Abstract

The Kerr reflection and the Faraday transmission relations are calculated for a magnetized slab of homogeneous isotropic material bounded by two nonmagnetic lossless media. Only the electric dipole contributions to optical properties of the media are considered. The light is obliquely incident on the slab and the applied magnetic field is placed in the polar, the longitudinal, and the transverse directions. Calculations for a single pass of the light through the slab are carried out for the transmitted light. The polar and longitudinal Faraday effects for a thin slab are shown to contain a constant term independent of thickness. The first-order transmission effect for a transverse magnetic field is independent of thickness.

© 1964 Optical Society of America

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References

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  1. W. Voigt, Magneto- und Electro-Optik (Teubner, Leipzig, 1908).
  2. W. Voigt, Handbuch der Elektrizitat und des Magnetismus, edited by L. Graetz (Johann Ambrosius Barth, Leipzig, 1920), Vol. IV.
  3. C. H. Luhrs, Proc. IRE 40, 76 (1952).
    [Crossref]
  4. M. Born and P. Jordan, Elementare Quantenmechanik (Springer-Verlag, Berlin1930).
  5. L. Rosenfeld, Z. Physik 57, 835 (1929).
    [Crossref]
  6. Y. R. Shen, Phys. Rev. 133, A511 (1964).
    [Crossref]
  7. R. Serber, Phys. Rev. 41, 489 (1932).
    [Crossref]
  8. J. Halpern, B. Lax, and Y. Nishina, Phys. Rev. 134, A140 (1964).
    [Crossref]
  9. P. N. Argyres, Phys. Rev. 97, 334 (1955).
    [Crossref]
  10. R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (John Wiley & Sons, Inc., New York, 1960).

1964 (2)

Y. R. Shen, Phys. Rev. 133, A511 (1964).
[Crossref]

J. Halpern, B. Lax, and Y. Nishina, Phys. Rev. 134, A140 (1964).
[Crossref]

1955 (1)

P. N. Argyres, Phys. Rev. 97, 334 (1955).
[Crossref]

1952 (1)

C. H. Luhrs, Proc. IRE 40, 76 (1952).
[Crossref]

1932 (1)

R. Serber, Phys. Rev. 41, 489 (1932).
[Crossref]

1929 (1)

L. Rosenfeld, Z. Physik 57, 835 (1929).
[Crossref]

Adler, R. B.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (John Wiley & Sons, Inc., New York, 1960).

Argyres, P. N.

P. N. Argyres, Phys. Rev. 97, 334 (1955).
[Crossref]

Born, M.

M. Born and P. Jordan, Elementare Quantenmechanik (Springer-Verlag, Berlin1930).

Chu, L. J.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (John Wiley & Sons, Inc., New York, 1960).

Fano, R. M.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (John Wiley & Sons, Inc., New York, 1960).

Halpern, J.

J. Halpern, B. Lax, and Y. Nishina, Phys. Rev. 134, A140 (1964).
[Crossref]

Jordan, P.

M. Born and P. Jordan, Elementare Quantenmechanik (Springer-Verlag, Berlin1930).

Lax, B.

J. Halpern, B. Lax, and Y. Nishina, Phys. Rev. 134, A140 (1964).
[Crossref]

Luhrs, C. H.

C. H. Luhrs, Proc. IRE 40, 76 (1952).
[Crossref]

Nishina, Y.

J. Halpern, B. Lax, and Y. Nishina, Phys. Rev. 134, A140 (1964).
[Crossref]

Rosenfeld, L.

L. Rosenfeld, Z. Physik 57, 835 (1929).
[Crossref]

Serber, R.

R. Serber, Phys. Rev. 41, 489 (1932).
[Crossref]

Shen, Y. R.

Y. R. Shen, Phys. Rev. 133, A511 (1964).
[Crossref]

Voigt, W.

W. Voigt, Magneto- und Electro-Optik (Teubner, Leipzig, 1908).

W. Voigt, Handbuch der Elektrizitat und des Magnetismus, edited by L. Graetz (Johann Ambrosius Barth, Leipzig, 1920), Vol. IV.

