Abstract

We report a novel vector model of Raman amplification in a fiber with randomly varying birefringence and unidirectional spin profile. Applying the model, we demonstrate for the first time simultaneous mitigation of polarization mode dispersion and polarization dependence of the Raman gain.

© 2008 Optical Society of America

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  1. A. J. Barlow, J. J. Ramskov-Hansen and D. N. Payne, "Birefringence and polarization mode-dispersion in spun single-mode fibers," Appl. Opt. 20,2962-2968 (1981).
    [CrossRef] [PubMed]
  2. H. S. Lassing, A. M. Oomens, R. Woltjer, P. C. T. van der Laan, and G. G. Woizak, "Development of a magneto-optic current sensor for high, pulsed currents," Rev. Sci. Instrum. 57,851-854 (1986).
    [CrossRef]
  3. I. G. Clarke, "Temperature-stable spun elliptical-core optical-fiber current transducer," Opt. Lett. 18,158-160 (1993).
    [CrossRef] [PubMed]
  4. Y. Wang and Ch.-Q. Xu, "Spun FBG sensors with low polarization dependence under transverse force," IEEE Photon. Technol. Lett. 19,477-479 (2007).
    [CrossRef]
  5. X. Zhu and R. Jain, "Detailed analysis of evolution of the state of polarization in all-fiber polarization transformers," Opt. Express 14, 10261-10277 (2006).
    [CrossRef] [PubMed]
  6. V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, "Chiral fiber gratings," Science 305, 74-76 (2004).
    [CrossRef] [PubMed]
  7. A. Hart, R. G. Huff, and K. L. Walker, "Method of making a fiber having low polarization mode dispersion due to a permanent spin," U.S. Patent 5298047 (1994).
  8. P. E. Blaszyk, W. R. Christoff, D. E. Gallagher, R. M. Hawk, and W. J. Kiefer, "Method and apparatus for introducing controlled spin in optical fibers," U.S. Patent 6324873 B1 (2001).
  9. R. E. Schuh, X. Shan, and A. S. Siddiqui, "Polarization mode dispersion in spun fibers with different linear birefringence and spinning parameters," J. Lightwave Technol. 16,1583-1588 (1998).
    [CrossRef]
  10. M. J. Li and D. A. Nolan, "Fiber spin-profile designs for producing fibers with low polarization mode dispersion," Opt. Lett. 23, 1659-1661 (1998).
    [CrossRef]
  11. D. A. Nolan, X. Chen, and M.-J. Li, "Fibers with low polarization-mode dispersion," J. Lightwave Technol. 22,1066-1077 (2004).
    [CrossRef]
  12. A. Galtarossa, L. Palmieri, and A. Pizzinat, "Optimized spinning design for low PMD fibers: an analytical approach," J. Lightwave Technol. 19,1502-1512 (2001).
    [CrossRef]
  13. A. Galtarossa, P. Griggio, A. Pizzinat, and L. Palmieri, "Calculation of mean differential group delay of periodically spun randomly birefringent fibers," Opt. Lett. 27,692-694 (2002).
    [CrossRef]
  14. A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks, and C. R. Menyuk, "An analytical formula for the mean differential group delay of randomly-birefringent spun fibers," J. Lightwave Technol. 21,1635-1643 (2003).
    [CrossRef]
  15. A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, "Influence of the model for random birefringence on the differential group delay of periodically spun fibers," IEEE Photon. Technol. Lett. 15,819-821 (2003).
    [CrossRef]
  16. G. Bouquet, L.-A. de Montmorillon, and P. Nouchi, "Analytical solution of polarization mode dispersion for triangular spun fibers," Opt. Lett. 29,2118-2120 (2004).
    [CrossRef] [PubMed]
  17. A. Galtarossa, L. Palmieri, A. Pizzinat, and L. Schenato, "Polarization properties of randomly-birefringent spun fibers," Opt. Fiber Technol. 12,205-216 (2006).
    [CrossRef]
  18. J. G. Ellison and A. S. Siddiqui, "Using polarimetric optical time domain reflectometry to extract spun fiber parameters," Proc. Inst. Electr. Eng.???Optoelectron. 148,176-182 (2001).
    [CrossRef]
  19. A. Galtarossa, L. Palmieri, and D. Sarchi, "Measure of spin period in randomly-birefringent low-PMD fibers," IEEE Photon. Technol. Lett. 16,1131-1133 (2004).
    [CrossRef]
  20. A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
    [CrossRef]
  21. M. N. Islam, C. DeWilde, and A. Kuditcher, "Wideband Raman amplifiers," in Raman Amplifiers for Telecommunications2: Sub-Systems and Systems, ed. Islam, M. N. (Springer, 2004), pp. 445-490.
  22. E. Bettini, A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Backward Raman Amplification in Unidirectionally Spun Fibers," IEEE Photon. Technol. Lett. 20,27-29 (2008).
    [CrossRef]
  23. Q. Lin and G. P. Agrawal, "Vector theory of stimulated Raman scattering and its application to fiber-based Raman amplifiers," J. Opt. Soc. Am. B 20, 1616-1631 (2003).
    [CrossRef]
  24. S. Sergeyev, S. Popov, and A. T. Friberg, "Modeling polarization-dependent gain in fiber Raman amplifiers with randomly varying birefringence," Opt. Commun. 262, 114-119 (2006).
    [CrossRef]
  25. S. Sergeyev, S. Popov, and A. T. Friberg, "Polarization dependent gain and gain fluctuations in a fiber Raman amplifier," J. Opt. A: Pure Appl. Opt. 9,1119-1122 (2007).
    [CrossRef]
  26. S. Popov, S. Sergeyev, and A. T. Friberg, "The impact of pump polarization on the polarization dependence of the Raman gain due to the breaking of a fiber???s circular symmetry," J. Opt. A: Pure Appl. Opt. 6, S72-S76 (2004).
    [CrossRef]
  27. H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).
  28. T. Tokura, T. Kogure, T. Sugihara, K. Shimizu, T. Mizuochi, & K. Motoshima, "Efficient pump depolarizer analysis for distributed Raman amplifier with low polarization dependence of gain," J. Lightwave Technol. 24,3889-3896 (2006).
    [CrossRef]

