Abstract

A novel formalism for determining the source-induced noise in Stokes parameter measurements is derived for sources with Gaussian statistics. The formalism is based on a concise expression for the autocovariance functions of the Stokes parameters in terms of the second-order correlation properties of the optical field. At the output of an optical system, source-induced noise can result not only from the intensity fluctuations of the source but also from phase or polarization fluctuations. To describe the effect of the system, another formalism for the propagation of the second-order correlation properties of the optical field is derived. We apply the formalisms to analyze source-induced noise at the output of a birefringent medium, and in coherence-multiplexing networks.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
  2. K. Takada, “Analysis of polarization dependence of optical low-coherence reflectometry using an active Faraday rotator,” J. Lightwave Technol. 21, 2916–2922 (2003).
    [CrossRef]
  3. J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
    [CrossRef]
  4. B. E. Bouma, G. J. Tearney, Handbook of Optical Coherence Tomography (Marcel Dekker, New York, 2002).
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    [CrossRef] [PubMed]
  6. M. Farhadiroushan, R. C. Youngquist, “Polarimetric coherence multiplexing using high-birefringence optical-fiber sensors and short coherence sources,” Opt. Lett. 15, 786–788 (1990).
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  7. K. W. Chu, F. M. Dickey, “Optical coherence multiplexing for interprocessor communications,” Opt. Eng. (Bellingham) 30, 337–344 (1991).
    [CrossRef]
  8. G. J. Pendock, D. D. Sampson, “Increasing the transmission capacity of coherence multiplexed communication systems by using differential detection,” IEEE Photonics Technol. Lett. 7, 1504–1506 (1995).
    [CrossRef]
  9. D. D. Sampson, G. J. Pendock, R. A. Griffin, “Photonic code-division multiple-access communications,” Fiber Integr. Opt. 16, 129–157 (1997).
    [CrossRef]
  10. P. Healy, “Dimensioning an optical-fiber spread-spectrum multiple-access communication system,” Opt. Lett. 12, 425–427 (1987).
    [CrossRef]
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    [CrossRef]
  12. G. C. Gupta, P. J. Legg, D. Utamchandani, I. Andonovich, “Capacity bounding of coherence multiplexed local area networks due to interferometric noise,” IEE Proc. J Optoelectron. 144, 69–74 (1997).
    [CrossRef]
  13. K. Takada, “Noise in low-coherence reflectometry,” IEEE J. Quantum Electron. 34, 1098–1108 (1998).
    [CrossRef]
  14. K. Takada, A. Himeno, K. Yukimatsu, “Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry,” Appl. Phys. Lett. 59, 2483–2485 (1991).
    [CrossRef]
  15. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
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    [CrossRef]
  17. M. Tur, E. Shafir, K. Blotekjaer, “Source-induced noise in optical systems driven by low-coherence sources,” J. Lightwave Technol. 8, 183–189 (1990).
    [CrossRef]
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  20. Y. Weissman, “Optical noise in frequency-periodic networks,” J. Lightwave Technol. 12, 1660–1667 (1994).
    [CrossRef]
  21. G. J. Pendock, D. D. Sampson, “Capacity of coherence-multiplexed CDMA networks,” Opt. Commun. 143, 109–117 (1997).
    [CrossRef]
  22. M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
    [CrossRef]
  23. D. P. Dave, T. Akkin, T. E. Milner, “Polarization-maintaining fiber-based optical low-coherence reflectometer for characterization and ranging of birefringence,” Opt. Lett. 28, 1775–1777 (2003).
    [CrossRef] [PubMed]
  24. J. F. de Boer, T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
    [CrossRef] [PubMed]
  25. S. Jiao, L. Wang, “Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography,” Opt. Lett. 27, 101–103 (2002).
    [CrossRef]
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    [CrossRef]
  27. M. Pircher, E. Goetzinger, R. Leitgeb, C. K. Hitzenberger, “Transversal phase resolved polarization sensitive optical coherence tomography,” Phys. Med. Biol. 49, 1257–1263 (2004).
    [CrossRef] [PubMed]
  28. R. A. Griffin, D. D. Sampson, D. A. Jackson, “Coherence coding for photonic code-division multiple access networks,” J. Lightwave Technol. 13, 1826–1837 (1995).
    [CrossRef]
  29. J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
  30. A. Eyal, D. Kuperman, O. Dimenstein, M. Tur, “Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL,” IEEE Photonics Technol. Lett. 14, 1515–1517 (2002).
    [CrossRef]
  31. S. Huard, Polarization of Light (Wiley, New York, 1997).
  32. R. H. Wentworth, “Optical noise in interferometric systems containing strongly unbalanced paths,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1988).
  33. R. A. Griffin, D. D. Sampson, D. A. Jackson, “Demonstration of data transmission using coherent correlation to reconstruct a coded pulse sequence,” IEEE Photonics Technol. Lett. 4, 513–515 (1992).
    [CrossRef]
  34. D. D. Sampson, R. A. Griffin, D. A. Jackson, “Photonic CDMA by coherent matched filtering using time-addressed coding in optical ladder networks,” J. Lightwave Technol. 12, 2001–2010 (1994).
    [CrossRef]
  35. J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).
  36. G. J. Pendock, D. D. Sampson, “Noise in coherence-multiplexed optical fiber systems,” Appl. Opt. 36, 9536–9540 (1997).
    [CrossRef]
  37. B. Moslehi, “Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time,” J. Lightwave Technol. 4, 1334–1351 (1986).
    [CrossRef]

