Abstract

Conventional low-coherence interferometry (LCI) can be employed in the measurement of polarization mode dispersion (PMD) of fiber-optic components and fibers. However, the smallest PMD, which can be measured using this technique, is limited by the coherence length of the source. We propose a biased π-shifted Michelson interferometer where a birefringent crystal is inserted in front of the interferometer to introduce a bias differential group delay (DGD) larger than the coherence time of the source. In this way, the limitation imposed by the source coherence time has been overcome and PMDs much smaller than the source coherence time, in the order of several femtoseconds, can be measured. Experimental results for the PMD have been shown and compared with Jones matrix eigen-analysis. The theoretical model confirms the experimental observations.

© 2000 Optical Society of America

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References

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  1. TIA/EIA Standard, FOTP-124, “Polarization Mode Dispersion Measurement for Single-Mode Optical Fibres by Interferometric Method,” Aug., 1996.
  2. P. Hernday, “Fibre Optic Test and Measurement,” Ed.D. Derickson, (Prentice Hall, N. J.1998), Ch. 10 and 12.
  3. Y. Namihira, K. Nakajima, and T. Kawazawa,, “Fully Automated Interferometric PMD Measurements for Active EDFA, Fibre-optic Components and Optical fibres,” Electron. Letters, 29, 18, 1649–1650 (993).
  4. P. Oberson, K. Juilliard, N. Gisin, R. Passy, and J. P. von der Weid, “Interferometric Polarization Mode Dispersion Measurements with Femtosecond Sensitivity”, J. Lightwave Tech.,  15, 10, 1852 (1997).
    [Crossref]
  5. P. Martin, G. LeBoudec, E. Tauflieb, and H. Lefevre, “Optimized Polarization Mode Dispersion Measurement with “π-shifted” White Light Interferometry,” Opt. Fiber Technology,  2, 207–212 (1996).
    [Crossref]
  6. C. D. Poole and R. E. Wagner, “Phenomenological Approach to Polarization Mode Dispersion in Long Singlemode Fibers,” Elect. Lett.,  22, 19, 1029 (1986).
    [Crossref]
  7. D. S. Kliger, J. W. Lewis, and C. E. Randall, “Polarized Light in Optics and Spectroscopy,” (Academic Press Inc., 1990), Ch. 4 and 5.
  8. B. L. Heffner, “Automatic measurement of polarization mode dispersion using Jones Matrix Eigenanalysis,” IEEE Ph. Tech. Let.,  4, 1066–1069 (1992).
    [Crossref]

1997 (1)

P. Oberson, K. Juilliard, N. Gisin, R. Passy, and J. P. von der Weid, “Interferometric Polarization Mode Dispersion Measurements with Femtosecond Sensitivity”, J. Lightwave Tech.,  15, 10, 1852 (1997).
[Crossref]

1996 (1)

P. Martin, G. LeBoudec, E. Tauflieb, and H. Lefevre, “Optimized Polarization Mode Dispersion Measurement with “π-shifted” White Light Interferometry,” Opt. Fiber Technology,  2, 207–212 (1996).
[Crossref]

1992 (1)

B. L. Heffner, “Automatic measurement of polarization mode dispersion using Jones Matrix Eigenanalysis,” IEEE Ph. Tech. Let.,  4, 1066–1069 (1992).
[Crossref]

1986 (1)

C. D. Poole and R. E. Wagner, “Phenomenological Approach to Polarization Mode Dispersion in Long Singlemode Fibers,” Elect. Lett.,  22, 19, 1029 (1986).
[Crossref]

Gisin, N.

P. Oberson, K. Juilliard, N. Gisin, R. Passy, and J. P. von der Weid, “Interferometric Polarization Mode Dispersion Measurements with Femtosecond Sensitivity”, J. Lightwave Tech.,  15, 10, 1852 (1997).
[Crossref]

Heffner, B. L.

B. L. Heffner, “Automatic measurement of polarization mode dispersion using Jones Matrix Eigenanalysis,” IEEE Ph. Tech. Let.,  4, 1066–1069 (1992).
[Crossref]

Hernday, P.

P. Hernday, “Fibre Optic Test and Measurement,” Ed.D. Derickson, (Prentice Hall, N. J.1998), Ch. 10 and 12.

Juilliard, K.

P. Oberson, K. Juilliard, N. Gisin, R. Passy, and J. P. von der Weid, “Interferometric Polarization Mode Dispersion Measurements with Femtosecond Sensitivity”, J. Lightwave Tech.,  15, 10, 1852 (1997).
[Crossref]

Kawazawa, T.

Y. Namihira, K. Nakajima, and T. Kawazawa,, “Fully Automated Interferometric PMD Measurements for Active EDFA, Fibre-optic Components and Optical fibres,” Electron. Letters, 29, 18, 1649–1650 (993).

Kliger, D. S.

D. S. Kliger, J. W. Lewis, and C. E. Randall, “Polarized Light in Optics and Spectroscopy,” (Academic Press Inc., 1990), Ch. 4 and 5.

