Abstract

A complete polarization analysis of fiber-recirculating delay line is conducted with particular emphasis given to controllability. An appropriate method of analyzing the polarization eigenmode structure of a general system is presented. It is shown that the eigenmode structure of a recirculating system constructed from normally birefringent fibers may be controlled through the use of in-line birefringence control devices such as fiber squeezers. As a result of this controllability, a nondestructive test for determining the splice-misalignment angle in the system is developed and demonstrated. The use of a recirculating delay-line filter as an in-line polarization control element is also developed from the eigenmode controllability. An additional investigation into the eigenmode structure of this type of system is also conducted. Excellent agreement between theoretical and experimental studies is achieved.

© 1992 Optical Society of America

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References

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  1. R. Ulrich, M. Johnson, “Fiber-ring interferometer: polarization analysis,” Opt. Lett. 4, 152–154 (1979).
    [CrossRef] [PubMed]
  2. P. Mouroulis, “Polarization fading effects in polarization-preserving fiber ring resonators,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 400–412 (1989).
  3. K. Hotate, K. Takiguchi, M. Murakami, “Bias of an optical passive ring-resonator due to the misalignment of the polarization axis in the resonator formed by the polarization-maintaining fiber,” in Optical Fiber Sensors 1989, H. J. Arditty, ed., Vol. 44 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1989), pp. 94–100.
    [CrossRef]
  4. B. Lamouroux, B. Prade, A. Orszag, “Polarization effect in optical-fiber ring resonator,” Opt. Lett. 7, 391–393 (1982).
    [CrossRef] [PubMed]
  5. I. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
    [CrossRef]
  6. S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
    [CrossRef]
  7. L. F. Stokes, M. Chodorow, H. J. Shaw, “Sensitive all-single-mode-fiber resonant ring interferometer,” IEEE J. Lightwave Technol. LT-1, 110–115 (1983).
    [CrossRef]
  8. E.-J. Bachus, R.-P. Braun, B. Strebel, “Polarization-maintaining single-mode-fiber resonator,” Electron Lett. 19, 1027–1028 (1983).
    [CrossRef]
  9. A. D. Kersey, A. Daindridge, A. B. Tveten, “Elimination of polarization induced signal fading in interferometric fiber sensors using input polarization control,” in Optical Fiber Sensors 1988 (Optical Society of America, Washington, D.C., 1988), pp. I/44–I/47.
  10. K. Iwatsuki, K. Hotate, M. Higashiguchi, “Eigenstate of polarization in a fiber ring resonator and its effect in an optical passive ring-resonator gyro,” Appl. Opt. 25, 2606–2612 (1986).
    [CrossRef] [PubMed]
  11. G. A. Sanders, R. B. Smith, G. F. Rouse, “Novel polarization-rotating fiber resonator for rotation sensing applications,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 373–381 (1989).
  12. Z. K. Ioannides, R. Kadiwar, I. P. Giles, “Polarization mode coupling in highly birefringent optical-fiber ring resonators,” Opt. Lett. 14, 520–522 (1989).
    [CrossRef]
  13. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488–503 (1941).
    [CrossRef]
  14. C. L. Chen, W. K. Burns, “Polarization characteristics of single-mode fiber couplers,” IEEE J. Quantum Electron. QE-18, 1589–1600 (1982).
    [CrossRef]
  15. B. Noble, J. W. Daniel, Applied Linear Algebra (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 308.
  16. M. Johnson, “In-line fiber-optical polarization transformer,” Appl. Opt. 18, 1288–1289 (1979).
    [CrossRef] [PubMed]
  17. L. Stokes, M. Chodorow, H. Shaw, “All-single-mode fiber resonator,” Opt. Lett. 7, 288–290 (1982).
    [CrossRef] [PubMed]
  18. M. Takahashi, S. Tai, K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarization-maintaining fiber coupler,” Electron Lett. 25, 600–602 (1989).
    [CrossRef]