2004 (1)

M. Pircher, E. Goetzinger, R. Leitgeb, C. K. Hitzenberger, “Transversal phase resolved polarization sensitive optical coherence tomography,” Phys. Med. Biol. 49, 1257–1263 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (4)

J. F. de Boer, T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[CrossRef] [PubMed]

S. Jiao, L. Wang, “Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography,” Opt. Lett. 27, 101–103 (2002).
[CrossRef]

B. Cense, T. C. Chen, B. H. Park, M. C. Pierce, J. F. de Boer, “In vivo depth-resolved birefringence measurements of the human retinal nerve fiber layer by polarization-sensitive optical coherence tomography,” Opt. Lett. 27, 1610–1612 (2002).
[CrossRef]

A. Eyal, D. Kuperman, O. Dimenstein, M. Tur, “Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL,” IEEE Photonics Technol. Lett. 14, 1515–1517 (2002).
[CrossRef]

2000 (1)

J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).

1999 (1)

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

1998 (1)

K. Takada, “Noise in low-coherence reflectometry,” IEEE J. Quantum Electron. 34, 1098–1108 (1998).
[CrossRef]

1997 (4)

G. C. Gupta, P. J. Legg, D. Utamchandani, I. Andonovich, “Capacity bounding of coherence multiplexed local area networks due to interferometric noise,” IEE Proc. J Optoelectron. 144, 69–74 (1997).
[CrossRef]

G. J. Pendock, D. D. Sampson, “Capacity of coherence-multiplexed CDMA networks,” Opt. Commun. 143, 109–117 (1997).
[CrossRef]

D. D. Sampson, G. J. Pendock, R. A. Griffin, “Photonic code-division multiple-access communications,” Fiber Integr. Opt. 16, 129–157 (1997).
[CrossRef]

G. J. Pendock, D. D. Sampson, “Noise in coherence-multiplexed optical fiber systems,” Appl. Opt. 36, 9536–9540 (1997).
[CrossRef]

1995 (3)

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Coherence coding for photonic code-division multiple access networks,” J. Lightwave Technol. 13, 1826–1837 (1995).
[CrossRef]

G. J. Pendock, D. D. Sampson, “Increasing the transmission capacity of coherence multiplexed communication systems by using differential detection,” IEEE Photonics Technol. Lett. 7, 1504–1506 (1995).
[CrossRef]

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett. 31, 1469–1470 (1995).
[CrossRef]

1994 (2)

Y. Weissman, “Optical noise in frequency-periodic networks,” J. Lightwave Technol. 12, 1660–1667 (1994).
[CrossRef]

D. D. Sampson, R. A. Griffin, D. A. Jackson, “Photonic CDMA by coherent matched filtering using time-addressed coding in optical ladder networks,” J. Lightwave Technol. 12, 2001–2010 (1994).
[CrossRef]

1992 (2)

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Demonstration of data transmission using coherent correlation to reconstruct a coded pulse sequence,” IEEE Photonics Technol. Lett. 4, 513–515 (1992).
[CrossRef]

M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
[CrossRef]

1991 (2)

K. Takada, A. Himeno, K. Yukimatsu, “Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry,” Appl. Phys. Lett. 59, 2483–2485 (1991).
[CrossRef]

K. W. Chu, F. M. Dickey, “Optical coherence multiplexing for interprocessor communications,” Opt. Eng. (Bellingham) 30, 337–344 (1991).
[CrossRef]

1990 (4)

1989 (1)

R. H. Wentworth, “Theoretical noise performance of coherence-multiplexed interferometric sensors,” J. Lightwave Technol. 7, 941–956 (1989).
[CrossRef]

1987 (3)

1986 (1)

B. Moslehi, “Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time,” J. Lightwave Technol. 4, 1334–1351 (1986).
[CrossRef]

Akkin, T.

Andonovich, I.

G. C. Gupta, P. J. Legg, D. Utamchandani, I. Andonovich, “Capacity bounding of coherence multiplexed local area networks due to interferometric noise,” IEE Proc. J Optoelectron. 144, 69–74 (1997).
[CrossRef]

Blotekjaer, K.

M. Tur, E. Shafir, K. Blotekjaer, “Source-induced noise in optical systems driven by low-coherence sources,” J. Lightwave Technol. 8, 183–189 (1990).
[CrossRef]

Bouma, B. E.

