Abstract

A general method to study dispersive effects on the Brewster angle in moving isotropic semi-infinite dielectrics is discussed. In particular, the Brewster angle and the index of refraction of NaCl are calculated as functions of its velocity. A law of dispersion without absorption, which is used in ionic crystals and contains the Lyddane–Sachs–Teller relation, is assumed. Two cases are considered: direction of motion parallel to the dielectric–vacuum interface and direction of motion perpendicular to the same interface.

© 1985 Optical Society of America

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References

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  1. V. P. Pyati, J. Appl. Phys. 38, 652 (1967).
    [CrossRef]
  2. C. Yeh, J. Appl. Phys. 38, 5194 (1967).
    [CrossRef]
  3. C. W. Chuang, H. C. Ko, J. Appl. Phys. 45, 1154 (1974).
    [CrossRef]
  4. M. Saca, Am. J. Phys. 48, 237 (1980).
    [CrossRef]
  5. S. N. Stolyarov, Sov. Phys. Tech. Phys. 8, 418 (1963).
  6. C. Yeh, J. Appl. Phys. 37, 3079 (1966).
    [CrossRef]
  7. C. Yeh, J. Appl. Phys. 38, 2871 (1967).
    [CrossRef]
  8. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), Sec. 11.4, pp. 360–364. In Eqs. (1) and (11), α is the angle of incidence of the wave. In our situation, α= αB and α′ = αB′. The geometry of the problem is shown in Fig. 1.
  9. C. Kittel, Introduction to Solid State Physics, 4th ed. (Wiley, New York, 1971), pp. 181–190.
  10. F. C. Brown, The Physics of Solids (Benjamin, New York, 1967), Sec. 8.5.
  11. According to Ref. 9, the data were taken at room temperature.
  12. For a given ω, the limiting values β→ ±1 correspond to ω′ → 0. This can be shown by using Eqs. (1) and (3) for the case of parallel motion [case (1)].

1980 (1)

M. Saca, Am. J. Phys. 48, 237 (1980).
[CrossRef]

1974 (1)

C. W. Chuang, H. C. Ko, J. Appl. Phys. 45, 1154 (1974).
[CrossRef]

1967 (3)

C. Yeh, J. Appl. Phys. 38, 2871 (1967).
[CrossRef]

V. P. Pyati, J. Appl. Phys. 38, 652 (1967).
[CrossRef]

C. Yeh, J. Appl. Phys. 38, 5194 (1967).
[CrossRef]

1966 (1)

C. Yeh, J. Appl. Phys. 37, 3079 (1966).
[CrossRef]

1963 (1)

S. N. Stolyarov, Sov. Phys. Tech. Phys. 8, 418 (1963).

Brown, F. C.

F. C. Brown, The Physics of Solids (Benjamin, New York, 1967), Sec. 8.5.

Chuang, C. W.

C. W. Chuang, H. C. Ko, J. Appl. Phys. 45, 1154 (1974).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), Sec. 11.4, pp. 360–364. In Eqs. (1) and (11), α is the angle of incidence of the wave. In our situation, α= αB and α′ = αB′. The geometry of the problem is shown in Fig. 1.

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 4th ed. (Wiley, New York, 1971), pp. 181–190.

Ko, H. C.

C. W. Chuang, H. C. Ko, J. Appl. Phys. 45, 1154 (1974).
[CrossRef]

Pyati, V. P.

V. P. Pyati, J. Appl. Phys. 38, 652 (1967).
[CrossRef]

Saca, M.

M. Saca, Am. J. Phys. 48, 237 (1980).
[CrossRef]

Stolyarov, S. N.

S. N. Stolyarov, Sov. Phys. Tech. Phys. 8, 418 (1963).

Yeh, C.

