Abstract

The temporal coherence properties of a dispersively propagating optical beam are clarified experimentally by means of a two-beam interferometer composed of optical fibers with 1.3- and 1.5-μm zero-chromatic-dispersion wavelengths. Experimental results fully explain and reflect theoretically predicted ones concerning both the magnitude of the degree of coherence and the shape of the coherence curve with respect to the optical path difference.

© 1987 Optical Society of America

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References

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  1. H. Kaiser, S. A. Werner, E. A. Gerge, “Direct measurement of the longitudinal coherence length of a thermal neutron beam,” Phys. Rev. Lett. 50, 560–563 (1983).
    [Crossref]
  2. A. G. Klein, G. I. Opat, W. A. Hamilton, “Longitudinal coherence in neutron interferometry,” Phys. Rev. Lett. 50, 563–565 (1983).
    [Crossref]
  3. W. A. Hamilton, A. G. Klein, G. I. Opat, “Longitudinal coherence and interferometry in dispersive media,” Phys. Rev. 28, 3149–3152 (1983).
    [Crossref]
  4. Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–934 (1981).
    [Crossref]
  5. T. Okoshi, “Heterodyne and coherent optical fiber communications: recent progress,” IEEE Trans. Microwave Theory Tech. MTT-30, 1138–1149 (1982).
    [Crossref]
  6. R. C. Hooper, J. E. Midwinter, D. W. Smith, I. W. Stanley, “Progress in monomode transmission techniques in the United Kingdom,” J. Lightwave Technol. LT-1, 569–611 (1983).
  7. L. G. Cohen, C. Lin, “A universal fiber-optic (UFO) measurement system based on a near-IR fiber Raman laser,” IEEE J. Quantum Electron. QE-14, 855–860 (1978).
    [Crossref]
  8. D. Marcuse, Principles of Optical Fiber Measurement (Academic, New York, 1981).
  9. A. R. Reisinger, C. D. David, K. L. Lawley, A. Yariv, “Coherence of a room-temperature CW GaAs/GaAlAs injection laser,” IEEE J. Quantum Electron. QE-15, 1382–1385 (1979).
    [Crossref]
  10. N. Shibata, M. Tsubokawa, S. Seikai, “Measurements of polarisation mode dispersion by optical heterodyne detection,” Electron. Lett. 20, 1055–1057 (1984).
    [Crossref]
  11. N. Shibata, M. Tsubokawa, S. Seikai, “Polarization mode dispersion in a coil of single-mode fiber,” Opt. Lett. 10, 92–94 (1985).
    [Crossref] [PubMed]
  12. M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, “Chromatic dispersion measurement of a single-mode fibre by improved optical heterodyne interferometry,” Electron. Lett. 21, 781–783 (1985).
    [Crossref]
  13. A. B. Duval, A. I. McIntosh, “Measurement of oscillator strength by tunable laser interferometry,”J. Phys. D 13, 1617–1624 (1980).
    [Crossref]

1985 (2)

N. Shibata, M. Tsubokawa, S. Seikai, “Polarization mode dispersion in a coil of single-mode fiber,” Opt. Lett. 10, 92–94 (1985).
[Crossref] [PubMed]

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, “Chromatic dispersion measurement of a single-mode fibre by improved optical heterodyne interferometry,” Electron. Lett. 21, 781–783 (1985).
[Crossref]

1984 (1)

N. Shibata, M. Tsubokawa, S. Seikai, “Measurements of polarisation mode dispersion by optical heterodyne detection,” Electron. Lett. 20, 1055–1057 (1984).
[Crossref]

1983 (4)

H. Kaiser, S. A. Werner, E. A. Gerge, “Direct measurement of the longitudinal coherence length of a thermal neutron beam,” Phys. Rev. Lett. 50, 560–563 (1983).
[Crossref]

A. G. Klein, G. I. Opat, W. A. Hamilton, “Longitudinal coherence in neutron interferometry,” Phys. Rev. Lett. 50, 563–565 (1983).
[Crossref]

W. A. Hamilton, A. G. Klein, G. I. Opat, “Longitudinal coherence and interferometry in dispersive media,” Phys. Rev. 28, 3149–3152 (1983).
[Crossref]

R. C. Hooper, J. E. Midwinter, D. W. Smith, I. W. Stanley, “Progress in monomode transmission techniques in the United Kingdom,” J. Lightwave Technol. LT-1, 569–611 (1983).