B. E. Bouma, G. J. Tearney, Handbook of Optical Coherence Tomography (Marcel Dekker, New York, 2002).

Carr, S.

Cense, B.

Chen, T. C.

Chida, K.

Chu, K. W.

K. W. Chu, F. M. Dickey, “Optical coherence multiplexing for interprocessor communications,” Opt. Eng. (Bellingham) 30, 337–344 (1991).
[CrossRef]

Dave, D. P.

Davies, D. E. N.

de Boer, J. F.

Dickey, F. M.

K. W. Chu, F. M. Dickey, “Optical coherence multiplexing for interprocessor communications,” Opt. Eng. (Bellingham) 30, 337–344 (1991).
[CrossRef]

Dimenstein, O.

A. Eyal, D. Kuperman, O. Dimenstein, M. Tur, “Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL,” IEEE Photonics Technol. Lett. 14, 1515–1517 (2002).
[CrossRef]

Eyal, A.

A. Eyal, D. Kuperman, O. Dimenstein, M. Tur, “Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL,” IEEE Photonics Technol. Lett. 14, 1515–1517 (2002).
[CrossRef]

Farhadiroushan, M.

Fujimoto, J. G.

Goetzinger, E.

M. Pircher, E. Goetzinger, R. Leitgeb, C. K. Hitzenberger, “Transversal phase resolved polarization sensitive optical coherence tomography,” Phys. Med. Biol. 49, 1257–1263 (2004).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Gordon, J. P.

J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).

Gough, P. T.

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett. 31, 1469–1470 (1995).
[CrossRef]

Griffin, R. A.

D. D. Sampson, G. J. Pendock, R. A. Griffin, “Photonic code-division multiple-access communications,” Fiber Integr. Opt. 16, 129–157 (1997).
[CrossRef]

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Coherence coding for photonic code-division multiple access networks,” J. Lightwave Technol. 13, 1826–1837 (1995).
[CrossRef]

D. D. Sampson, R. A. Griffin, D. A. Jackson, “Photonic CDMA by coherent matched filtering using time-addressed coding in optical ladder networks,” J. Lightwave Technol. 12, 2001–2010 (1994).
[CrossRef]

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Demonstration of data transmission using coherent correlation to reconstruct a coded pulse sequence,” IEEE Photonics Technol. Lett. 4, 513–515 (1992).
[CrossRef]

Gupta, G. C.

G. C. Gupta, P. J. Legg, D. Utamchandani, I. Andonovich, “Capacity bounding of coherence multiplexed local area networks due to interferometric noise,” IEE Proc. J Optoelectron. 144, 69–74 (1997).
[CrossRef]

Healy, P.

Hee, M. R.

Himeno, A.

K. Takada, A. Himeno, K. Yukimatsu, “Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry,” Appl. Phys. Lett. 59, 2483–2485 (1991).
[CrossRef]

Hitzenberger, C. K.

M. Pircher, E. Goetzinger, R. Leitgeb, C. K. Hitzenberger, “Transversal phase resolved polarization sensitive optical coherence tomography,” Phys. Med. Biol. 49, 1257–1263 (2004).
[CrossRef] [PubMed]

Huang, D.

Huard, S.

S. Huard, Polarization of Light (Wiley, New York, 1997).

Jackson, D. A.

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Coherence coding for photonic code-division multiple access networks,” J. Lightwave Technol. 13, 1826–1837 (1995).
[CrossRef]

D. D. Sampson, R. A. Griffin, D. A. Jackson, “Photonic CDMA by coherent matched filtering using time-addressed coding in optical ladder networks,” J. Lightwave Technol. 12, 2001–2010 (1994).
[CrossRef]

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Demonstration of data transmission using coherent correlation to reconstruct a coded pulse sequence,” IEEE Photonics Technol. Lett. 4, 513–515 (1992).
[CrossRef]

Jiao, S.

Kogelnik, H.

J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).

Kuperman, D.

A. Eyal, D. Kuperman, O. Dimenstein, M. Tur, “Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL,” IEEE Photonics Technol. Lett. 14, 1515–1517 (2002).
[CrossRef]

Legg, P. J.

G. C. Gupta, P. J. Legg, D. Utamchandani, I. Andonovich, “Capacity bounding of coherence multiplexed local area networks due to interferometric noise,” IEE Proc. J Optoelectron. 144, 69–74 (1997).
[CrossRef]

Leitgeb, R.

M. Pircher, E. Goetzinger, R. Leitgeb, C. K. Hitzenberger, “Transversal phase resolved polarization sensitive optical coherence tomography,” Phys. Med. Biol. 49, 1257–1263 (2004).
[CrossRef] [PubMed]

Milner, T. E.

D. P. Dave, T. Akkin, T. E. Milner, “Polarization-maintaining fiber-based optical low-coherence reflectometer for characterization and ranging of birefringence,” Opt. Lett. 28, 1775–1777 (2003).
[CrossRef] [PubMed]

J. F. de Boer, T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[CrossRef] [PubMed]

Moslehi, B.

