Abstract

A formalism is presented for treating birefringence and polarization in fiber optic sensors. This formalism is applied to study theoretical characteristics of fiber gyroscopes which are operated with various states of polarization of the input light including nonpolarized and partially polarized light, which have potentially useful characteristics. Measurements supporting the theoretical predictions are described.

© 1982 Optical Society of America

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References

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  1. R. Ulrich, A. Simon, Appl. Opt. 18, 2241 (1979).
    [CrossRef] [PubMed]
  2. R. Ulrich, S. C. Rashleigh, W. Eickhoff, Opt. Lett. 5, 273 (1980).
    [CrossRef] [PubMed]
  3. V. Ramaswamy, R. H. Stolen, M. D. Divino, W. Pleibel, Appl. Opt. 18, 4080 (1979).
    [CrossRef] [PubMed]
  4. R. Ulrich, M. Johnson, Opt. Lett. 4, 152 (1979).
    [CrossRef] [PubMed]
  5. G. Franschetti, C. Smith, J. Opt. Soc. Am. 71, 1487 (1981).
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), p. 544-553.
  7. R. Ulrich, Opt. Lett. 5, 173 (1980).
    [CrossRef] [PubMed]
  8. E. Kintner, Opt. Lett. 6, 154 (1981).
    [CrossRef] [PubMed]
  9. If the beam splitter is not ideal, two beam splitters must be used to guarantee reciprocity.

1981 (2)

1980 (2)

1979 (3)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), p. 544-553.

Divino, M. D.

Eickhoff, W.

Franschetti, G.

Johnson, M.

Kintner, E.

Pleibel, W.

Ramaswamy, V.

Rashleigh, S. C.

Simon, A.

Smith, C.

Stolen, R. H.

Ulrich, R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), p. 544-553.

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Figures (12)

Fig. 1
Fig. 1

Four-port linear system model of a single-mode fiber. The ports are x1, x2, y1, y2 corresponding to linear polarizations. The channels between the ports are shown schematically along with their complex scattering coefficients.

Fig. 2
Fig. 2

Model of a single-mode fiber in which the two polarization modes are coupled at a point Z and are uncoupled at all other points.

Fig. 3
Fig. 3

Schematic of the fiber optic rotation sensor, which is analyzed.

Fig. 4
Fig. 4

Normalized intensity vs Sagnac phase shift for polarized input. The polarizer passes the input polarization. The parameter θ is (a) 0, (b) 30, (c) 60.

Fig. 5
Fig. 5

Normalized intensity vs Sagnac phase shift for polarized input. The polarizer rejects the input polarization. The parameters θ and ϕ are (a) (90,180), (b) (60,90), (c) (30,45).

Fig. 6
Fig. 6

Normalized intensity vs Sagnac phase shift for polarized input. No polarizer is used. The parameters θ and ϕ are (a) (0,0), (b) (30,45), (c) (60,90).

Fig. 7
Fig. 7

Normalized intensity vs Sagnac phase shift for completely unpolarized input. No polarizer is used. The parameters θ and ϕ are (a) (0,0), (b) (30,45), (c) (60,90).

Fig. 8
Fig. 8

Normalized intensity vs Sagnac phase shift for partially polarized input. No polarizer is used. The parameters θ and ϕ are (45,90). The degree of polarization is (a) 1, (b) 0.5, (c) 0.

Fig. 9
Fig. 9

Measured intensity vs Sagnac phase shift using polarized input light with polarizer passing the input polarization for different birefringent conditions in the fiber.

Fig. 10
Fig. 10

Measured intensity vs Sagnac phase shift using polarized input light with polarizer rejecting the input polarization for different birefringent conditions in the fiber.

Fig. 11
Fig. 11

Measured intensity vs Sagnac phase shift using polarized input light with no polarizer for different birefringent conditions in the fiber.

Fig. 12
Fig. 12

Measured intensity vs Sagnac phase shift using input light of 5% degree of polarization for different birefringent conditions in the fiber.

Equations (28)

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J = ( E K E K * E K E L * E L E K * E L E L * ) ,
J K L = J L K * ,
P = | λ 1 λ 2 | / ( λ 1 + λ 2 ) ,
I = T r J .
J out = SJ in S + .
S 12 = ( t ( X 1 , X 2 ) t ( X 1 , Y 2 ) t ( Y 1 , X 2 ) t ( Y 1 , Y 2 ) ) ,
S 21 = ( t ( X 2 , X 1 ) t ( X 2 , Y 1 ) t ( Y 2 , X 1 ) t ( Y 2 , Y 1 ) ) ,
t ( k , l ) = t ( l , k ) .
S 12 = exp ( j β ¯ L ) × ( cos θ exp ( j Δ β L 2 ) sin θ exp [ j Δ β ( L 2 z ) ] sin θ exp [ j Δ β ( L 2 z ) ] cos θ exp ( j Δ β L / 2 ) ) ,
S 12 = exp ( j β ¯ L ) × ( cos θ exp ( j Δ β L 2 ) sin θ exp [ j Δ β ( L 2 z ) ] sin θ exp [ j Δ β ( L 2 z ) ] cos θ exp ( j Δ β L / 2 ) ) ,
S 12 = exp [ j ϕ ¯ ( L ) ] ( cos θ ( L ) exp [ j ξ ( L ) / 2 ] sin θ ( L ) exp [ j ϕ ( L ) / 2 ] sin θ ( L ) exp [ j ϕ ( L ) / 2 ] cos θ ( L ) exp [ j ξ ( L ) / 2 ] ) ,
S 21 = exp [ j ϕ ¯ ( L ) ] ( cos θ ( L ) exp [ j ξ ( L ) / 2 ] sin θ ( L ) exp [ j ϕ ( L ) / 2 ] sin θ ( L ) exp [ j ϕ ( L ) / 2 ] cos θ ( L ) exp [ j ξ ( L ) / 2 ] ) .
S 12 = exp ( j ϕ s / 2 ) S 12 ,
S 21 = exp ( j ϕ s / 2 ) S 21 .
P x = ( 1 0 0 0 ) ,
P y = ( 0 0 0 1 ) .
T = exp ( j π / 4 ) 2 ( 1 0 0 1 ) ,
R = exp ( j π / 4 ) 2 ( 1 0 0 1 ) .
G = P j ( R S 12 R + T S 21 T ) ,
J in = ( 1 0 0 0 ) .
I = ½ cos 2 θ ( 1 cos ϕ s ) .
I = ½ sin 2 θ [ 1 + cos ( ϕ s + ϕ ) ] .
I = ½ [ 1 cos 2 θ cos ϕ s + sin 2 θ cos ( ϕ s + ϕ ) ] .
J in = ( 1 / 2 0 0 1 / 2 ) .
I = ½ [ 1 ( cos 2 θ sin 2 θ cos ϕ ) cos ϕ s ] .
J in = ( ( ½ ) ( 1 + P ) 0 0 ( ½ ) ( 1 P ) ) .
J in = ( P 0 0 0 ) + ( ( ½ ) ( 1 P ) 0 0 ( ½ ) ( 1 P ) ) .
I = ½ [ 1 ( cos 2 θ sin 2 θ cos ϕ ) cos ϕ s ] P / 2 sin 2 θ sin ϕ sin ϕ s .

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