Abstract

We have measured the Faraday effect in silica standard optical fibers in the wavelength range 458–1523 nm. An effective Verdet constant V ef that exhibits a linear dependence on the square of the optical frequency ν is defined: V ef = (0.142 ± 0.004) × 10−28 ν 2 rad T−1 m−1. We demonstrate that the negative effects of a small linear birefringence can be minimized by adjustment of the input polarization to an optimum state.

© 1996 Optical Society of America

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References

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  1. D. Tang, A. H. Rose, G. W. Day, S. E. Etzel, “Annealing of linear birefringence in single-mode fiber coils: applications to optical fiber current sensors,” J. Lightwave Technol. 9, 1031–1037 (1991).
    [Crossref]
  2. V. Annovazi-Lodi, S. Donati, S. Merlo, “Coiled-fiber sensor for vectorial measurement of magnetic field,” J. Lightwave Technol. 10, 2006–2010 (1992).
    [Crossref]
  3. S. C. Rashleigh, R. Ulrich, “Magneto-optic current sensing with birefringent fibers,” Appl. Phys. Lett. 34, 768–770 (1979).
    [Crossref]
  4. G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Faraday rotation in coiled, monomode optical fibers: isolators, filters, and magnetic sensors,” Opt. Lett. 7, 238–240 (1982).
    [Crossref] [PubMed]
  5. R. Ulrich, S. C. Rashleigh, W. Eickhoff, “Bending-induced birefringence in single-mode fibers,” Opt. Lett. 5, 273–275 (1980).
    [Crossref] [PubMed]
  6. E. H. Turner, R. H. Stolen, “Fiber Faraday circulator or isolator,” Opt. Lett. 6, 322–323 (1981).
    [Crossref] [PubMed]
  7. H. C. Lefevre, “Single mode fractional wave device and polarisation controllers,” Electron. Lett. 16, 778–780 (1980).
    [Crossref]
  8. N. Kaliteevski, Optique Ondulatoire (Mir, Moscow, 1980), Chap. IV, p. 152.
  9. K. Turvey, “Determination of Verdet constant from combined ac and dc measurements,” Rev. Sci. Instrum. 64, 1561–1568 (1993).
    [Crossref]
  10. J. Noda, T. Hosaka, Y. Sasaki, R. Ulrich, “Dispersion of Verdet constant in stress-birefringent silica fibre,” Electron. Lett. 20, 906–908 (1984).
    [Crossref]
  11. A. M. Smith, “Polarization and magnetooptic properties of single-mode optical fiber,” Appl. Opt. 17, 52–56 (1978).
    [Crossref] [PubMed]
  12. R. H. Stolen, E. H. Turner, “Faraday rotation in highly birefringent optical fibers,” Appl. Opt. 19, 842–845 (1980).
    [Crossref] [PubMed]
  13. A. M. Smith, “Faraday effect in single-mode optical fibre using an injection laser light source,” Electron. Lett. 16, 206–208 (1980).
    [Crossref]

1993 (1)

K. Turvey, “Determination of Verdet constant from combined ac and dc measurements,” Rev. Sci. Instrum. 64, 1561–1568 (1993).
[Crossref]

1992 (1)

V. Annovazi-Lodi, S. Donati, S. Merlo, “Coiled-fiber sensor for vectorial measurement of magnetic field,” J. Lightwave Technol. 10, 2006–2010 (1992).
[Crossref]

1991 (1)

D. Tang, A. H. Rose, G. W. Day, S. E. Etzel, “Annealing of linear birefringence in single-mode fiber coils: applications to optical fiber current sensors,” J. Lightwave Technol. 9, 1031–1037 (1991).
[Crossref]

1984 (1)

J. Noda, T. Hosaka, Y. Sasaki, R. Ulrich, “Dispersion of Verdet constant in stress-birefringent silica fibre,” Electron. Lett. 20, 906–908 (1984).
[Crossref]

1982 (1)

1981 (1)

1980 (4)

H. C. Lefevre, “Single mode fractional wave device and polarisation controllers,” Electron. Lett. 16, 778–780 (1980).
[Crossref]

R. Ulrich, S. C. Rashleigh, W. Eickhoff, “Bending-induced birefringence in single-mode fibers,” Opt. Lett. 5, 273–275 (1980).
[Crossref] [PubMed]

R. H. Stolen, E. H. Turner, “Faraday rotation in highly birefringent optical fibers,” Appl. Opt. 19, 842–845 (1980).
[Crossref] [PubMed]

A. M. Smith, “Faraday effect in single-mode optical fibre using an injection laser light source,” Electron. Lett. 16, 206–208 (1980).
[Crossref]

1979 (1)

S. C. Rashleigh, R. Ulrich, “Magneto-optic current sensing with birefringent fibers,” Appl. Phys. Lett. 34, 768–770 (1979).
[Crossref]

1978 (1)

Annovazi-Lodi, V.

V. Annovazi-Lodi, S. Donati, S. Merlo, “Coiled-fiber sensor for vectorial measurement of magnetic field,” J. Lightwave Technol. 10, 2006–2010 (1992).
[Crossref]

Barlow, A. J.