B. Moslehi, “Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time,” J. Lightwave Technol. 4, 1334–1351 (1986).
[CrossRef]

Noda, J.

Park, B. H.

Pendock, G. J.

G. J. Pendock, D. D. Sampson, “Capacity of coherence-multiplexed CDMA networks,” Opt. Commun. 143, 109–117 (1997).
[CrossRef]

D. D. Sampson, G. J. Pendock, R. A. Griffin, “Photonic code-division multiple-access communications,” Fiber Integr. Opt. 16, 129–157 (1997).
[CrossRef]

G. J. Pendock, D. D. Sampson, “Noise in coherence-multiplexed optical fiber systems,” Appl. Opt. 36, 9536–9540 (1997).
[CrossRef]

G. J. Pendock, D. D. Sampson, “Increasing the transmission capacity of coherence multiplexed communication systems by using differential detection,” IEEE Photonics Technol. Lett. 7, 1504–1506 (1995).
[CrossRef]

Pierce, M. C.

Pircher, M.

M. Pircher, E. Goetzinger, R. Leitgeb, C. K. Hitzenberger, “Transversal phase resolved polarization sensitive optical coherence tomography,” Phys. Med. Biol. 49, 1257–1263 (2004).
[CrossRef] [PubMed]

Proakis, J. G.

J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).

Sampson, D. D.

G. J. Pendock, D. D. Sampson, “Noise in coherence-multiplexed optical fiber systems,” Appl. Opt. 36, 9536–9540 (1997).
[CrossRef]

G. J. Pendock, D. D. Sampson, “Capacity of coherence-multiplexed CDMA networks,” Opt. Commun. 143, 109–117 (1997).
[CrossRef]

D. D. Sampson, G. J. Pendock, R. A. Griffin, “Photonic code-division multiple-access communications,” Fiber Integr. Opt. 16, 129–157 (1997).
[CrossRef]

G. J. Pendock, D. D. Sampson, “Increasing the transmission capacity of coherence multiplexed communication systems by using differential detection,” IEEE Photonics Technol. Lett. 7, 1504–1506 (1995).
[CrossRef]

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Coherence coding for photonic code-division multiple access networks,” J. Lightwave Technol. 13, 1826–1837 (1995).
[CrossRef]

D. D. Sampson, R. A. Griffin, D. A. Jackson, “Photonic CDMA by coherent matched filtering using time-addressed coding in optical ladder networks,” J. Lightwave Technol. 12, 2001–2010 (1994).
[CrossRef]

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Demonstration of data transmission using coherent correlation to reconstruct a coded pulse sequence,” IEEE Photonics Technol. Lett. 4, 513–515 (1992).
[CrossRef]

Schmitt, J. M.

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

Shafir, E.

M. Tur, E. Shafir, K. Blotekjaer, “Source-induced noise in optical systems driven by low-coherence sources,” J. Lightwave Technol. 8, 183–189 (1990).
[CrossRef]

Smith, E. D. J.

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett. 31, 1469–1470 (1995).
[CrossRef]

Swanson, E. A.

Takada, K.

K. Takada, “Analysis of polarization dependence of optical low-coherence reflectometry using an active Faraday rotator,” J. Lightwave Technol. 21, 2916–2922 (2003).
[CrossRef]

K. Takada, “Noise in low-coherence reflectometry,” IEEE J. Quantum Electron. 34, 1098–1108 (1998).
[CrossRef]

K. Takada, A. Himeno, K. Yukimatsu, “Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry,” Appl. Phys. Lett. 59, 2483–2485 (1991).
[CrossRef]

K. Takada, I. Yokohama, K. Chida, J. Noda, “New measurement system for fault location in optical waveguide devices based on an interferometric technique,” Appl. Opt. 26, 1603–1606 (1987).
[CrossRef] [PubMed]

Taylor, D. P.

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett. 31, 1469–1470 (1995).
[CrossRef]

Tearney, G. J.

B. E. Bouma, G. J. Tearney, Handbook of Optical Coherence Tomography (Marcel Dekker, New York, 2002).

Tur, M.

A. Eyal, D. Kuperman, O. Dimenstein, M. Tur, “Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL,” IEEE Photonics Technol. Lett. 14, 1515–1517 (2002).
[CrossRef]

M. Tur, E. Shafir, K. Blotekjaer, “Source-induced noise in optical systems driven by low-coherence sources,” J. Lightwave Technol. 8, 183–189 (1990).
[CrossRef]

Utamchandani, D.

G. C. Gupta, P. J. Legg, D. Utamchandani, I. Andonovich, “Capacity bounding of coherence multiplexed local area networks due to interferometric noise,” IEE Proc. J Optoelectron. 144, 69–74 (1997).
[CrossRef]

Wang, L.