Phys. Rev. (4)

Y. R. Shen, Phys. Rev. 133, A511 (1964).
[Crossref]

R. Serber, Phys. Rev. 41, 489 (1932).
[Crossref]

J. Halpern, B. Lax, and Y. Nishina, Phys. Rev. 134, A140 (1964).
[Crossref]

P. N. Argyres, Phys. Rev. 97, 334 (1955).
[Crossref]

Proc. IRE (1)

C. H. Luhrs, Proc. IRE 40, 76 (1952).
[Crossref]

Z. Physik (1)

L. Rosenfeld, Z. Physik 57, 835 (1929).
[Crossref]

Other (4)

M. Born and P. Jordan, Elementare Quantenmechanik (Springer-Verlag, Berlin1930).

W. Voigt, Magneto- und Electro-Optik (Teubner, Leipzig, 1908).

W. Voigt, Handbuch der Elektrizitat und des Magnetismus, edited by L. Graetz (Johann Ambrosius Barth, Leipzig, 1920), Vol. IV.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (John Wiley & Sons, Inc., New York, 1960).

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Figures (3)

F. 1
F. 1

Conditions for the polar magneto-optic effects.

F. 2
F. 2

Conditions for the longitudinal magneto-optic effects.

F. 3
F. 3

Conditions for the transverse magneto-optic effects.

Equations (55)