LeBoudec, G.

P. Martin, G. LeBoudec, E. Tauflieb, and H. Lefevre, “Optimized Polarization Mode Dispersion Measurement with “π-shifted” White Light Interferometry,” Opt. Fiber Technology,  2, 207–212 (1996).
[Crossref]

Lefevre, H.

P. Martin, G. LeBoudec, E. Tauflieb, and H. Lefevre, “Optimized Polarization Mode Dispersion Measurement with “π-shifted” White Light Interferometry,” Opt. Fiber Technology,  2, 207–212 (1996).
[Crossref]

Lewis, J. W.

D. S. Kliger, J. W. Lewis, and C. E. Randall, “Polarized Light in Optics and Spectroscopy,” (Academic Press Inc., 1990), Ch. 4 and 5.

Martin, P.

P. Martin, G. LeBoudec, E. Tauflieb, and H. Lefevre, “Optimized Polarization Mode Dispersion Measurement with “π-shifted” White Light Interferometry,” Opt. Fiber Technology,  2, 207–212 (1996).
[Crossref]

Nakajima, K.

Y. Namihira, K. Nakajima, and T. Kawazawa,, “Fully Automated Interferometric PMD Measurements for Active EDFA, Fibre-optic Components and Optical fibres,” Electron. Letters, 29, 18, 1649–1650 (993).

Namihira, Y.

Y. Namihira, K. Nakajima, and T. Kawazawa,, “Fully Automated Interferometric PMD Measurements for Active EDFA, Fibre-optic Components and Optical fibres,” Electron. Letters, 29, 18, 1649–1650 (993).

Oberson, P.

P. Oberson, K. Juilliard, N. Gisin, R. Passy, and J. P. von der Weid, “Interferometric Polarization Mode Dispersion Measurements with Femtosecond Sensitivity”, J. Lightwave Tech.,  15, 10, 1852 (1997).
[Crossref]

Passy, R.

P. Oberson, K. Juilliard, N. Gisin, R. Passy, and J. P. von der Weid, “Interferometric Polarization Mode Dispersion Measurements with Femtosecond Sensitivity”, J. Lightwave Tech.,  15, 10, 1852 (1997).
[Crossref]

Poole, C. D.

C. D. Poole and R. E. Wagner, “Phenomenological Approach to Polarization Mode Dispersion in Long Singlemode Fibers,” Elect. Lett.,  22, 19, 1029 (1986).
[Crossref]

Randall, C. E.

D. S. Kliger, J. W. Lewis, and C. E. Randall, “Polarized Light in Optics and Spectroscopy,” (Academic Press Inc., 1990), Ch. 4 and 5.

Tauflieb, E.

P. Martin, G. LeBoudec, E. Tauflieb, and H. Lefevre, “Optimized Polarization Mode Dispersion Measurement with “π-shifted” White Light Interferometry,” Opt. Fiber Technology,  2, 207–212 (1996).
[Crossref]

von der Weid, J. P.

P. Oberson, K. Juilliard, N. Gisin, R. Passy, and J. P. von der Weid, “Interferometric Polarization Mode Dispersion Measurements with Femtosecond Sensitivity”, J. Lightwave Tech.,  15, 10, 1852 (1997).
[Crossref]

Wagner, R. E.

C. D. Poole and R. E. Wagner, “Phenomenological Approach to Polarization Mode Dispersion in Long Singlemode Fibers,” Elect. Lett.,  22, 19, 1029 (1986).
[Crossref]

Elect. Lett. (1)

C. D. Poole and R. E. Wagner, “Phenomenological Approach to Polarization Mode Dispersion in Long Singlemode Fibers,” Elect. Lett.,  22, 19, 1029 (1986).
[Crossref]

IEEE Ph. Tech. Let. (1)

B. L. Heffner, “Automatic measurement of polarization mode dispersion using Jones Matrix Eigenanalysis,” IEEE Ph. Tech. Let.,  4, 1066–1069 (1992).
[Crossref]

J. Lightwave Tech. (1)

P. Oberson, K. Juilliard, N. Gisin, R. Passy, and J. P. von der Weid, “Interferometric Polarization Mode Dispersion Measurements with Femtosecond Sensitivity”, J. Lightwave Tech.,  15, 10, 1852 (1997).
[Crossref]

Opt. Fiber Technology (1)

P. Martin, G. LeBoudec, E. Tauflieb, and H. Lefevre, “Optimized Polarization Mode Dispersion Measurement with “π-shifted” White Light Interferometry,” Opt. Fiber Technology,  2, 207–212 (1996).
[Crossref]

Other (4)

TIA/EIA Standard, FOTP-124, “Polarization Mode Dispersion Measurement for Single-Mode Optical Fibres by Interferometric Method,” Aug., 1996.

P. Hernday, “Fibre Optic Test and Measurement,” Ed.D. Derickson, (Prentice Hall, N. J.1998), Ch. 10 and 12.

Y. Namihira, K. Nakajima, and T. Kawazawa,, “Fully Automated Interferometric PMD Measurements for Active EDFA, Fibre-optic Components and Optical fibres,” Electron. Letters, 29, 18, 1649–1650 (993).

