Abstract

An analysis is made of the depolarizing properties of the Lyot depolarizer on light of arbitrary polarization and spectral properties. It is shown that the percentage modulation of the intensity transmitted by a rotating polarizer placed behind the depolarizer is a simple function of the Fourier transform of the frequency power spectrum of the incident light. Some consequences of this behavior are examined for commonly encountered spectra, notable among which is a periodic dependence of the modulation factor on the thickness of the depolarizer when the incident beam is generated by a semiconductor laser.

© 1979 Optical Society of America

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References

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  1. B. Lyot, Ann. Obs. Astron. Phys. Paris (Meudon) Tomi i Fasc. 1-2 8, 102 (1928).
  2. B. H. Billings, “A monochromatic depolarizer,” J. Opt. Soc. Am. 41, 966–975 (1951).
    [Crossref]
  3. K. Serkowski, “Polarization techniques,” in Methods of Experimental Physics (Academic, New York, 1974), Vol. 12, Part A, pp. 361–414.
    [Crossref]
  4. D. H. Martin and E. Puplett, “Polarised interferometric spectrometry for the millimetre and submillimetre spectrum,” in Infrared Physics (Pergamon, New York, 1969), Vol. 10, pp. 105–109.
    [Crossref]

1951 (1)

1928 (1)

B. Lyot, Ann. Obs. Astron. Phys. Paris (Meudon) Tomi i Fasc. 1-2 8, 102 (1928).

Billings, B. H.

Lyot, B.

B. Lyot, Ann. Obs. Astron. Phys. Paris (Meudon) Tomi i Fasc. 1-2 8, 102 (1928).

Martin, D. H.

D. H. Martin and E. Puplett, “Polarised interferometric spectrometry for the millimetre and submillimetre spectrum,” in Infrared Physics (Pergamon, New York, 1969), Vol. 10, pp. 105–109.
[Crossref]

Puplett, E.

D. H. Martin and E. Puplett, “Polarised interferometric spectrometry for the millimetre and submillimetre spectrum,” in Infrared Physics (Pergamon, New York, 1969), Vol. 10, pp. 105–109.
[Crossref]

Serkowski, K.

K. Serkowski, “Polarization techniques,” in Methods of Experimental Physics (Academic, New York, 1974), Vol. 12, Part A, pp. 361–414.
[Crossref]

Ann. Obs. Astron. Phys. Paris (Meudon) Tomi i Fasc. 1-2 (1)

B. Lyot, Ann. Obs. Astron. Phys. Paris (Meudon) Tomi i Fasc. 1-2 8, 102 (1928).

J. Opt. Soc. Am. (1)

Other (2)

K. Serkowski, “Polarization techniques,” in Methods of Experimental Physics (Academic, New York, 1974), Vol. 12, Part A, pp. 361–414.
[Crossref]

D. H. Martin and E. Puplett, “Polarised interferometric spectrometry for the millimetre and submillimetre spectrum,” in Infrared Physics (Pergamon, New York, 1969), Vol. 10, pp. 105–109.
[Crossref]

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Equations (44)

