Abstract

Longitudinal coherence properties of the waves propagating through a birefringent fiber are investigated theoretically and experimentally. Significant loss due to the polarization-dispersion slope is observed clearly for the interference between the two orthogonally polarized HE11 modes. The results obtained experimentally reflect the theoretical predictions well for both the modulus of the degree of coherence and its curve shape versus the optical path difference in the wavelength region from 816 to 1540 nm.

© 1987 Optical Society of America

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References

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  1. F. Mengel, Electron. Lett. 20, 66 (1984).
    [Crossref]
  2. N. Shibata, M. Tsubokawa, Y. Kimura, S. Seikai, Electron. Lett. 21, 1087 (1985).
    [Crossref]
  3. N. Shibata, M. Tsubokawa, T. Nakashima, S. Seikai, J. Opt. Soc. Am. A 4, 494 (1987).
    [Crossref]
  4. Y. Sasaki, T. Hosaka, J. Noda, Electron. Lett. 20, 784 (1984).
    [Crossref]
  5. K. Okamoto, M. P. Varnham, D. N. Payne, Appl. Opt. 22, 2370 (1983).
    [Crossref] [PubMed]
  6. N. Shibata, M. Tsubokawa, S. Seikai, Opt. Lett. 10, 92 (1985).
    [Crossref] [PubMed]
  7. M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, Electron. Lett. 21, 781 (1985).
    [Crossref]

1987 (1)

1985 (3)

N. Shibata, M. Tsubokawa, Y. Kimura, S. Seikai, Electron. Lett. 21, 1087 (1985).
[Crossref]

N. Shibata, M. Tsubokawa, S. Seikai, Opt. Lett. 10, 92 (1985).
[Crossref] [PubMed]

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, Electron. Lett. 21, 781 (1985).
[Crossref]

1984 (2)

F. Mengel, Electron. Lett. 20, 66 (1984).
[Crossref]

Y. Sasaki, T. Hosaka, J. Noda, Electron. Lett. 20, 784 (1984).
[Crossref]

1983 (1)

Higashi, T.

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, Electron. Lett. 21, 781 (1985).
[Crossref]

Hosaka, T.

Y. Sasaki, T. Hosaka, J. Noda, Electron. Lett. 20, 784 (1984).
[Crossref]

Kimura, Y.

N. Shibata, M. Tsubokawa, Y. Kimura, S. Seikai, Electron. Lett. 21, 1087 (1985).
[Crossref]

Mengel, F.

F. Mengel, Electron. Lett. 20, 66 (1984).
[Crossref]

Nakashima, T.

Noda, J.

Y. Sasaki, T. Hosaka, J. Noda, Electron. Lett. 20, 784 (1984).
[Crossref]

Okamoto, K.

Payne, D. N.

Sasaki, Y.

Y. Sasaki, T. Hosaka, J. Noda, Electron. Lett. 20, 784 (1984).
[Crossref]

Seikai, S.

N. Shibata, M. Tsubokawa, T. Nakashima, S. Seikai, J. Opt. Soc. Am. A 4, 494 (1987).
[Crossref]

N. Shibata, M. Tsubokawa, Y. Kimura, S. Seikai, Electron. Lett. 21, 1087 (1985).
[Crossref]

N. Shibata, M. Tsubokawa, S. Seikai, Opt. Lett. 10, 92 (1985).
[Crossref] [PubMed]

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, Electron. Lett. 21, 781 (1985).
[Crossref]

Shibata, N.

N. Shibata, M. Tsubokawa, T. Nakashima, S. Seikai, J. Opt. Soc. Am. A 4, 494 (1987).
[Crossref]

N. Shibata, M. Tsubokawa, Y. Kimura, S. Seikai, Electron. Lett. 21, 1087 (1985).
[Crossref]

N. Shibata, M. Tsubokawa, S. Seikai, Opt. Lett. 10, 92 (1985).
[Crossref] [PubMed]

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, Electron. Lett. 21, 781 (1985).
[Crossref]

Tsubokawa, M.