2008 (1)

E. Bettini, A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Backward Raman Amplification in Unidirectionally Spun Fibers," IEEE Photon. Technol. Lett. 20,27-29 (2008).
[CrossRef]

2007 (2)

S. Sergeyev, S. Popov, and A. T. Friberg, "Polarization dependent gain and gain fluctuations in a fiber Raman amplifier," J. Opt. A: Pure Appl. Opt. 9,1119-1122 (2007).
[CrossRef]

Y. Wang and Ch.-Q. Xu, "Spun FBG sensors with low polarization dependence under transverse force," IEEE Photon. Technol. Lett. 19,477-479 (2007).
[CrossRef]

2006 (5)

X. Zhu and R. Jain, "Detailed analysis of evolution of the state of polarization in all-fiber polarization transformers," Opt. Express 14, 10261-10277 (2006).
[CrossRef] [PubMed]

A. Galtarossa, L. Palmieri, A. Pizzinat, and L. Schenato, "Polarization properties of randomly-birefringent spun fibers," Opt. Fiber Technol. 12,205-216 (2006).
[CrossRef]

T. Tokura, T. Kogure, T. Sugihara, K. Shimizu, T. Mizuochi, & K. Motoshima, "Efficient pump depolarizer analysis for distributed Raman amplifier with low polarization dependence of gain," J. Lightwave Technol. 24,3889-3896 (2006).
[CrossRef]

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, "Modeling polarization-dependent gain in fiber Raman amplifiers with randomly varying birefringence," Opt. Commun. 262, 114-119 (2006).
[CrossRef]

2004 (5)

S. Popov, S. Sergeyev, and A. T. Friberg, "The impact of pump polarization on the polarization dependence of the Raman gain due to the breaking of a fiber???s circular symmetry," J. Opt. A: Pure Appl. Opt. 6, S72-S76 (2004).
[CrossRef]

G. Bouquet, L.-A. de Montmorillon, and P. Nouchi, "Analytical solution of polarization mode dispersion for triangular spun fibers," Opt. Lett. 29,2118-2120 (2004).
[CrossRef] [PubMed]

A. Galtarossa, L. Palmieri, and D. Sarchi, "Measure of spin period in randomly-birefringent low-PMD fibers," IEEE Photon. Technol. Lett. 16,1131-1133 (2004).
[CrossRef]

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, "Chiral fiber gratings," Science 305, 74-76 (2004).
[CrossRef] [PubMed]

D. A. Nolan, X. Chen, and M.-J. Li, "Fibers with low polarization-mode dispersion," J. Lightwave Technol. 22,1066-1077 (2004).
[CrossRef]

2003 (4)

A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks, and C. R. Menyuk, "An analytical formula for the mean differential group delay of randomly-birefringent spun fibers," J. Lightwave Technol. 21,1635-1643 (2003).
[CrossRef]

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, "Influence of the model for random birefringence on the differential group delay of periodically spun fibers," IEEE Photon. Technol. Lett. 15,819-821 (2003).
[CrossRef]

H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).