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V 1 = D V 0 ,
V = A V 1 ,
V 0 ( ω ) = ( I 0 ( ω ) M 0 ( ω ) C 0 ( ω ) S 0 ( ω ) ) , etc .
R = ( 1 0 0 0 0 r 22 r 23 r 24 0 r 32 r 33 r 34 0 r 42 r 43 r 44 ) ,
p = 1 2 ( 1 p 12 p 13 0 p 21 p 22 p 23 0 p 31 p 32 p 33 0 0 0 0 0 ) .
D = ( 1 0 0 0 0 d 22 d 23 d 24 0 d 32 d 33 d 34 0 d 42 d 43 d 44 ) .
I ( ω ) = ½ [ I 1 ( ω ) + p 12 M 1 ( ω ) + p 22 C 1 ( ω ) ] ,
p 12 = cos 2 θ p 22 = sin 2 θ ,
I 1 ( ω ) = I 0 ( ω ) , M 1 ( ω ) = [ d 22 M 0 ( ω ) + d 23 C 0 ( ω ) + d 24 S 0 ( ω ) , C 1 ( ω ) = [ d 32 M 0 ( ω ) + d 33 C 0 ( ω ) + d 34 S 0 ( ω ) .
D = R 2 ( τ 2 , π / 4 ) R 1 ( t 1 , 0 )
τ i = ( n 0 n e ) t i / c , i = 1 , 2 , sin ω τ i = s i , cos ω τ i = c i ,
R 1 = ( 1 0 0 0 0 1 0 0 0 0 c 1 s 1 0 0 s 1 c 1 ) , R 2 = ( 1 0 0 0 0 c 2 0 s 2 0 0 1 0 0 s 2 0 c 2 )
D = R 2 R 1 = ( 1 0 0 0 0 c 2 s 1 s 2 c 1 s 2 0 0 c 1 s 1 0 s 2 s 1 c 2 c 1 c 2 ) .
M 1 ( ω ) = c 2 M 0 ( ω ) + s 1 s 2 C 0 ( ω ) c 1 s 2 S 0 ( ω ) , C 1 ( ω ) = c 1 C 0 ( ω ) + s 1 S 0 ( ω ) .
sin ω τ 1 sin ω τ 2 = ½ [ cos ω ( τ 2 τ 1 ) cos ω ( τ 2 + τ 1 ) ] , cos ω τ 1 sin ω τ 2 = ½ [ sin ω ( τ 2 τ 1 ) + sin ω ( τ 2 + τ 1 ) ] ,
I ( ω ) = ½ ( I 0 ( ω ) + cos 2 θ { [ M 0 ( ω ) cos ω τ 2 + ½ C 0 ( ω ) [ cos ω ( τ 2 τ 1 ) cos ω ( τ 2 + τ 1 ) ] ½ S 0 ( ω ) [ sin ω ( τ 2 τ 1 ) + sin ω ( τ 2 + τ 1 ) ] } + sin 2 θ [ C 0 ( ω ) cos ω τ 1 + S 0 ( ω ) sin ω τ 1 ] ) .
I = 0 I ( ω ) d ω ,
V 0 ( ω ) = I 0 ( ω ) ( 1 m 0 c 0 s 0 ) ,
m 0 2 + c 0 2 + s 0 2 = 1
I = ( I 0 / 2 ) [ 1 + f ( τ 1 , τ 2 ) ] ,
f ( τ 1 , τ 2 ) = cos 2 θ { m 0 Φ c ( τ 2 ) + ½ c 0 [ Φ c ( τ 2 τ 1 ) Φ c ( τ 2 + τ 1 ) ] ½ s 0 [ Φ s ( τ 2 τ 1 ) + Φ s ( τ 2 + τ 1 ) ] } + sin 2 θ [ c 0 Φ c ( τ 1 ) + s 0 Φ s ( τ 1 ) ] ,
I 0 = 0 I ( ω ) d ω ,
Φ c ( τ ) = 1 I 0 0 I 0 ( ω ) cos ω τ d ω , Φ s ( τ ) = 1 I 0 0 I 0 ( ω ) sin ω τ d ω .