1989 (2)

M. Takahashi, S. Tai, K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarization-maintaining fiber coupler,” Electron Lett. 25, 600–602 (1989).
[CrossRef]

Z. K. Ioannides, R. Kadiwar, I. P. Giles, “Polarization mode coupling in highly birefringent optical-fiber ring resonators,” Opt. Lett. 14, 520–522 (1989).
[CrossRef]

1986 (1)

1983 (3)

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

L. F. Stokes, M. Chodorow, H. J. Shaw, “Sensitive all-single-mode-fiber resonant ring interferometer,” IEEE J. Lightwave Technol. LT-1, 110–115 (1983).
[CrossRef]

E.-J. Bachus, R.-P. Braun, B. Strebel, “Polarization-maintaining single-mode-fiber resonator,” Electron Lett. 19, 1027–1028 (1983).
[CrossRef]

1982 (3)

1981 (1)

I. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

1979 (2)

1941 (1)

Bachus, E.-J.

E.-J. Bachus, R.-P. Braun, B. Strebel, “Polarization-maintaining single-mode-fiber resonator,” Electron Lett. 19, 1027–1028 (1983).
[CrossRef]

Braun, R.-P.

E.-J. Bachus, R.-P. Braun, B. Strebel, “Polarization-maintaining single-mode-fiber resonator,” Electron Lett. 19, 1027–1028 (1983).
[CrossRef]

Burns, W. K.

C. L. Chen, W. K. Burns, “Polarization characteristics of single-mode fiber couplers,” IEEE J. Quantum Electron. QE-18, 1589–1600 (1982).
[CrossRef]

Chen, C. L.

C. L. Chen, W. K. Burns, “Polarization characteristics of single-mode fiber couplers,” IEEE J. Quantum Electron. QE-18, 1589–1600 (1982).
[CrossRef]

Chodorow, M.

L. F. Stokes, M. Chodorow, H. J. Shaw, “Sensitive all-single-mode-fiber resonant ring interferometer,” IEEE J. Lightwave Technol. LT-1, 110–115 (1983).
[CrossRef]

L. Stokes, M. Chodorow, H. Shaw, “All-single-mode fiber resonator,” Opt. Lett. 7, 288–290 (1982).
[CrossRef] [PubMed]

Daindridge, A.

A. D. Kersey, A. Daindridge, A. B. Tveten, “Elimination of polarization induced signal fading in interferometric fiber sensors using input polarization control,” in Optical Fiber Sensors 1988 (Optical Society of America, Washington, D.C., 1988), pp. I/44–I/47.

Daniel, J. W.

B. Noble, J. W. Daniel, Applied Linear Algebra (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 308.

Giles, I. P.

Higashiguchi, M.

Hotate, K.

K. Iwatsuki, K. Hotate, M. Higashiguchi, “Eigenstate of polarization in a fiber ring resonator and its effect in an optical passive ring-resonator gyro,” Appl. Opt. 25, 2606–2612 (1986).
[CrossRef] [PubMed]

K. Hotate, K. Takiguchi, M. Murakami, “Bias of an optical passive ring-resonator due to the misalignment of the polarization axis in the resonator formed by the polarization-maintaining fiber,” in Optical Fiber Sensors 1989, H. J. Arditty, ed., Vol. 44 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1989), pp. 94–100.
[CrossRef]

Ioannides, Z. K.

Iwatsuki, K.

Johnson, M.

Jones, R. C.

Kadiwar, R.

Kaminow, I.

I. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

Kersey, A. D.

A. D. Kersey, A. Daindridge, A. B. Tveten, “Elimination of polarization induced signal fading in interferometric fiber sensors using input polarization control,” in Optical Fiber Sensors 1988 (Optical Society of America, Washington, D.C., 1988), pp. I/44–I/47.

Kyuma, K.