Weissman, Y.

Wentworth, R. H.

R. H. Wentworth, “Theoretical noise performance of coherence-multiplexed interferometric sensors,” J. Lightwave Technol. 7, 941–956 (1989).
[CrossRef]

R. H. Wentworth, “Optical noise in interferometric systems containing strongly unbalanced paths,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1988).

Yokohama, I.

Youngquist, R. C.

Yukimatsu, K.

K. Takada, A. Himeno, K. Yukimatsu, “Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry,” Appl. Phys. Lett. 59, 2483–2485 (1991).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

K. Takada, A. Himeno, K. Yukimatsu, “Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry,” Appl. Phys. Lett. 59, 2483–2485 (1991).
[CrossRef]

Electron. Lett. (1)

E. D. J. Smith, P. T. Gough, D. P. Taylor, “Noise limits of optical spectral-encoding CDMA systems,” Electron. Lett. 31, 1469–1470 (1995).
[CrossRef]

Fiber Integr. Opt. (1)

D. D. Sampson, G. J. Pendock, R. A. Griffin, “Photonic code-division multiple-access communications,” Fiber Integr. Opt. 16, 129–157 (1997).
[CrossRef]

IEE Proc. J Optoelectron. (1)

G. C. Gupta, P. J. Legg, D. Utamchandani, I. Andonovich, “Capacity bounding of coherence multiplexed local area networks due to interferometric noise,” IEE Proc. J Optoelectron. 144, 69–74 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Takada, “Noise in low-coherence reflectometry,” IEEE J. Quantum Electron. 34, 1098–1108 (1998).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[CrossRef]

IEEE Photonics Technol. Lett. (3)

G. J. Pendock, D. D. Sampson, “Increasing the transmission capacity of coherence multiplexed communication systems by using differential detection,” IEEE Photonics Technol. Lett. 7, 1504–1506 (1995).
[CrossRef]

A. Eyal, D. Kuperman, O. Dimenstein, M. Tur, “Polarization dependence of the intensity modulation transfer function of an optical system with PMD and PDL,” IEEE Photonics Technol. Lett. 14, 1515–1517 (2002).
[CrossRef]

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Demonstration of data transmission using coherent correlation to reconstruct a coded pulse sequence,” IEEE Photonics Technol. Lett. 4, 513–515 (1992).
[CrossRef]

J. Biomed. Opt. (1)

J. F. de Boer, T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359–371 (2002).
[CrossRef] [PubMed]

J. Lightwave Technol. (7)

Y. Weissman, “Optical noise in frequency-periodic networks,” J. Lightwave Technol. 12, 1660–1667 (1994).
[CrossRef]

D. D. Sampson, R. A. Griffin, D. A. Jackson, “Photonic CDMA by coherent matched filtering using time-addressed coding in optical ladder networks,” J. Lightwave Technol. 12, 2001–2010 (1994).
[CrossRef]

R. A. Griffin, D. D. Sampson, D. A. Jackson, “Coherence coding for photonic code-division multiple access networks,” J. Lightwave Technol. 13, 1826–1837 (1995).
[CrossRef]

K. Takada, “Analysis of polarization dependence of optical low-coherence reflectometry using an active Faraday rotator,” J. Lightwave Technol. 21, 2916–2922 (2003).
[CrossRef]

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Opt. Commun. (1)

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J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).

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Figures (2)

Fig. 1
Fig. 1

Configuration for scalar implementation of coherence multiplexing.

Fig. 2
Fig. 2

Configuration for implementation of polarization-coherence multiplexing.

Equations (71)

