can be found in H.-P. Chiang, P. T. Leung, and Wan-Sun Tse, "Optical properties of composite materials at high temperatures," Solid State Commun. 101, 45-50 (1997).
[CrossRef]

Turhan-Sayan, G.

S. K. Ozdemir and G. Turhan-Sayan, "Temperature effects on surface plasmon resonance: design considerations for an optical temperature sensor," J. Lightwave Tech. 21, 805-814 (2003).
[CrossRef]

Ujihahr, K.

See, e.g. K. Ujihahr, "Reflectivity of metals at high temperatures," J. App. Phys. 43, 2376-2383 (1972).
[CrossRef]

Wang, Y.-C.

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse," Surface plasmon resonance monitoring of temperature via phase measurement," Opt. Commun. 241, 409-418 (2004).
[CrossRef]

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse, "A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance," Opt. Commun. 188, 283 (2001).
[CrossRef]

Wild, W. J.

W. J. Wild and C. L. Giles, "Goos-Hänchen shifts from absorbing media," Phys. Rev. A 25, 2099-2101 (1982).
[CrossRef]

Wu, F. Q.

D. Z. Han, F. Q. Wu, X. Li, X. H. Liu, and J. Zi, "Enhanced transmission of optically thick metallic films at infrared wavelengths," Appl. Phys. Lett. 88, 161110 (2006).
[CrossRef]

Yin, X.

X. Yin and L. Hesselink, "Goos-Hänchen shift surface plasmon resonance sensor," Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Zi, J.

D. Z. Han, F. Q. Wu, X. Li, X. H. Liu, and J. Zi, "Enhanced transmission of optically thick metallic films at infrared wavelengths," Appl. Phys. Lett. 88, 161110 (2006).
[CrossRef]

Ann. Phys. (2)

F. Goos and H. Hänchen, "Ein neue und fundamentaler Versuch zur total reflection," Ann. Phys. 1, 333-346 (1947).
[CrossRef]

F. Goos and H. Hänchen, "Neumessung des strahlversetzungseffektes bei totalreflexion," Ann. Phys. 5, 251-252 (1949).
[CrossRef]

Appl. Phys. Lett. (2)

D. Z. Han, F. Q. Wu, X. Li, X. H. Liu, and J. Zi, "Enhanced transmission of optically thick metallic films at infrared wavelengths," Appl. Phys. Lett. 88, 161110 (2006).
[CrossRef]

X. Yin and L. Hesselink, "Goos-Hänchen shift surface plasmon resonance sensor," Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

J. App. Phys. (1)

See, e.g. K. Ujihahr, "Reflectivity of metals at high temperatures," J. App. Phys. 43, 2376-2383 (1972).
[CrossRef]

J. Lightwave Tech. (1)

S. K. Ozdemir and G. Turhan-Sayan, "Temperature effects on surface plasmon resonance: design considerations for an optical temperature sensor," J. Lightwave Tech. 21, 805-814 (2003).
[CrossRef]

J. Phys. IV (1)

See, e.g., Y. Liu, M. Choy, A. Mandelis, J. Batista, and B. Li, "Laser thermoreflectance temperature measurements of metal coating alloys on a rotating platform," J. Phys. IV 125, 601-604 (2005), and references therein.

New J. Phys. (1)

See, e.g., F. Lang and P. Leiderer, "Liquid-vapour phase transitions at interfaces: sub-nanosecond investigations by monitoring the ejection of thin liquid films," New J. Phys. 8, 14 (2006), and references therein.
[CrossRef]

Opt. Commun. (2)

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse," Surface plasmon resonance monitoring of temperature via phase measurement," Opt. Commun. 241, 409-418 (2004).
[CrossRef]

P. T. Leung, C.-W. Chen, and H.-P. Chiang, "Large negative Goos-Hänchen shift at metal surfaces," Opt. Commun. 276, 206-208 (2007).
[CrossRef]

Opt. Commun. (1)

H.-P. Chiang, Y.-C. Wang, P. T. Leung, and Wan-Sun Tse, "A theoretical model for the temperature-dependent sensitivity of the optical sensor based on surface plasmon resonance," Opt. Commun. 188, 283 (2001).
[CrossRef]

Opt. Fiber Tech. (1)

A. K. Sharma and B. D. Gupta, "Theoretical model of a fiber optic remote sensor based on surface plasmon resonance for temperature detection," Opt. Fiber Tech. 12, 87-100 (2006).
[CrossRef]

Opt. Lett. (1)

Optik (3)

For an earlier comprehensive review, see H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 116-137 (1970).

H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 299-319 (1971).

H. Lotsch, "Beam displacement at total reflection: the Goos-Hänchen effect," Optik 32, 553-569 (1971).

Phys. Rev. B (1)

Strictly speaking the effective mass does have a minor dependence on temperature, the theoretical modeling of such dependence will be extremely complicated. This was discussed, e.g., in a recent article by M. Rashidi-Huyeh and B. Palpant, "Counterintuitive thermo-optical response of metal-dielectric nanocomposite materials as a result of local electromagnetic field enhancement," Phys. Rev. B 74, 075405 (2006).
[CrossRef]

Phys. Rev. A (1)

W. J. Wild and C. L. Giles, "Goos-Hänchen shifts from absorbing media," Phys. Rev. A 25, 2099-2101 (1982).
[CrossRef]

Solid State Commun. (1)

Most of the details for the temperature model can be found in H.-P. Chiang, P. T. Leung, and Wan-Sun Tse, "Optical properties of composite materials at high temperatures," Solid State Commun. 101, 45-50 (1997).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(Color online) Typical results for Goos–Hänchen shift and reflectivity as a function of incident angle for p-polarized light at long wavelengths ( λ = 3390   nm ) calculated using the Drude model for the metal at room temperature. Also shown are the corresponding results for s-polarized (broken lines). The incidence is from vacuum onto a silver surface.

Fig. 2
Fig. 2

Goos–Hänchen shifts as a function of temperature of the metal at an incident wavelength of 3390   nm at two different incident angles below and above the Brewster angle of the metal. The GH shifts for both s- and p-polarized waves [(a) and (b)], as well as the difference between them [(c)] are plotted.

Fig. 3
Fig. 3

Schematic design of the GH shift sensing proposed in this work.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

D = 1 k d φ d θ = cos 2 φ k d tan φ d θ ,
D P = I m { ln [ n ^ 2 2 cos     θ n 1 ( n ^ 2 2 n 1 2 sin 2 θ ) 1 / 2 n ^ 2 2 cos    θ + n 1 ( n ^ 2 2 n 1 2 sin 2 θ ) 1 / 2 ] } ,
tan φ 2 κ 2 cos θ ( κ 2 + sin 2 θ ) 1 / 2 κ 4 cos 2 θ κ 2 sin 2 θ ,
sin 2 θ = κ 2 ( κ 2 1 ) κ 4 + 1 .
ε ^ 2 = 1 ω P 2 ω ( ω + i ω c ) ,
ω p = 4 π N e 2 m * ,
ω p = ω p 0 [ 1 + γ ( T T 0 ) ] 1 / 2 ,
ω c = ω cp + ω ce ,
ω c p ( T ) = ω 0 [ 2 5 + 4 ( T θ ) 5 0 θ / T z 4 d z e z 1 ] ,
ω ce (T) = 1 12 π 3 Γ Δ ħ E F [ ( k B T) 2 + ( ħ ω / 2 π ) 2 ] ,

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