M. Takahashi, S. Tai, K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarization-maintaining fiber coupler,” Electron Lett. 25, 600–602 (1989).
[CrossRef]

Lamouroux, B.

Mouroulis, P.

P. Mouroulis, “Polarization fading effects in polarization-preserving fiber ring resonators,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 400–412 (1989).

Murakami, M.

K. Hotate, K. Takiguchi, M. Murakami, “Bias of an optical passive ring-resonator due to the misalignment of the polarization axis in the resonator formed by the polarization-maintaining fiber,” in Optical Fiber Sensors 1989, H. J. Arditty, ed., Vol. 44 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1989), pp. 94–100.
[CrossRef]

Noble, B.

B. Noble, J. W. Daniel, Applied Linear Algebra (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 308.

Orszag, A.

Prade, B.

Rashleigh, S. C.

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

Rouse, G. F.

G. A. Sanders, R. B. Smith, G. F. Rouse, “Novel polarization-rotating fiber resonator for rotation sensing applications,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 373–381 (1989).

Sanders, G. A.

G. A. Sanders, R. B. Smith, G. F. Rouse, “Novel polarization-rotating fiber resonator for rotation sensing applications,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 373–381 (1989).

Shaw, H.

Shaw, H. J.

L. F. Stokes, M. Chodorow, H. J. Shaw, “Sensitive all-single-mode-fiber resonant ring interferometer,” IEEE J. Lightwave Technol. LT-1, 110–115 (1983).
[CrossRef]

Smith, R. B.

G. A. Sanders, R. B. Smith, G. F. Rouse, “Novel polarization-rotating fiber resonator for rotation sensing applications,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 373–381 (1989).

Stokes, L.

Stokes, L. F.

L. F. Stokes, M. Chodorow, H. J. Shaw, “Sensitive all-single-mode-fiber resonant ring interferometer,” IEEE J. Lightwave Technol. LT-1, 110–115 (1983).
[CrossRef]

Strebel, B.

E.-J. Bachus, R.-P. Braun, B. Strebel, “Polarization-maintaining single-mode-fiber resonator,” Electron Lett. 19, 1027–1028 (1983).
[CrossRef]

Tai, S.

M. Takahashi, S. Tai, K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarization-maintaining fiber coupler,” Electron Lett. 25, 600–602 (1989).
[CrossRef]

Takahashi, M.

M. Takahashi, S. Tai, K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarization-maintaining fiber coupler,” Electron Lett. 25, 600–602 (1989).
[CrossRef]

Takiguchi, K.

K. Hotate, K. Takiguchi, M. Murakami, “Bias of an optical passive ring-resonator due to the misalignment of the polarization axis in the resonator formed by the polarization-maintaining fiber,” in Optical Fiber Sensors 1989, H. J. Arditty, ed., Vol. 44 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1989), pp. 94–100.
[CrossRef]

Tveten, A. B.

A. D. Kersey, A. Daindridge, A. B. Tveten, “Elimination of polarization induced signal fading in interferometric fiber sensors using input polarization control,” in Optical Fiber Sensors 1988 (Optical Society of America, Washington, D.C., 1988), pp. I/44–I/47.

Ulrich, R.

Appl. Opt. (2)

Electron Lett. (2)

M. Takahashi, S. Tai, K. Kyuma, “Nondestructive measuring technique for misaligned angle in polarization-maintaining fiber coupler,” Electron Lett. 25, 600–602 (1989).
[CrossRef]

E.-J. Bachus, R.-P. Braun, B. Strebel, “Polarization-maintaining single-mode-fiber resonator,” Electron Lett. 19, 1027–1028 (1983).
[CrossRef]

IEEE J. Lightwave Technol. (2)

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

L. F. Stokes, M. Chodorow, H. J. Shaw, “Sensitive all-single-mode-fiber resonant ring interferometer,” IEEE J. Lightwave Technol. LT-1, 110–115 (1983).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. L. Chen, W. K. Burns, “Polarization characteristics of single-mode fiber couplers,” IEEE J. Quantum Electron. QE-18, 1589–1600 (1982).
[CrossRef]

I. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (4)

Other (5)

B. Noble, J. W. Daniel, Applied Linear Algebra (Prentice-Hall, Englewood Cliffs, N.J., 1977), p. 308.

A. D. Kersey, A. Daindridge, A. B. Tveten, “Elimination of polarization induced signal fading in interferometric fiber sensors using input polarization control,” in Optical Fiber Sensors 1988 (Optical Society of America, Washington, D.C., 1988), pp. I/44–I/47.

P. Mouroulis, “Polarization fading effects in polarization-preserving fiber ring resonators,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 400–412 (1989).

K. Hotate, K. Takiguchi, M. Murakami, “Bias of an optical passive ring-resonator due to the misalignment of the polarization axis in the resonator formed by the polarization-maintaining fiber,” in Optical Fiber Sensors 1989, H. J. Arditty, ed., Vol. 44 of Springer Proceedings in Physics (Springer-Verlag, Berlin, 1989), pp. 94–100.
[CrossRef]

G. A. Sanders, R. B. Smith, G. F. Rouse, “Novel polarization-rotating fiber resonator for rotation sensing applications,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 373–381 (1989).

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Figures (9)

Fig. 1
Fig. 1

System diagram for a RDL filter constructed from a directional coupler.

Fig. 2
Fig. 2

Fiber-section splice-misalignment geometry.

Fig. 3
Fig. 3

(a) Experimental results versus (b) simulation data; κx = κy = 0.66, Δ+ = 1.135 rad, Δ = 0, γx = γy = 0.05, γs,x = γs,y = 0.05, θs = 47°, θin = −25°, and θp = 175°. Intensity is displayed in arbitrary units.

Fig. 4
Fig. 4

(a) Experimental results versus (b) simulation data; κx = κy = 0.66, Δ+ = 1.135 rad, Δ = 0, γx = γy = 0.05, γs,x = γs,y = 0.05, θs = 47°, θin = 15°, and θp = 175°. Intensity is displayed in arbitrary units.

Fig. 5
Fig. 5

(a) Experimental results versus (b) simulation data; κx = κy = 0.66, Δ+ = 1.135 rad, Δ = 0, γx = γy = 0.05, γs,x = γs,y = 0.05, θs = 47°, θin = 65°, and θp = 175°. Intensity is displayed in arbitrary units.

Fig. 6
Fig. 6

Plot of theoretical output-polarization rotation (given a linearly polarized input field) as a function of βL, with θs as a parameter. The RDL system of Fig. 1 has been adjusted for circular eigenmodes in this simulation.

Fig. 7
Fig. 7

Plot of theoretical minimum resonance spacing as a function of Δ+ with θs as a parameter (κ = 0.7).

Fig. 8
Fig. 8

Plot of experimentally determined minimum resonance spacing as a function of voltage applied to the solenoid (Vsol). The minimum separation is approximately 94°.

Fig. 9
Fig. 9

Experimental verification of the tunability of the resonance location. The solid curve, displaying resonances a, b, and c, shows the output of one of the polarization detectors with Vsol = 0 V. The resonances a and c are separated by βL = 2π, as are a′ and c′. The dotted curve (resonances a′, b′, and c′) demonstrates that the spacing between resonances a′ and b′ has been changed to approximately π rad, with Vsol = approximately 45 V. Intensity is displayed in arbitrary units.