Day, G. W.

D. Tang, A. H. Rose, G. W. Day, S. E. Etzel, “Annealing of linear birefringence in single-mode fiber coils: applications to optical fiber current sensors,” J. Lightwave Technol. 9, 1031–1037 (1991).
[Crossref]

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Faraday rotation in coiled, monomode optical fibers: isolators, filters, and magnetic sensors,” Opt. Lett. 7, 238–240 (1982).
[Crossref] [PubMed]

Donati, S.

V. Annovazi-Lodi, S. Donati, S. Merlo, “Coiled-fiber sensor for vectorial measurement of magnetic field,” J. Lightwave Technol. 10, 2006–2010 (1992).
[Crossref]

Eickhoff, W.

Etzel, S. E.

D. Tang, A. H. Rose, G. W. Day, S. E. Etzel, “Annealing of linear birefringence in single-mode fiber coils: applications to optical fiber current sensors,” J. Lightwave Technol. 9, 1031–1037 (1991).
[Crossref]

Hosaka, T.

J. Noda, T. Hosaka, Y. Sasaki, R. Ulrich, “Dispersion of Verdet constant in stress-birefringent silica fibre,” Electron. Lett. 20, 906–908 (1984).
[Crossref]

Kaliteevski, N.

N. Kaliteevski, Optique Ondulatoire (Mir, Moscow, 1980), Chap. IV, p. 152.

Lefevre, H. C.

H. C. Lefevre, “Single mode fractional wave device and polarisation controllers,” Electron. Lett. 16, 778–780 (1980).
[Crossref]

Merlo, S.

V. Annovazi-Lodi, S. Donati, S. Merlo, “Coiled-fiber sensor for vectorial measurement of magnetic field,” J. Lightwave Technol. 10, 2006–2010 (1992).
[Crossref]

Noda, J.

J. Noda, T. Hosaka, Y. Sasaki, R. Ulrich, “Dispersion of Verdet constant in stress-birefringent silica fibre,” Electron. Lett. 20, 906–908 (1984).
[Crossref]

Payne, D. N.

Ramskov-Hansen, J. J.

Rashleigh, S. C.

R. Ulrich, S. C. Rashleigh, W. Eickhoff, “Bending-induced birefringence in single-mode fibers,” Opt. Lett. 5, 273–275 (1980).
[Crossref] [PubMed]

S. C. Rashleigh, R. Ulrich, “Magneto-optic current sensing with birefringent fibers,” Appl. Phys. Lett. 34, 768–770 (1979).
[Crossref]

Rose, A. H.

D. Tang, A. H. Rose, G. W. Day, S. E. Etzel, “Annealing of linear birefringence in single-mode fiber coils: applications to optical fiber current sensors,” J. Lightwave Technol. 9, 1031–1037 (1991).
[Crossref]

Sasaki, Y.

J. Noda, T. Hosaka, Y. Sasaki, R. Ulrich, “Dispersion of Verdet constant in stress-birefringent silica fibre,” Electron. Lett. 20, 906–908 (1984).
[Crossref]

Smith, A. M.

A. M. Smith, “Faraday effect in single-mode optical fibre using an injection laser light source,” Electron. Lett. 16, 206–208 (1980).
[Crossref]

A. M. Smith, “Polarization and magnetooptic properties of single-mode optical fiber,” Appl. Opt. 17, 52–56 (1978).
[Crossref] [PubMed]

Stolen, R. H.

Tang, D.

D. Tang, A. H. Rose, G. W. Day, S. E. Etzel, “Annealing of linear birefringence in single-mode fiber coils: applications to optical fiber current sensors,” J. Lightwave Technol. 9, 1031–1037 (1991).
[Crossref]

Turner, E. H.

Turvey, K.

K. Turvey, “Determination of Verdet constant from combined ac and dc measurements,” Rev. Sci. Instrum. 64, 1561–1568 (1993).
[Crossref]

Ulrich, R.

J. Noda, T. Hosaka, Y. Sasaki, R. Ulrich, “Dispersion of Verdet constant in stress-birefringent silica fibre,” Electron. Lett. 20, 906–908 (1984).
[Crossref]

R. Ulrich, S. C. Rashleigh, W. Eickhoff, “Bending-induced birefringence in single-mode fibers,” Opt. Lett. 5, 273–275 (1980).
[Crossref] [PubMed]

S. C. Rashleigh, R. Ulrich, “Magneto-optic current sensing with birefringent fibers,” Appl. Phys. Lett. 34, 768–770 (1979).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

S. C. Rashleigh, R. Ulrich, “Magneto-optic current sensing with birefringent fibers,” Appl. Phys. Lett. 34, 768–770 (1979).
[Crossref]

Electron. Lett. (3)

H. C. Lefevre, “Single mode fractional wave device and polarisation controllers,” Electron. Lett. 16, 778–780 (1980).
[Crossref]