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J ( t ,   τ ) E ( t + τ ) E ( t ) .
J ( t ,   τ ) = 1 2   σ S ( t ,   τ ) ,
S k ( t ,   τ ) = trace [ J ( t ,   τ ) σ k ] = E ( t ) σ k E ( t + τ ) .
σ 0 = 1 0 0 1 , σ 1 = 1 0 0 - 1 , σ 2 = 0 1 1 0 ,
σ 3 = 0 - j j 0 .
C k I ( τ ) = [ S k ( t + τ ,   0 ) - S k ( 0 ) ] [ S k ( t ,   0 ) - S k ( 0 ) ] = Γ k I ( τ ) - S k ( 0 ) 2 .
Γ k I ( τ ) = E ( t + τ ) σ k E ( t + τ ) E ( t ) σ k E ( t ) = E ( t + τ ) σ k J ( t ,   τ ) σ k E ( t ) .
Γ k I ( τ ) = 1 2   [ E ( t + τ ) σ k σ σ k E ( t ) ] S ( t ,   τ ) ,
σ k σ σ k = ( σ 0 ,   j k ( 1 - k ) σ 1 ,   j k ( 2 - k ) σ 2 ,   j k ( 3 - k ) σ 3 ) ,
k = 0 3 .
Γ k I ( τ ) = 1 2 E ( t + τ ) σ E ( t ) N k S ( t ,   τ ) = 1 2   S ( t ,   τ ) N k S ( t ,   τ ) .
C k I ( τ ) = 1 2   S ( τ ) N k S ( τ ) .
E x out ( t ) = H 11 ( t )   *   E x in ( t ) + H 12 ( t )   *   E y in ( t ) ,
E y out ( t ) = H 21 ( t )   *   E x in ( t ) + H 22 ( t )   *   E y in ( t ) ,
J out ( t ,   τ ) = H ( t )   *   E in ( t + τ ) E in ( t )   *   H ( t ) = H ( t ) E in ( t + τ - t ) E in ( t - t ) H ( t ) d t d t = H ( t ) J in ( t - t ,   τ + t - t ) H ( t ) d t d t .
σ S out ( τ ) = H ( t ) σ S in ( τ + t - t ) H ( t ) d t d t = [ H ( t ) σ H ( t ) ] S in ( τ + t - t ) d t d t .
σ S out ( τ ) = H ( η ) σ H ( η - ξ ) d η S in ( τ - ξ ) d ξ .
m kj ( ξ ) 1 2   trace H ( η ) σ j H ( η - ξ ) d η σ k ,
S out ( τ ) = M ( ξ ) S in ( τ - ξ ) d ξ M ( τ )   *   S in ( τ ) .
J out ( τ ) = n = 1 N J out n ( τ ) ,
S out ( τ ) = n = 1 N M n ( τ )   *   S in n ( τ ) .
H ( t ) = l = 1 L h l δ ( t - t l ) ,
m kj ( ξ ) 1 2   trace l = 1 L i = 1 L h l σ j h i δ ( η - t l ) δ ( η - ξ - t i ) d η σ k .
m kj ( ξ ) 1 2   l = 1 L i = 1 L trace ( h l σ j h i σ k ) δ ( ξ + t i - t l ) .
H ( t ) = 1 2   δ ( t + τ 0 / 2 ) + δ ( t - τ 0 / 2 ) δ ( t + τ 0 / 2 ) - δ ( t - τ 0 / 2 ) δ ( t + τ 0 / 2 ) - δ ( t - τ 0 / 2 ) δ ( t + τ 0 / 2 ) + δ ( t - τ 0 / 2 ) .
M ( τ ) = δ ( τ ) 0 0 0 0 1 2 δ ( τ - τ 0 ) + 1 2 δ ( τ + τ 0 ) 0 - j 2 δ ( τ - τ 0 ) + j 2 δ ( τ + τ 0 ) 0 0 δ ( τ ) 0 0 j 2 δ ( τ - τ 0 ) - j 2 δ ( τ + τ 0 ) 0 1 2 δ ( τ - τ 0 ) + 1 2 δ ( τ + τ 0 ) .
S in ( τ ) = Γ in E ( τ ) Γ in E ( τ ) 0 0 ,
S out ( τ ) = Γ in E ( τ ) 1 2 Γ in E ( τ - τ 0 ) + 1 2 Γ in E ( τ + τ 0 ) 0 j 2 Γ in E ( τ - τ 0 ) - j 2 Γ in E ( τ + τ 0 ) .
C 0 , out I ( τ ) = 1 2 S out ( τ ) N 0 S out ( τ ) = 1 2 | Γ in E ( τ ) | 2 + 1 8 | Γ in E ( τ - τ 0 ) + Γ in E ( τ + τ 0 ) | 2 + 1 8 | Γ in E ( τ - τ 0 ) - Γ in E ( τ + τ 0 ) | 2 = 1 4 ( 2 | Γ in E ( τ ) | 2 + | Γ in E ( τ + τ 0 ) | 2 + | Γ in E ( τ - τ 0 ) | 2 ) .
P out , 0 ( ω ) = 1 2 [ 1 + cos ( ω τ 0 ) ] P in ( ω ) .
P in ( ω ) - 1 2 S in ( τ ) N 0 S in ( τ ) exp ( j ω τ ) d τ = - | Γ in E ( τ ) | 2   exp ( j ω τ ) d τ