1982 (1)

T. Okoshi, “Heterodyne and coherent optical fiber communications: recent progress,” IEEE Trans. Microwave Theory Tech. MTT-30, 1138–1149 (1982).
[Crossref]

1981 (1)

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–934 (1981).
[Crossref]

1980 (1)

A. B. Duval, A. I. McIntosh, “Measurement of oscillator strength by tunable laser interferometry,”J. Phys. D 13, 1617–1624 (1980).
[Crossref]

1979 (1)

A. R. Reisinger, C. D. David, K. L. Lawley, A. Yariv, “Coherence of a room-temperature CW GaAs/GaAlAs injection laser,” IEEE J. Quantum Electron. QE-15, 1382–1385 (1979).
[Crossref]

1978 (1)

L. G. Cohen, C. Lin, “A universal fiber-optic (UFO) measurement system based on a near-IR fiber Raman laser,” IEEE J. Quantum Electron. QE-14, 855–860 (1978).
[Crossref]

Cohen, L. G.

L. G. Cohen, C. Lin, “A universal fiber-optic (UFO) measurement system based on a near-IR fiber Raman laser,” IEEE J. Quantum Electron. QE-14, 855–860 (1978).
[Crossref]

David, C. D.

A. R. Reisinger, C. D. David, K. L. Lawley, A. Yariv, “Coherence of a room-temperature CW GaAs/GaAlAs injection laser,” IEEE J. Quantum Electron. QE-15, 1382–1385 (1979).
[Crossref]

Duval, A. B.

A. B. Duval, A. I. McIntosh, “Measurement of oscillator strength by tunable laser interferometry,”J. Phys. D 13, 1617–1624 (1980).
[Crossref]

Gerge, E. A.

H. Kaiser, S. A. Werner, E. A. Gerge, “Direct measurement of the longitudinal coherence length of a thermal neutron beam,” Phys. Rev. Lett. 50, 560–563 (1983).
[Crossref]

Hamilton, W. A.

A. G. Klein, G. I. Opat, W. A. Hamilton, “Longitudinal coherence in neutron interferometry,” Phys. Rev. Lett. 50, 563–565 (1983).
[Crossref]

W. A. Hamilton, A. G. Klein, G. I. Opat, “Longitudinal coherence and interferometry in dispersive media,” Phys. Rev. 28, 3149–3152 (1983).
[Crossref]

Higashi, T.

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, “Chromatic dispersion measurement of a single-mode fibre by improved optical heterodyne interferometry,” Electron. Lett. 21, 781–783 (1985).
[Crossref]

Hooper, R. C.

R. C. Hooper, J. E. Midwinter, D. W. Smith, I. W. Stanley, “Progress in monomode transmission techniques in the United Kingdom,” J. Lightwave Technol. LT-1, 569–611 (1983).

Kaiser, H.

H. Kaiser, S. A. Werner, E. A. Gerge, “Direct measurement of the longitudinal coherence length of a thermal neutron beam,” Phys. Rev. Lett. 50, 560–563 (1983).
[Crossref]

Kimura, T.

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–934 (1981).
[Crossref]

Klein, A. G.

A. G. Klein, G. I. Opat, W. A. Hamilton, “Longitudinal coherence in neutron interferometry,” Phys. Rev. Lett. 50, 563–565 (1983).
[Crossref]

W. A. Hamilton, A. G. Klein, G. I. Opat, “Longitudinal coherence and interferometry in dispersive media,” Phys. Rev. 28, 3149–3152 (1983).
[Crossref]

Lawley, K. L.

A. R. Reisinger, C. D. David, K. L. Lawley, A. Yariv, “Coherence of a room-temperature CW GaAs/GaAlAs injection laser,” IEEE J. Quantum Electron. QE-15, 1382–1385 (1979).
[Crossref]

Lin, C.

L. G. Cohen, C. Lin, “A universal fiber-optic (UFO) measurement system based on a near-IR fiber Raman laser,” IEEE J. Quantum Electron. QE-14, 855–860 (1978).
[Crossref]

Marcuse, D.

D. Marcuse, Principles of Optical Fiber Measurement (Academic, New York, 1981).

McIntosh, A. I.

A. B. Duval, A. I. McIntosh, “Measurement of oscillator strength by tunable laser interferometry,”J. Phys. D 13, 1617–1624 (1980).
[Crossref]

Midwinter, J. E.

R. C. Hooper, J. E. Midwinter, D. W. Smith, I. W. Stanley, “Progress in monomode transmission techniques in the United Kingdom,” J. Lightwave Technol. LT-1, 569–611 (1983).

Okoshi, T.

T. Okoshi, “Heterodyne and coherent optical fiber communications: recent progress,” IEEE Trans. Microwave Theory Tech. MTT-30, 1138–1149 (1982).
[Crossref]

Opat, G. I.