D. S. Kliger, J. W. Lewis, and C. E. Randall, “Polarized Light in Optics and Spectroscopy,” (Academic Press Inc., 1990), Ch. 4 and 5.

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Figures (8)

Fig. 1.
Fig. 1.

Schematics of the biased π-shifted Michelson interferometer.

Fig. 2.
Fig. 2.

Pictorial representation of the polarized light waves passing through the DUT and the biasing crystal where the DUT’s and the crystal’s axes are misaligned by an angle ρ.

Fig. 3.
Fig. 3.

Measured DGD due to polarization for the bias crystal using the Jones Matrix Eigenanalysis method.

Fig. 5.
Fig. 5.

Measured DGD for the second crystal (DUT) using the Jones Matrix Eigenanalysis method.

Fig. 4.
Fig. 4.

Interference patterns obtained from the biased π-shifted Michelson interferometer in the case of a second crystal with rotateable axes used as DUT: navy blue line — reference scan with the bias crystal only; pink line — DUT, polarization axes aligned with those of the bias crystal (ρ=0 deg); light blue line — DUT polarization axes crossed with those of the bias crystal (ρ=90 deg); reddish-brown line - DUT polarization axes at an arbitrary angle (ρ=45 deg). For comparison, the orange line in the center represents fringe pattern resulting from the DUT only without the bias.

Fig. 6.
Fig. 6.

Interference patterns for a fiber-optic circulator: navy blue line — reference scan with the bias crystal only; pink line — DUT, polarization axes misaligned with those of the bias crystal (ρ≠0 deg).

Fig. 7.
Fig. 7.

Interference pattern for the fiber-optic circulator with its polarization axes aligned with those of the bias crystal (ρ=0 deg): navy blue line — reference scan with the bias crystal; pink line — DUT.

Fig. 8.
Fig. 8.

Measured DGD for the fiber-optic circulator using the Jones Matrix Eigenanalysis method.

Equations (17)

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J crys . = e i δ 2 0 0 e i δ 2
J QWP = e i π 4 cos 2 ρ + e i π 4 sin 2 ρ 2 sin ρ cos ρ 2 sin ρ cos ρ e i π 4 cos 2 ρ + e i π 4 sin 2 ρ .
I ( τ ) E 1 ( t τ ) 2 + E 2 ( t ) 2 + E 1 ( t τ ) * E 2 ( t ) e i ϖ τ + E 1 ( t τ ) E 2 ( t ) * e i ϖ τ
I d ω d ω ' E ˜ 1 ( ω , L ) E ˜ 2 * ( ω ' , L ) .
E ˜ 1 ( ω ) = E ˜ in ( ω ) T 1 ( ω ) e 1 and E ˜ 2 ( ω ) = E ˜ in ( ω ) T 2 ( ω ) e 2
E 1 ( t τ ) = ( E 1 x ( t τ ) 0 ) + ( 0 E 1 y ( t τ ) ) = J crys . ( A e i ϕ A e i ϕ + π 2 ) e i π + 2 π i λ - L
E 2 ( t ) = ( E 2 x ( t ) 0 ) + ( 0 E 2 y ( t ) ) = J QWP 2 J crys . ( A e i ϕ A e i ϕ + π 2 ) e i π .
I 2 A 2 exp [ ( 2 Δ τ τ coh ) 2 ] { sin ( 2 ρ ) [ cos ( 2 π λ ¯ L δ ) + cos ( 2 π λ ¯ L + δ ) ] +
2 cos ( 2 ρ ) sin ( 2 π λ ¯ L ) } .
Δ τ = 2 L c
J DUT = e i Δ 2 cos 2 ρ + e i Δ 2 sin 2 ρ 2 sin ρ cos ρ sin Δ 2 2 sin ρ cos ρ sin Δ 2 e i Δ 2 cos 2 ρ + e i Δ 2 sin 2 ρ .
E 1 ( t τ ) = ( E 1 x ( t τ ) 0 ) + ( 0 E 1 y ( t τ ) ) = J crys . J DUT ( A e i ϕ A e i ϕ + π 2 ) e i π + 2 π i λ ¯ L
E 2 ( t ) = ( E 2 x ( t ) 0 ) + ( 0 E 2 y ( t ) ) = J QWP 2 J crys . J DUT ( A e i ϕ A e i ϕ + π 2 ) e i π .
I 2 A 2 exp [ ( 2 Δ τ τ coh ) 2 ] { sin 2 ρ [ cos ( 2 π λ - L ( δ Δ ) ) + cos ( 2 π λ - L + ( δ Δ ) ) ] +
cos 2 ρ [ cos ( 2 π λ - L ( δ + Δ ) ) + cos ( 2 π λ - L + ( δ + Δ ) ) ] .
Δ τ DUT = Δ τ crys . ± DUT Δ τ crys . .
Δ τ - DUT = ( Δ τ DUT + + Δ τ DUT ) 2 .

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