C 0 , out I ( τ ) = 1 2 S out ( τ ) N 1 S out ( τ ) = 1 2 | Γ in E ( τ ) | 2 + 1 8 | Γ in E ( τ - τ 0 ) + Γ in E ( τ + τ 0 ) | 2 - 1 8 | Γ in E ( τ - τ 0 ) - Γ in E ( τ + τ 0 ) | 2 = 1 2 { | Γ in E ( τ ) | 2 + Re [ Γ in E ( τ - τ 0 ) Γ in E ( τ + τ 0 ) * ] } .
C 1 , out I ( τ ) = 1 2 | Γ in E ( τ ) | 2 P out , 1 ( ω ) = 1 2 P in ( ω ) .
    M ( τ ) = 1 2   δ ( τ ) 1 4   δ ( τ - τ 0 ) + 1 4   δ ( τ + τ 0 ) 0 - j 4   δ ( τ - τ 0 ) + j 4   δ ( τ + τ 0 ) 1 2   δ ( τ ) 1 4   δ ( τ - τ 0 ) + 1 4   δ ( τ + τ 0 ) 0 - j 4   δ ( τ - τ 0 ) + j 4   δ ( τ + τ 0 ) 0 0 0 0 0 0 0 0 .
P out , 0 ( ω ) = 1 4 [ 1 + 1 2   cos ( ω τ 0 ) ] P in ( ω ) .
H n ( t ) = H 11 H 12 H 21 H 22 ,
H 11 ( t ) = 1 4 { exp ( j φ n ) δ ( t ) - δ ( t - τ n ) - exp ( j φ n ) δ ( t - τ m ) + δ [ t - ( τ n + τ m ) ] } ,
H 12 ( t ) = j 4 { exp ( j φ n ) δ ( t ) + δ ( t - τ n ) - exp ( j φ n ) δ ( t - τ m ) - δ [ t - ( τ n + τ m ) ] } ,
H 21 ( t ) = j 4 { exp ( j φ n ) δ ( t ) - δ ( t - τ n ) + exp ( j φ n ) δ ( t - τ m ) - δ [ t - ( τ n + τ m ) ] } ,
H 22 ( t ) = - 1   4 { exp ( j φ n ) δ ( t ) + δ ( t - τ n ) + exp ( j φ n ) δ ( t - τ m ) + δ [ t - ( τ n + τ m ) ] } .
W = T 4   cos ( φ m ) I in = ± T 4   I in ,
    S out ( τ ) = 1 16   8 N Γ in E ( τ ) - 4 Γ in E ( τ - τ m ) - 4 Γ in E ( τ + τ m ) - 4 n m N exp ( j φ n ) Γ in E ( τ - τ n ) - 4 n m N exp ( j φ n ) Γ in E ( τ + τ n ) 4 Γ in E ( τ ) - 4 N Γ in E ( τ - τ m ) - 4 N Γ in E ( τ + τ m ) + 2 n = 1 N exp ( j φ n ) Γ in E [ τ - ( τ m + τ n ) ] + 2 n = 1 N exp ( j φ n ) Γ in E [ τ + ( τ m + τ n ) ] + 2 n m N exp ( j φ n ) Γ in E [ τ - ( τ m - τ n ) ] + 2 n m N exp ( j φ n ) Γ in E [ τ + ( τ m - τ n ) ] - 4 jN Γ in E ( τ - τ m ) + 4 jN Γ in E ( τ + τ m ) + 2 j n = 1 N exp ( j φ n ) Γ in E [ τ - ( τ m + τ n ) ] - 2 j n = 1 N exp ( j φ n ) Γ in E [ τ + ( τ m + τ n ) ] - 2 j n m N exp ( j φ n ) Γ in E [ τ - ( τ m - τ n ) ] + 2 j n m N exp ( j φ n ) Γ in E [ τ + ( τ m - τ n ) ] 0 .
C 1 , out I ( τ ) = 1 32   ( 4 N 2 + 1 ) | Γ in E ( τ ) | 2 + n = 1 N [ | Γ in E ( τ - τ n ) | 2 + | Γ in E ( τ + τ n ) | 2 ] .
W 2 - W 2 = T - C 1 I ( τ ) d τ = I in 2 τ c T 32   ( 4 N 2 + 2 N + 1 ) .
SNR T 2 τ c N 2 .
H n ( t ) = H 11 H 12 H 21 H 22 ,
H 11 ( t ) = a   exp ( j φ n ) δ ( t - τ m ) + b δ [ t - ( τ n + τ m ) ] ,
H 12 ( t ) = - a   exp ( j φ n ) δ ( t - τ m ) + b δ [ t - ( τ n + τ m ) ] ,
H 21 ( t ) = - b * exp ( j φ n ) δ ( t ) + a * δ ( t - τ n ) ,
H 22 ( t ) = b * exp ( j φ n ) δ ( t ) + a * δ ( t - τ n ) .
W = T   cos ( φ m ) I in = ± TI in .
S 0 , out ( τ ) = N Γ in E ( τ ) ,
S 1 , out ( τ ) = n = 1 N exp ( j φ n ) a n * b n Γ in E ( τ - τ n ) + n = 1 N exp ( j φ n ) a n b n * Γ in E ( τ + τ n ) ,
S 2 , out ( τ ) = cos ( φ m ) Γ in E ( τ ) + 1 2 n m N   exp ( j φ n ) a n 2 Γ in E [ τ - ( τ m - τ n ) ] + n m N   exp ( j φ n ) a n * 2 Γ in E [ τ + ( τ m - τ n ) ] + n = 1 N   exp ( j φ n ) b n 2 Γ in E [ τ - ( τ m + τ n ) ] - n = 1 N   exp ( j φ n ) b n * 2 Γ in E [ τ + ( τ m + τ n ) ]  