N. Shibata, M. Tsubokawa, T. Nakashima, S. Seikai, J. Opt. Soc. Am. A 4, 494 (1987).
[Crossref]

N. Shibata, M. Tsubokawa, Y. Kimura, S. Seikai, Electron. Lett. 21, 1087 (1985).
[Crossref]

N. Shibata, M. Tsubokawa, S. Seikai, Opt. Lett. 10, 92 (1985).
[Crossref] [PubMed]

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, Electron. Lett. 21, 781 (1985).
[Crossref]

Varnham, M. P.

Appl. Opt. (1)

Electron. Lett. (4)

F. Mengel, Electron. Lett. 20, 66 (1984).
[Crossref]

N. Shibata, M. Tsubokawa, Y. Kimura, S. Seikai, Electron. Lett. 21, 1087 (1985).
[Crossref]

Y. Sasaki, T. Hosaka, J. Noda, Electron. Lett. 20, 784 (1984).
[Crossref]

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, Electron. Lett. 21, 781 (1985).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of a two-beam interferometer containing a birefringent fiber.

Fig. 2
Fig. 2

Measured polarization dispersion τp as a function of wavelength λ, and wavelength dependence of dτp/dλ obtained by fitting a curve to the measured τp.

Fig. 3
Fig. 3

|γ| obtained experimentally for the interference between the two identically polarized modes and for the interference between the HE 11 x and HE 11 y modes: (a) λ0 = 816 nm, Δλ = 0.1 nm, Δλe = 1.7 nm, Δλs = 0.4 nm, (dτp/dλ)0 = 10−3 psec km−1 nm−1; (b) λ0 = 1270 nm, Δλ = 0.1 nm, Δλe = 4 nm, ΔλS = 0.9 nm, (dτp/dλ)0 = 0.20 psec km−1 nm−1; (c) λ0 = 1540 nm, Δλ = 0.1 nm, Δλe = 5 nm, Δλs = 1.2 nm, (dτp/dλ)0 = 0.46 psec km−1 nm−1.

Fig. 4
Fig. 4

Theoretical results for |γ| as a function of δL. The values of Δλ, Δλe, and Δλs experimentally evaluated for the spectral shape of LD1–LD3 and the dispersion slope of the test fiber were used for the calculation.

Equations (8)

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γ = Γ ( L , L + δ z ) / Γ ( 0 , 0 ) ,
Γ ( L , L + Δ z ) = S ( ω ) exp ( i { [ β x ( ω ) β y ( ω ) ] L ω δ L / c } d ω ) .
β j ( ω ) = β j ( ω 0 ) + ( ω ω 0 ) ( d β j / d ω ) 0 + ( ½ ) ( ω ω 0 ) 2 ( d 2 β j / d ω 2 ) 0 = ω 0 / υ p j + ( ω ω 0 ) / υ g j + ( ½ ) × ( ω ω 0 ) 2 ( d 2 β j / d ω 2 ) 0 ,
S ( ω ) = n N exp [ ( n Δ ω s ) 2 / 2 Δ ω 2 ] × exp [ ( ω ω 0 n Δ ω s ) 2 / 2 Δ ω 2 ] ,
| γ ( L , δ L ) | = | n N α 1 / 2 exp [ ( n Δ λ s ) 2 2 ( 1 Δ λ 2 + 1 Δ λ e 2 ) 1 2 α ( i n Δ λ s Δ λ + 2 π Δ δ L λ 0 2 ) 2 ] m N exp [ ( m Δ λ s ) 2 2 ( 1 Δ λ 2 + 1 Δ λ e 2 ) + 1 2 ( m Δ λ s 2 Δ λ 0 ) 2 ] | ,
δ L = ( 1 / υ g x 1 / υ g y ) c L δ z ,
α = 1 i ( D x D y ) ( 2 π c L ) ( Δ λ / λ 0 ) 2 ,
D x D y = ( λ 0 2 / 2 π c ) [ ( d 2 β x / d λ 2 ) 0 ( d 2 β y / d λ 2 ) 0 ] = d τ p / d λ .

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