Tables (2)

Tables Icon

Table 1 H Eigenmode Orthogonality Studya

Tables Icon

Table 2 H, R Controllabilitya

Equations (28)

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[ E 3 E 4 ] = [ p q - q * p * ] [ E 1 E 2 ] .
p = 1 - γ 1 - κ 2 ,             q = j κ 1 - γ .
E 2 = exp ( j β L ) E 3 ,             β L = N ω L / c ,
| E out E in | 2 = | E 4 E 1 | 2 = | - q * + ( p 2 + q 2 ) exp ( j β L ) 1 - q exp ( j β L ) | 2 ,
| E 3 E 1 | 2 = | p 1 - q exp ( j β L ) | 2 .
β L = m 2 π - π 2 ,
E 4 = H E 1 ,
E out , i = M i E in , i ,
M = exp ( j β L ) [ exp ( - j d 2 2 ) 0 0 exp ( j d 2 2 ) ] [ c s - s c ] × [ 1 - γ s , x 0 0 1 - γ s , y ] [ exp ( - j d 1 2 ) 0 0 exp ( j d 1 2 ) ] = exp ( j β L ) [ 1 - γ s , x c × exp ( - j Δ + ) 1 - γ s , y s × exp ( j Δ - ) - 1 - γ s , x s × exp ( - j Δ - ) 1 - γ s , y c × exp ( j Δ + ) ] ,
[ E 3 E 4 ] = [ P Q - Q * P ] [ E 1 E 2 ] ,
P = [ [ ( 1 - γ x ) ( 1 - κ x 2 ) ] 1 / 2 0 0 [ ( 1 - γ y ) ( 1 - κ y 2 ) ] 1 / 2 ] , Q = [ j κ x 1 - γ x 0 0 j κ y 1 - γ y ] .
E 2 = M E 3 .
E 4 = [ Q + PM ( I - QM ) - 1 P ] E 1 = H E 1 ,
E 3 = ( I - QM ) - 1 P E 1 = P E 1 + QME 3 = P E 1 + R E 3 ,
H E i = λ i E i ,
H = [ A B C D ] ,
λ 1 , 2 = ½ ( A + D ) ± ½ [ ( A - D ) 2 + 4 B C ] 1 / 2 ,
E 1 = [ 1 λ 1 - A B ] ,             E 2 = [ λ 2 - D C 1 ] .
H = ( 1 - κ 2 ) exp ( j β L ) δ [ h 11 h 12 - h 12 * h 22 ] ,
h 11 = j δ ( 1 - κ 2 ) κ exp ( - j β L ) + c exp ( - j Δ + ) - j κ exp ( j β L ) , h 12 = s exp ( j Δ - ) , h 22 = j δ ( 1 - κ 2 ) κ exp ( - j β L ) + c exp ( j Δ + ) - j κ exp ( j β L ) , R = j κ exp ( j β L ) [ c exp ( - j Δ + ) s exp ( j Δ - ) - s exp ( - j Δ - ) c exp ( j Δ + ) ] ,
δ = 1 - 2 j c κ exp ( j β L ) cos Δ + - κ 2 exp ( 2 j β L ) .
H = [ Γ + c exp ( - j Δ + ) s exp ( j Δ - ) - s exp ( - j Δ - ) Γ + c exp ( j Δ + ) ] = Γ I + 1 - κ 2 j κ δ R ,
E in = [ cos θ in sin θ in ] = 1 2 exp ( - j θ in ) [ 1 j ] + 1 2 exp ( + j θ in ) [ 1 - j ] .
λ i = exp ( j ρ i ) .
E o u t = 1 2 exp ( - j θ i n ) exp ( j ρ 1 ) [ 1 j ] + 1 2 exp ( + j θ i n ) exp ( j ρ 2 ) [ 1 - j ] = [ cos ( θ in - ρ 1 - ρ 2 2 ) sin ( θ in - ρ 1 - ρ 2 2 ) ] .
exp ( j β L ) = - j cos θ s cos Δ + ± ( 1 - cos 2 θ s cos 2 Δ + ) 1 / 2 .
β L = m 2 π - π 2 ± cos - 1 ( cos θ s cos Δ + ) .
T = 2 cos - 1 ( cos θ s cos Δ + ) .

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