W. A. Hamilton, A. G. Klein, G. I. Opat, “Longitudinal coherence and interferometry in dispersive media,” Phys. Rev. 28, 3149–3152 (1983).
[Crossref]

A. G. Klein, G. I. Opat, W. A. Hamilton, “Longitudinal coherence in neutron interferometry,” Phys. Rev. Lett. 50, 563–565 (1983).
[Crossref]

Reisinger, A. R.

A. R. Reisinger, C. D. David, K. L. Lawley, A. Yariv, “Coherence of a room-temperature CW GaAs/GaAlAs injection laser,” IEEE J. Quantum Electron. QE-15, 1382–1385 (1979).
[Crossref]

Seikai, S.

N. Shibata, M. Tsubokawa, S. Seikai, “Polarization mode dispersion in a coil of single-mode fiber,” Opt. Lett. 10, 92–94 (1985).
[Crossref] [PubMed]

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, “Chromatic dispersion measurement of a single-mode fibre by improved optical heterodyne interferometry,” Electron. Lett. 21, 781–783 (1985).
[Crossref]

N. Shibata, M. Tsubokawa, S. Seikai, “Measurements of polarisation mode dispersion by optical heterodyne detection,” Electron. Lett. 20, 1055–1057 (1984).
[Crossref]

Shibata, N.

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, “Chromatic dispersion measurement of a single-mode fibre by improved optical heterodyne interferometry,” Electron. Lett. 21, 781–783 (1985).
[Crossref]

N. Shibata, M. Tsubokawa, S. Seikai, “Polarization mode dispersion in a coil of single-mode fiber,” Opt. Lett. 10, 92–94 (1985).
[Crossref] [PubMed]

N. Shibata, M. Tsubokawa, S. Seikai, “Measurements of polarisation mode dispersion by optical heterodyne detection,” Electron. Lett. 20, 1055–1057 (1984).
[Crossref]

Smith, D. W.

R. C. Hooper, J. E. Midwinter, D. W. Smith, I. W. Stanley, “Progress in monomode transmission techniques in the United Kingdom,” J. Lightwave Technol. LT-1, 569–611 (1983).

Stanley, I. W.

R. C. Hooper, J. E. Midwinter, D. W. Smith, I. W. Stanley, “Progress in monomode transmission techniques in the United Kingdom,” J. Lightwave Technol. LT-1, 569–611 (1983).

Tsubokawa, M.

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, “Chromatic dispersion measurement of a single-mode fibre by improved optical heterodyne interferometry,” Electron. Lett. 21, 781–783 (1985).
[Crossref]

N. Shibata, M. Tsubokawa, S. Seikai, “Polarization mode dispersion in a coil of single-mode fiber,” Opt. Lett. 10, 92–94 (1985).
[Crossref] [PubMed]

N. Shibata, M. Tsubokawa, S. Seikai, “Measurements of polarisation mode dispersion by optical heterodyne detection,” Electron. Lett. 20, 1055–1057 (1984).
[Crossref]

Werner, S. A.

H. Kaiser, S. A. Werner, E. A. Gerge, “Direct measurement of the longitudinal coherence length of a thermal neutron beam,” Phys. Rev. Lett. 50, 560–563 (1983).
[Crossref]

Yamamoto, Y.

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–934 (1981).
[Crossref]

Yariv, A.

A. R. Reisinger, C. D. David, K. L. Lawley, A. Yariv, “Coherence of a room-temperature CW GaAs/GaAlAs injection laser,” IEEE J. Quantum Electron. QE-15, 1382–1385 (1979).
[Crossref]

Electron. Lett. (2)

N. Shibata, M. Tsubokawa, S. Seikai, “Measurements of polarisation mode dispersion by optical heterodyne detection,” Electron. Lett. 20, 1055–1057 (1984).
[Crossref]

M. Tsubokawa, N. Shibata, S. Seikai, T. Higashi, “Chromatic dispersion measurement of a single-mode fibre by improved optical heterodyne interferometry,” Electron. Lett. 21, 781–783 (1985).
[Crossref]

IEEE J. Quantum Electron. (3)

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–934 (1981).
[Crossref]

L. G. Cohen, C. Lin, “A universal fiber-optic (UFO) measurement system based on a near-IR fiber Raman laser,” IEEE J. Quantum Electron. QE-14, 855–860 (1978).
[Crossref]

A. R. Reisinger, C. D. David, K. L. Lawley, A. Yariv, “Coherence of a room-temperature CW GaAs/GaAlAs injection laser,” IEEE J. Quantum Electron. QE-15, 1382–1385 (1979).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

T. Okoshi, “Heterodyne and coherent optical fiber communications: recent progress,” IEEE Trans. Microwave Theory Tech. MTT-30, 1138–1149 (1982).
[Crossref]

J. Lightwave Technol. (1)

R. C. Hooper, J. E. Midwinter, D. W. Smith, I. W. Stanley, “Progress in monomode transmission techniques in the United Kingdom,” J. Lightwave Technol. LT-1, 569–611 (1983).