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κ = N 2 | 1 + S i Q 0 i Q 1 + S 0 0 0 1 | .
× H = i ω 0 κ E ,
× E = i ω μ 0 H .
× × E = ω 2 0 μ 0 κ E .
exp i ω [ t ( N / c ) ( α x + β y + γ z ) ]
α 2 + β 2 + γ 2 = 1
N 2 N 2 { [ 1 + 1 2 ( 1 + γ 2 ) S 1 2 ( α 2 + β 2 ) Q 2 ± 1 2 [ 4 γ 2 Q 2 + ( 1 γ 2 ) 2 ( Q 2 S 2 ) 2 ] 1 2 } .
| G x , y ± ( z ) Z x , y r , l ± A r , l ± B r , l ± | = | E x , y l ± ( z ) E x , y r , l ± ( z ) E x , y r , l ± E y , x r , l ± E x r , l ± E y r , l ± E z r , l ± E y r , l ± | .
N + r , l α + r , l = N 1 α 1 = N α ,
N + r , l γ + r , l = N γ [ 1 ± ( Q / 2 γ ) ] = N γ ( 1 ± Δ ) .
G x , y + ( z ) = G x , y + ( 0 ) e i 2 ω N γ Δ z / c .
Z y + r , l = ( 1 / N γ ) ( μ 0 / 0 ) 1 2 ( 1 Δ ) = Z y ( 1 Δ ) ,
Z x + r , l = ( γ / N ) ( μ 0 / 0 ) 1 2 ( 1 Δ ) = Z x ( 1 Δ ) .
A + r , l = i γ [ 1 ( α 2 S / 2 γ Q ) ] = i γ ( 1 Δ ) ,
B + r , l = i { α 2 γ [ ( α 2 S / Q ) Q ] α } .
| E y 2 ( z ) H x 2 ( z ) E x 2 ( z ) H y 2 ( z ) | = | [ 1 + G y + ( z ) ] [ 1 + G y ( z ) ] { ( 1 / Z y + r ) + [ G y + ( z ) / Z y + l ] } { ( 1 / Z y r ) + [ G y ( z ) / Z y l ] } [ A + r + A + l G y + ( z ) ] [ A r + A l G y ( z ) { ( A + r / Z x + r ) + [ A + l G y + ( z ) / Z x + l ] } { ( A r / Z x r ) + [ A l G y ( z ) / Z x l ] } | | E y 2 + r ( z ) E y 2 r ( z ) | .
| T p T s | = | t p p t p s t s p t s s | | I p I s | .
G y + ( 0 ) = 1 .
G y ( d ) = Γ 23 y Γ 32 x + G y + ( d ) ( Γ 23 y + Γ 32 x ) Γ 23 y + Γ 32 x + G y + ( d ) ( Γ 23 y Γ 32 x ) .
| t p p t p s t s p t s s | = | B D e i ρ cos θ A D e i ρ sin θ B C e i ρ sin θ A C e i ρ cos θ | ,
| A B C D ρ θ | = | 2 N 1 γ 1 / ( N 1 γ 1 + N 2 γ 2 ) 2 N 1 γ 1 / ( N 1 γ 2 + N 2 γ 1 ) 2 N 2 γ 2 / ( N 2 γ 2 + N 3 γ 3 ) 2 N 2 γ 2 / ( N 2 γ 3 + N 3 γ 2 ) ω N γ d / c ω NQd / 2 c | .
| R p R s | = | r p p r p s r s p r s s | | I p I s |
G y + ( 0 ) = 1 + ϒ 21 x Δ 2 Δ .
G x + ( 0 ) = 1 + ϒ 21 y Δ + 2 Δ .
r p s = r s p = i N 1 N 2 γ 1 Q ( N 1 γ 1 + N 2 γ 2 ) ( N 1 γ 2 + N 2 γ 1 ) .
e i 2 ω N γ Δ d / c 1 + ( i 2 ω N γ Δ d / c ) = 1 + Δ .
G y ( d ) = 1 + ( ϒ 23 x ϒ 32 y Γ 23 x ϒ 21 x ) Δ Γ 23 x Δ + 2 Γ 23 y Δ Γ 23 y ,
G x ( d ) = 1 + ( ϒ 23 y ϒ 32 x + Γ 32 y ϒ 21 y ) Δ + Γ 32 y Δ 2 Γ 23 x Δ Γ 23 x .
[ π N 2 d λ 0 i 2 γ 2 ( N 2 γ 1 N 2 γ 1 + N 1 γ 2 N 3 γ 3 N 2 γ 2 + N 3 γ 3 ) ] Q .
[ π N 2 d λ 0 i 2 γ 2 ( N 2 γ 2 N 1 γ 1 + N 2 γ 2 N 3 γ 2 N 2 γ 3 + N 3 γ 2 ) ] Q .
N 1 γ 1 = N r , l γ r , l = N γ ,
N r , l β r , l = N β [ 1 ± ( γ Q / 2 β 2 ) ] = N β ( 1 ± Δ ) ,
G x , z + ( y ) = G x , z + ( 0 ) e i 2 ω N β Δ y / c ,
Z x + r , l = ( 1 / N β ) ( μ 0 / 0 ) 1 2 ( 1 Δ ) = Z x ( 1 Δ ) ,
Z x + r , l = ( β / N ) ( μ 0 / 0 ) 1 2 ( 1 ± Δ ) = Z z ( 1 ± Δ ) ,
A + r , l = i β { 1 [ ( β 2 S / 2 γ Q ) ( Q / 2 γ β 2 ) ] } = i β ( 1 Δ ) ,
B + r , l = i [ ( β 2 S / 2 Q ) 1 2 ( β 2 + γ ) Q ± γ ] .
θ = ω N 2 γ 2 Q d / 2 c β 2
G x + ( 0 ) = 1 ϒ 21 z Δ 2 Δ ,
G z + ( 0 ) = 1 + ϒ 21 x Δ + 2 Δ .
r p s = r s p = i N 1 2 γ 1 β 1 Q β 2 ( N 1 β 1 + N 2 β 2 ) ( N 1 β 2 + N 2 β 1 ) .
Δ = i 2 ω N β Δ d / c .
G x ( d ) = 1 ( Γ 32 z ϒ 21 z + ϒ 23 x ϒ 23 z ) Δ Γ 32 z Δ + 2 Γ 23 x Δ Γ 23 x ,
G z ( d ) = 1 + ( Γ 32 x ϒ 21 x + ϒ 23 z ϒ 23 x ) Δ + Γ 32 x Δ + 2 Γ 23 z Δ Γ 23 z .
[ π N 2 d λ 0 + i 2 β 2 ( N 2 β 1 N 1 β 2 + N 2 β 1 N 2 β 2 N 2 β 2 + N 3 β 3 ) ] γ 2 β 2 Q .
[ π N 2 d λ 0 + i 2 β 2 ( N 2 β 3 N 2 β 3 + N 3 β 2 N 2 β 2 N 1 β 1 + N 2 β 2 ) ] γ 2 β 2 Q .
N s = N ,
N p = N [ 1 + 1 2 ( S Q 2 ) ] .
N β = N β ,
N α = N α [ 1 + ( S Q 2 ) / 2 α 2 ] .
Z y ± = ± ( 1 / N ) ( μ 0 / 0 ) 1 2 ( α ± i Q β ) .
E y 2 ( x ) = E y 2 + ( x ) + E y 2 ( x ) ,
H z 2 ( x ) = [ E y 2 + ( x ) / Z y + ] + [ E y 2 ( x ) / Z y ] .
r p p = [ N 2 α 1 N 1 ( α 2 + i Q B 2 ) ] / [ N 2 α 1 + N 1 ( α 2 + i Q B 2 ) ]
t p p = 4 N 1 N 2 α 1 α 2 e i ω N 2 α 2 d / c [ N 2 α 3 + N 3 ( α 2 i Q β 2 ) ] [ N 2 α 1 + N 1 ( α 2 + i Q β 2 ) ] .