Abstract

An expression for the Faraday rotation produced by a system of thin layers containing a single thick layer is derived for the situation in which the thin layers exhibit fully developed interference fringes, and the fringes caused by the thick layer are completely suppressed. All layers are assumed to be homogeneous and isotropic. The suppression of the fringes produced by the thick layer is assumed to arise from the presence of a frequency distribution in the incident radiation. Restrictions are imposed in order that the result should not depend on the exact details of the frequency distribution.

© 1971 Optical Society of America

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References

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  1. H. Piller, Appl. Phys. 37, 763 (1966).
    [CrossRef]
  2. E. D. Palik, J. R. Stevenson, J. Webster, J. Appl. Phys. 37, 1982 (1966).
    [CrossRef]
  3. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962), Chap. 12.
  4. V. K. Miloslavskii, Opt. Spectrosc. 14, 282 (1963) [Opt. Spectrosk. 14, 532 (1963)].
  5. B. Donovan, L. Medcalf, Brit. J. Appl. Phys. 15, 1139 (1964).
    [CrossRef]
  6. For example, see R. E. Collen, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), p. 91.
  7. P. H. Berning, J. Opt. Soc. Am. 46, 779 (1959).
    [CrossRef]
  8. C. J. Gabriel, H. Piller, Appl. Opt. 6, 661 (1967).
    [CrossRef] [PubMed]
  9. M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 628.

1967 (1)

1966 (2)

H. Piller, Appl. Phys. 37, 763 (1966).
[CrossRef]

E. D. Palik, J. R. Stevenson, J. Webster, J. Appl. Phys. 37, 1982 (1966).
[CrossRef]

1964 (1)

B. Donovan, L. Medcalf, Brit. J. Appl. Phys. 15, 1139 (1964).
[CrossRef]

1963 (1)

V. K. Miloslavskii, Opt. Spectrosc. 14, 282 (1963) [Opt. Spectrosk. 14, 532 (1963)].

1959 (1)

Berning, P. H.

Born, M.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 628.

Collen, R. E.

For example, see R. E. Collen, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), p. 91.

Donovan, B.

B. Donovan, L. Medcalf, Brit. J. Appl. Phys. 15, 1139 (1964).
[CrossRef]

Gabriel, C. J.

Medcalf, L.

B. Donovan, L. Medcalf, Brit. J. Appl. Phys. 15, 1139 (1964).
[CrossRef]

Miloslavskii, V. K.

V. K. Miloslavskii, Opt. Spectrosc. 14, 282 (1963) [Opt. Spectrosk. 14, 532 (1963)].

Palik, E. D.

E. D. Palik, J. R. Stevenson, J. Webster, J. Appl. Phys. 37, 1982 (1966).
[CrossRef]

Papoulis, A.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962), Chap. 12.

Piller, H.

Stevenson, J. R.

E. D. Palik, J. R. Stevenson, J. Webster, J. Appl. Phys. 37, 1982 (1966).
[CrossRef]

Webster, J.

E. D. Palik, J. R. Stevenson, J. Webster, J. Appl. Phys. 37, 1982 (1966).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 628.

Appl. Opt. (1)

Appl. Phys. (1)

H. Piller, Appl. Phys. 37, 763 (1966).
[CrossRef]

Brit. J. Appl. Phys. (1)

B. Donovan, L. Medcalf, Brit. J. Appl. Phys. 15, 1139 (1964).
[CrossRef]

J. Appl. Phys. (1)

E. D. Palik, J. R. Stevenson, J. Webster, J. Appl. Phys. 37, 1982 (1966).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Spectrosc. (1)

V. K. Miloslavskii, Opt. Spectrosc. 14, 282 (1963) [Opt. Spectrosk. 14, 532 (1963)].

Other (3)

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 628.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962), Chap. 12.

For example, see R. E. Collen, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), p. 91.

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Equations (37)

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U ( ω ) = 1 2 [ T + ( ω ) ( x ^ + i y ^ ) + T - ( ω ) ( x ^ - i y ^ ) ] .
U ( ξ , ω ) = U ( ω ) · A ,
A = ½ [ exp ( - i ξ ) ( x ^ + i y ^ ) + exp ( i ξ ) ( x ^ - i y ^ ) ] .
U ( ξ , ω ) = ½ [ T - ( ω ) exp ( - i ξ ) + T + ( ω ) exp ( i ξ ) ] .
L ( ξ ) - S ( ω ) d ω = - S ( ω ) U ( ξ , ω ) 2 d ω ,
d L ( ξ ) / d ξ = 0
- S ( ω ) ξ U ( ξ , ω ) 2 d ω = 0.
exp ( i 4 γ ) 0 T + ( ω ) T - * ( ω ) S ( ω ) d ω = 0 T + * ( ω ) T - ( ω ) S ( ω ) d ω ,
γ = 1 2 [ Φ - ( ω 0 ) - Φ + ( ω 0 ) ] ,
T ± = T A ± T B ± exp ( - α ± ) exp ( - i β ± ) 1 - R A ± R B ± exp ( - 2 α ± ) exp ( - 2 i β ± ) ,
i σ i ± Δ ω / ω 1
R A ± R B ± exp ( - α ± ) < 1
T A + T B + T A - * T B - * l , m = 0 ( R A + R B + ) m ( R A - * R B - * ) l × exp [ - ( l + m + 1 ) ( η + i 2 θ ) - ( m - l ) ( + i 2 ϕ ) ] ,
θ Δ ω / ω 1 ,
η Δ ω / ω 1 ,
Δ ω / ω 1 ,
0 S ( ω ) exp [ - i 2 ( m - l ) ϕ ] d ω .
ϕ Δ ω / ω 1 ,
exp ( i 4 γ ) = exp ( i 4 θ ) × T A + * T B + * T A - T B - { 1 - R A + R B + R A - * R B - * exp [ - 2 ( η + i 2 θ ) ] } T A + T B + T A - * T B - * { 1 - R A + * R B + * R A - R B - exp [ - 2 ( η - i 2 θ ) ] } ,
T A ± T B ± = T A ± T B ± exp ( - i τ ± ) ,
R A ± R B ± = R A ± R B ± exp ( - i ρ ± ) ,
K = R A + B + R A - R B - exp ( - 2 η ) .
exp ( i 2 Γ ) = exp ( i 2 ) [ 1 - K exp ( - i 4 ) ] / 1 - K exp ( - i 4 ) ,
tan 2 Γ = [ ( 1 + K ) / ( 1 - K ) ] tan 2 .
T A ± = t 01 ± t 12 ± exp ( - i σ 1 ± ) 1 + r 01 ± r 12 ± exp ( - 2 i σ 1 ± ) ,
T B ± = t 20 ± ,
R A ± = - r 12 ± + r 01 ± exp ( - 2 i σ 1 ± ) 1 + r 01 ± r 12 ± exp ( - 2 i σ 1 ± ) ,
R B ± = r 20 ± ,
σ j ± = N j ± ω d j / c             j = 1 , 2 ;
r i j = N i ± - N j ± N i ± + N j ±             i , j = 1 , 2 ,
t i j = 2 N i ± N i ± + N j ±             i , j = 1 , 2 ,
η j = ω d j c ( k j + + k j - ) ,
j = ω d j c ( k j + + k j - ) ,
θ j = ω d j 2 c ( n j + - n j - ) ,
ϕ j = ω d j 2 c ( n j + + n j - ) ,
k j ± = k j ± c j 2 ω d j             j = 1 , 2 ,
n j ± = n j ± c θ j ω d j             j = 1 , 2 ,

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