Δ ω Δ τ ½ ,
Φ c ( τ ) = 1 I 0 ( cos ω 0 τ I 0 ( ω + ω 0 ) cos ω τ d ω sin ω 0 τ I 0 ( ω + ω 0 ) sin ω τ d ω ) , Φ s ( τ ) = 1 I 0 ( sin ω 0 τ I 0 ( ω + ω 0 ) cos ω τ d ω + cos ω 0 τ I 0 ( ω + ω 0 ) sin ω τ d τ ) ,
Φ c ( τ ) = ( cos ω 0 ) Ψ ( τ ) , Φ s ( τ ) = ( sin ω 0 τ ) Ψ ( τ ) ,
Ψ ( τ ) = 1 I 0 I 0 ( ω + ω 0 ) cos ω τ d ω ,
f ( τ 1 , τ 2 ) = cos 2 θ { m 0 cos ω 0 τ 2 ) ψ ( τ 2 ) + ½ [ c 0 cos ω 0 ( τ 2 τ 1 ) s 0 sin ω 0 ( τ 2 τ 1 ) ] ψ ( τ 2 τ 1 ) ½ [ c 0 cos ω 0 ( τ 2 + τ 1 ) + s 0 sin ω 0 ( τ 2 + τ 1 ) ] ψ ( τ 2 + τ 1 ) ] } + sin 2 θ ( cos 0 ω 0 τ 2 + s 0 sin ω 0 τ 1 ) ψ ( τ 1 ) .
f ( τ ) = [ 1 2 ( c 0 cos ω 0 τ 3 s 0 sin ω 0 τ 3 ) cos 2 θ + ( c 0 cos ω 0 τ 3 + s 0 sin ω 0 τ 3 ) sin 2 θ ] ψ ( τ / 3 ) + ( m 0 cos 2 ω 0 τ 3 cos 2 θ ) ψ 2 τ 3 ½ [ ( c 0 cos ω 0 τ + s 0 sin ω 0 τ ) cos 2 θ ] ψ ( τ ) ,
f ( τ ) = m 0 cos 2 θ + [ ( c 0 cos ω 0 τ + s 0 sin ω 0 τ ) sin 2 θ ] ψ ( τ ) ,
V 0 ( ω ) = I 0 ( ω ) ( 1 cos 2 ϕ sin 2 ϕ 0 ) ,
f ( τ ) = cos 2 ϕ cos 2 θ + ( sin 2 ϕ sin 2 θ cos ω 0 τ ) ψ ( τ ) .
f ( τ ) = sin 2 θ ( cos ω 0 τ ) ψ ( τ ) .
f ( τ ) = { [ sin 2 ϕ cos ( ω 0 τ / 3 ) ] ( ½ cos 2 θ + sin 2 θ } ψ ( τ / 3 ) + [ cos 2 ϕ cos 2 θ cos ( 2 ω 0 τ / 3 ) ] ψ ( 2 τ / 3 ) [ ½ sin 2 ϕ cos 2 θ cos ω 0 τ ] ψ ( τ ) ,
f ( τ ) = cos 2 θ cos ( 2 ω 0 τ / 3 ) ] ψ ( 2 τ / 3 ) .
f ( τ ) [ 1 2 ( c 0 cos ω 0 τ 3 s 0 sin ω 0 τ 3 ) cos 2 θ + ( c 0 cos ω 0 τ 3 + s 0 sin ω 0 τ 3 ) sin 2 θ ] ψ ( τ / 3 ) ,
I 0 ( ω + ω 0 ) = [ I 0 / ( 2 Δ ω ) 1 / 2 ] exp [ ω 2 / 4 ( Δ ω ) 2 ] ,
ψ ( τ ) = exp [ ( Δ ω ) 2 τ 2 ] .
τ min = 3 λ 0 2 [ ln ( 1 / ) ] 1 / 2 / 2 π ( n 0 n e ) Δ λ .
I 0 ( ω + ω 0 ) = I m E ( ω ) n = G n cos ( n ω τ 0 ) ,
G n = τ 0 2 π π / π 0 π / τ 0 g ( ω ) cos ( n ω τ 0 ) d ω ,
ψ ( τ ) = ψ 0 n = G n ψ e ( τ + n τ 0 ) ,
ψ e ( τ ) = E ( ω ) cos ω τ d ω ,
ψ ( τ ) = ψ 0 n = exp [ ( Δ ω ) 2 ( τ + n τ 0 ) 2 ] ,