S 3 , out ( τ ) = sin ( φ m ) Γ in E ( τ ) + j 2 n m N   exp ( j φ n ) a n 2 Γ in E [ τ - ( τ m - τ n ) ] - n m N   exp ( j φ n ) a n * 2 Γ in E [ τ + ( τ m - τ n ) ] + n = 1 N   exp ( j φ n ) b n 2 Γ in E [ τ - ( τ m + τ n ) ] + n = 1 N   exp ( j φ n ) b n * 2 Γ in E [ τ + ( τ m + τ n ) ]
C 2 , out I ( τ ) = 1 2 ( N 2 + 1 ) | Γ in E ( τ ) | 2 - n m N | a n | 2 | b n | 2 [ | Γ in E ( τ - τ n ) | 2 + | Γ in E ( τ + τ n ) | 2 ] ,
W 2 - W 2 = T - C 2 I ( τ ) d τ = I in 2 τ c T 2 N 2 + 1 - n m N | a n | 2 ( 1 - | a n | 2 ) I in 2 τ c T 2   ( N 2 + 1 ) .
SNR 2 T τ c N 2 .
Γ k I ( τ ) = 1 2 S ( t ,   τ ) N k S ( t ,   τ ) ,
N 0 = 1 1 1 1 , N 1 = 1 1 - 1 - 1 ,
N 2 = 1 - 1 1 - 1 ,   N 3 = 1 - 1 - 1 1 .
Γ 0 I ( τ ) = E x * ( t ) E x ( t + τ ) E x ( t ) E x * ( t + τ ) + E y * ( t ) E y ( t + τ ) E y ( t ) E y * ( t + τ ) + E x * ( t ) E y ( t + τ ) E x ( t ) E y * ( t + τ ) + E y * ( t ) E x ( t + τ ) E y ( t ) E x * ( t + τ ) .
u 1 * u 2 * u 3 u 4 = u 1 * u 3 u 2 * u 4 + u 1 * u 4 u 2 * u 3 .
Γ 0 I ( τ ) = E x * ( t ) E x ( t ) E x * ( t + τ ) E x ( t + τ ) + E x * ( t ) E x ( t + τ ) E x ( t ) E x * ( t + τ ) + E y * ( t ) E y ( t ) E y * ( t + τ ) E y ( t + τ ) + E y * ( t ) E y ( t + τ ) E y ( t ) E y * ( t + τ ) + E x * ( t ) E x ( t ) E y * ( t + τ ) E y ( t + τ ) + E x * ( t ) E y ( t + τ ) E x ( t ) E y * ( t + τ ) + E y * ( t ) E y ( t ) E x * ( t + τ ) E x ( t + τ ) + E y * ( t ) E x ( t + τ ) E y ( t ) E x * ( t + τ ) .
E x * ( t ) E x ( t ) E x * ( t + τ ) E x ( t + τ )
+ E y * ( t ) E y ( t ) E y * ( t + τ ) E y ( t + τ ) + E x * ( t ) E x ( t ) E y * ( t + τ ) E y ( t + τ ) + E y * ( t ) E y ( t ) E x * ( t + τ ) E x ( t + τ )
= [ E x * ( t ) E x ( t ) + E y * ( t ) E y ( t ) ] [ E x * ( t + τ ) E x ( t + τ ) + E y * ( t + τ ) E y ( t + τ ) ] = S 0 ( 0 ) S 0 ( 0 ) = S 0 ( 0 ) 2 .
C 0 I ( τ ) = E x * ( t ) E x ( t + τ ) E x ( t ) E x * ( t + τ ) + E y * ( t ) E y ( t + τ ) E y ( t ) E y * ( t + τ ) + E x * ( t ) E y ( t + τ ) E x ( t ) E y * ( t + τ ) + E y * ( t ) E x ( t + τ ) E y ( t ) E x * ( t + τ ) .
1 2 E x * ( t ) E x ( t + τ ) E y ( t ) E y * ( t + τ ) + c . c . ,
1 2 E x * ( t ) E y ( t + τ ) E y ( t ) E x * ( t + τ ) + c . c . ,
C 0 I ( τ ) = 1 2 | E x * ( t ) E x ( t + τ ) + E y * ( t ) E y ( t + τ ) | 2 + 1 2 | E x * ( t ) E x ( t + τ ) - E y * ( t ) E y ( t + τ ) | 2 + 1 2 | E x * ( t ) E y ( t + τ ) + E y * ( t ) E x ( t + τ ) | 2 + 1 2 | E x * ( t ) E y ( t + τ ) - E y * ( t ) E x ( t + τ ) | 2 = 1 2 [ | S 0 ( τ ) | 2 + | S 1 ( τ ) | 2 + | S 2 ( τ ) | 2 + | S 3 ( τ ) | 2 ] = 1 2 S ( τ ) N 0 S ( τ ) .

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