A. M. Smith, “Faraday effect in single-mode optical fibre using an injection laser light source,” Electron. Lett. 16, 206–208 (1980).
[Crossref]

J. Noda, T. Hosaka, Y. Sasaki, R. Ulrich, “Dispersion of Verdet constant in stress-birefringent silica fibre,” Electron. Lett. 20, 906–908 (1984).
[Crossref]

J. Lightwave Technol. (2)

D. Tang, A. H. Rose, G. W. Day, S. E. Etzel, “Annealing of linear birefringence in single-mode fiber coils: applications to optical fiber current sensors,” J. Lightwave Technol. 9, 1031–1037 (1991).
[Crossref]

V. Annovazi-Lodi, S. Donati, S. Merlo, “Coiled-fiber sensor for vectorial measurement of magnetic field,” J. Lightwave Technol. 10, 2006–2010 (1992).
[Crossref]

Opt. Lett. (3)

Rev. Sci. Instrum. (1)

K. Turvey, “Determination of Verdet constant from combined ac and dc measurements,” Rev. Sci. Instrum. 64, 1561–1568 (1993).
[Crossref]

Other (1)

N. Kaliteevski, Optique Ondulatoire (Mir, Moscow, 1980), Chap. IV, p. 152.

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Figures (6)

Fig. 1
Fig. 1

Maximum slope m 0 as a function of Δβz: a, linear input polarization, P = 1/2, δ = 0; b, optimum input polarization, P = 1/2, δ= −Δβz/2.

Fig. 2
Fig. 2

Large Faraday effect: E x 2 / E 0 2 is shown as a function of F for z = 1 m. a, linear input polarization (P = 1/2, δ= 0) and no birefringence (Δβ= 0); b, linear input polarization and Δβz = π/2 rad; c, optimum input polarization (P = 1/2, δ= −Δβz/2) and Δβz = π/2 rad.

Fig. 3
Fig. 3

Experimental arrangement for effective Verdet constant measurements: M, microscope objective; PC, polarization controller; L, interaction length of the fiber;A, analyzer; D, photodiode.

Fig. 4
Fig. 4

Magnetic field along the solenoid axis for a 1-A current: ●, experimental; ——, theoretical.

Fig. 5
Fig. 5

Measured R AC/DC, i.e., effective Faraday rotation Γef, as a function of the solenoid current at different wavelengths.

Fig. 6
Fig. 6

Measured effective Verdet constant versus the square of the optical frequency.

Tables (1)

Tables Icon

Table 1 Measured Effective Verdet Constant

Equations (16)

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Γ = V L B d l ,
V = 2 G v p 2 c n ( v 0 2 v 2 ) v 2 ,
( E x ( z ) E y ( z ) ) = [ cos Φ z 2 j Δβ Φ   sin Φ z 2 2 F Φ   sin Φ z 2 2 F Φ   sin Φ z 2 cos Φ z 2 + j Δβ Φ   sin Φ z 2 ]                  × ( E x ( 0 ) E y ( 0 ) ) ,
Φ 2 = Δ β 2 + ( 2 F ) 2 .
m lim F 0 [ 1 z E 0 2 E x ( z ) 2 F ] = 4 P 1 P 1 Δβ z   sin ( Δβ z 2 ) cos ( Δβ z 2 + δ ) ,
( E x ( 0 ) E y ( 0 ) ) = E 0 2 ( P 1 P exp ( j δ ) ) .
m 0 =   sin ( Δβ z ) Δβ z ,
m 0 = 2 Δβ z   sin ( Δβ z 2 ) .
E x ( z ) 2 E 0 2 = 1 2 [ 1 + 2 F Φ   sin ( Φ z ) cos  δ       4 F Φ Δβ Φ   sin 2 ( Φ z 2 ) sin  δ ] .
V ef V m 0 = V 2 Δβ z   sin ( Δβ z 2 ) ,
R AC / DC Γ = V I L B I ( z ) d z ,
B I ( z ) = B 0 { z + L 2 [ R 2 + ( z + L 2 ) 2 ] 1 / 2     z L 2 [ R 2 + ( z L 2 ) 2 ] 1 / 2 } ,
L / 2 + L / 2 B I ( z ) d z = 2 B 0 { [ R 2 + ( L 2 + L 2 ) 2 ] 1 / 2        [ R 2 + ( L 2 L 2 ) 2 ] 1 / 2 } ,
m ( γ ) lim F 0 [ 1 z E 0 2 E γ ( z ) 2 F ] = 4 P 1 P 1 Δβ z   sin ( Δβ z 2 ) cos ( Δβ z 2 + δ )    × cos ( 2 γ ) + ( 1 2 P ) 1 Δβ z   sin ( Δβ z )   sin ( 2 γ ) .
δ = Δβ z z , 1 2 P 2 P 1 P = t g ( 2 γ ) cos ( Δβ z 2 ) .
m 0 = 2 Δβ z   sin ( Δβ z 2 ) [ 1   sin 2 ( 2 γ )   sin 2 ( Δβ z 2 ) ] 1 / 2 .

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