J. Phys. D (1)

A. B. Duval, A. I. McIntosh, “Measurement of oscillator strength by tunable laser interferometry,”J. Phys. D 13, 1617–1624 (1980).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (1)

W. A. Hamilton, A. G. Klein, G. I. Opat, “Longitudinal coherence and interferometry in dispersive media,” Phys. Rev. 28, 3149–3152 (1983).
[Crossref]

Phys. Rev. Lett. (2)

H. Kaiser, S. A. Werner, E. A. Gerge, “Direct measurement of the longitudinal coherence length of a thermal neutron beam,” Phys. Rev. Lett. 50, 560–563 (1983).
[Crossref]

A. G. Klein, G. I. Opat, W. A. Hamilton, “Longitudinal coherence in neutron interferometry,” Phys. Rev. Lett. 50, 563–565 (1983).
[Crossref]

Other (1)

D. Marcuse, Principles of Optical Fiber Measurement (Academic, New York, 1981).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a fiber-optic interferometer for clarifying temporal coherence properties of dispersively propagating HE11-mode beams: S, laser diode; HM1 and HM2, half-mirrors; M1, M2, and M, mirrors.

Fig. 2
Fig. 2

Wavelength dependence of chromatic dispersion for fibers A–C used in the experiments.

Fig. 3
Fig. 3

Spectrum of the emitting light from the laser diode used in the experiment and its fitting Gaussian curve.

Fig. 4
Fig. 4

Experimentally obtained degree of temporal coherence as a function of fiber length L for (a) combination of fiber A and fiber B and (b) combination of fiber A and fiber C.

Fig. 5
Fig. 5

Length dependence of the degree of temporal coherence on chromatic dispersion D predicted theoretically for (a) the combination of fiber A and fiber B and (b) the combination of fiber A and fiber C.

Equations (14)

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ψ out = ( 1 / 2 ) [ ψ ( z + 2 d , t ) + ψ ( z , t ) ] ,
ψ ( z , t ) = A ( ω ) exp { i [ k ( ω ) z - ω t ] } d ω ,
ψ out ( z , t ) = ( 1 / 2 ) A ( ω ) exp ( - i ω t ) × { exp [ i ( ω / c ) ( z + 2 d - L 1 ) ] exp [ i β 1 ( ω ) L 1 ] + exp [ i ( ω / c ) ( z - L 2 ) ] exp [ i β 2 ( ω ) L 2 ] } d ω ,
I = ψ out ( z , t ) 2 = ( 1 / 2 ) S ( ω ) [ 1 + Re ( exp { i [ β 2 ( ω ) L 2 - β 1 ( ω ) L 1 - ω ( L 2 - L 1 + 2 d ) / c ] } ) ] d ω ,
β ( ω ) = β ( ω 0 ) + ( ω - ω 0 ) ( d β / d ω ) 0 + 1 / 2 ( ω - ω 0 ) 2 ( d 2 β / d ω 2 ) 0 + = ω 0 / v p + ( ω - ω 0 ) / v g + 1 / 2 ( ω - ω 0 ) 2 ( d 2 β / d ω 2 ) 0 + ,
D = ( 1 / L ) ( d τ / d λ ) ,
D = - ( ω 0 2 / 2 π c ) ( d 3 β / d ω 2 ) 0 .
Γ ( Z , T ) = - S ( ω ) exp { i [ k ( ω ) Z - ω T ] } d ω ,
γ ( Z , T ) = Γ ( Z , T ) / Γ ( 0 , 0 ) .
I = I 0 [ 1 + Re ( exp { i [ - ω 0 ( 1 / v p 1 - 1 / v g 1 ) L 1 ] } ) × γ 2 [ L 2 , L 1 / v g 1 + ( L 2 - L 1 + 2 d ) / c ) ] ,
S ( ω ) = exp [ - ( ω - ω 0 ) 2 / 2 ( Δ ω ) 2 ] / ( 2 π ) 1 / 2 Δ ω ;
γ = exp [ - 2 π 2 ( Δ λ / λ 0 2 ) 2 ( δ d ) 2 / X ] / X 1 / 4 ,
X = 1 + ( Δ λ / λ 0 ) 4 ( 2 π c D L ) 2
δ d = c L ( 1 / v g 2 - 1 / v g 1 ) - 2 d ,

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