C. Yeh, J. Appl. Phys. 38, 2871 (1967).
[CrossRef]

C. Yeh, J. Appl. Phys. 38, 5194 (1967).
[CrossRef]

C. Yeh, J. Appl. Phys. 37, 3079 (1966).
[CrossRef]

Am. J. Phys. (1)

M. Saca, Am. J. Phys. 48, 237 (1980).
[CrossRef]

J. Appl. Phys. (5)

V. P. Pyati, J. Appl. Phys. 38, 652 (1967).
[CrossRef]

C. Yeh, J. Appl. Phys. 38, 5194 (1967).
[CrossRef]

C. W. Chuang, H. C. Ko, J. Appl. Phys. 45, 1154 (1974).
[CrossRef]

C. Yeh, J. Appl. Phys. 37, 3079 (1966).
[CrossRef]

C. Yeh, J. Appl. Phys. 38, 2871 (1967).
[CrossRef]

Sov. Phys. Tech. Phys. (1)

S. N. Stolyarov, Sov. Phys. Tech. Phys. 8, 418 (1963).

Other (5)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), Sec. 11.4, pp. 360–364. In Eqs. (1) and (11), α is the angle of incidence of the wave. In our situation, α= αB and α′ = αB′. The geometry of the problem is shown in Fig. 1.

C. Kittel, Introduction to Solid State Physics, 4th ed. (Wiley, New York, 1971), pp. 181–190.

F. C. Brown, The Physics of Solids (Benjamin, New York, 1967), Sec. 8.5.

According to Ref. 9, the data were taken at room temperature.

For a given ω, the limiting values β→ ±1 correspond to ω′ → 0. This can be shown by using Eqs. (1) and (3) for the case of parallel motion [case (1)].

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Figures (3)

Fig. 1
Fig. 1

The incident wave and Brewster’s angle in the frame S′.

Fig. 2
Fig. 2

The Brewster angle and index of refraction versus β. Direction of motion parallel to the interface and to the plane of incidence.

Fig. 3
Fig. 3

The Brewster angle and index of refraction versus β. Direction of motion perpendicular to the interface. Plane of incidence has an arbitrary orientation.

Equations (14)

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ω = γ ω ( 1 - β sin α ) ,
sin α B = [ β + n ( 1 - β 2 ) ( 1 + n 2 ) 1 / 2 ] / [ n 2 ( 1 - β 2 ) + 1 ] ,
sin α B = [ n + β ( n 2 + 1 ) 1 / 2 ] / [ n β + ( n 2 + 1 ) 1 / 2 ] ,
n ( ω ) = n ( 0 ) [ 1 - ( ω / ω L ) 2 ] 1 / 2 [ 1 - ( ω / ω T ) 2 ] - 1 / 2 ,
( ω L 2 / ω T 2 ) = [ ( 0 ) / ( ) ] .
- 1 β - 2 n ( n 2 + 1 ) 1 / 2 / ( 2 n 2 + 1 )
- 2 n ( n 2 + 1 ) 1 / 2 / ( 2 n 2 + 1 ) β 0.
sin α B = β - 1 { 1 - ( ω γ ) - 1 [ n 2 - n 2 ( 0 ) n 2 ω T 2 - n 2 ( 0 ) ω L 2 ] 1 / 2 } .
β ± = n ( n 2 + 1 ) 1 / 2 n 2 ( 1 + F 2 ) + F 2 { - 1 ± F n [ F 2 ( n 2 + 1 ) - 1 ] 1 / 2 } ,
F = [ n 2 - n 2 ( ) ] 1 / 2 / [ n 2 - n 2 ( 0 ) ] 1 / 2 .
ω = γ ω ( 1 + β cos α )
cos α B = [ 1 - β ( n 2 + 1 ) 1 / 2 ] / [ ( n 2 + 1 ) 1 / 2 - β ]
β ± = E - 1 ( n + 1 ) 1 / 2 { ( n 2 n 2 ( 0 ) - 1 ) ± [ ( 1 - ω T 2 ω L 2 ) × E + ( n 2 n 2 ( 0 ) - 1 ) 2 ] 1 / 2 } ,
E = { n 2 ( n 2 + 2 ) n 2 ( 0 ) - [ 1 + ω T 2 ( n 2 + 1 ) ω L 2 ] } .

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