Q. Lin and G. P. Agrawal, "Vector theory of stimulated Raman scattering and its application to fiber-based Raman amplifiers," J. Opt. Soc. Am. B 20, 1616-1631 (2003).
[CrossRef]

2002 (1)

2001 (2)

J. G. Ellison and A. S. Siddiqui, "Using polarimetric optical time domain reflectometry to extract spun fiber parameters," Proc. Inst. Electr. Eng.???Optoelectron. 148,176-182 (2001).
[CrossRef]

A. Galtarossa, L. Palmieri, and A. Pizzinat, "Optimized spinning design for low PMD fibers: an analytical approach," J. Lightwave Technol. 19,1502-1512 (2001).
[CrossRef]

1998 (2)

1993 (1)

1986 (1)

H. S. Lassing, A. M. Oomens, R. Woltjer, P. C. T. van der Laan, and G. G. Woizak, "Development of a magneto-optic current sensor for high, pulsed currents," Rev. Sci. Instrum. 57,851-854 (1986).
[CrossRef]

1981 (1)

Agrawal, G. P.

Barlow, A. J.

Bettini, E.

E. Bettini, A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Backward Raman Amplification in Unidirectionally Spun Fibers," IEEE Photon. Technol. Lett. 20,27-29 (2008).
[CrossRef]

Bouquet, G.

Chao, N.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, "Chiral fiber gratings," Science 305, 74-76 (2004).
[CrossRef] [PubMed]

Chen, X.

Churikov, V. M.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, "Chiral fiber gratings," Science 305, 74-76 (2004).
[CrossRef] [PubMed]

Clarke, I. G.

de Montmorillon, L.-A.

Ellison, J. G.

J. G. Ellison and A. S. Siddiqui, "Using polarimetric optical time domain reflectometry to extract spun fiber parameters," Proc. Inst. Electr. Eng.???Optoelectron. 148,176-182 (2001).
[CrossRef]

Emori, Y.

H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).

Friberg, A. T.

S. Sergeyev, S. Popov, and A. T. Friberg, "Polarization dependent gain and gain fluctuations in a fiber Raman amplifier," J. Opt. A: Pure Appl. Opt. 9,1119-1122 (2007).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, "Modeling polarization-dependent gain in fiber Raman amplifiers with randomly varying birefringence," Opt. Commun. 262, 114-119 (2006).
[CrossRef]

S. Popov, S. Sergeyev, and A. T. Friberg, "The impact of pump polarization on the polarization dependence of the Raman gain due to the breaking of a fiber???s circular symmetry," J. Opt. A: Pure Appl. Opt. 6, S72-S76 (2004).
[CrossRef]

Galtarossa, A.

E. Bettini, A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Backward Raman Amplification in Unidirectionally Spun Fibers," IEEE Photon. Technol. Lett. 20,27-29 (2008).
[CrossRef]

A. Galtarossa, L. Palmieri, A. Pizzinat, and L. Schenato, "Polarization properties of randomly-birefringent spun fibers," Opt. Fiber Technol. 12,205-216 (2006).
[CrossRef]

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

A. Galtarossa, L. Palmieri, and D. Sarchi, "Measure of spin period in randomly-birefringent low-PMD fibers," IEEE Photon. Technol. Lett. 16,1131-1133 (2004).
[CrossRef]

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, "Influence of the model for random birefringence on the differential group delay of periodically spun fibers," IEEE Photon. Technol. Lett. 15,819-821 (2003).
[CrossRef]

A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks, and C. R. Menyuk, "An analytical formula for the mean differential group delay of randomly-birefringent spun fibers," J. Lightwave Technol. 21,1635-1643 (2003).
[CrossRef]

A. Galtarossa, P. Griggio, A. Pizzinat, and L. Palmieri, "Calculation of mean differential group delay of periodically spun randomly birefringent fibers," Opt. Lett. 27,692-694 (2002).
[CrossRef]

A. Galtarossa, L. Palmieri, and A. Pizzinat, "Optimized spinning design for low PMD fibers: an analytical approach," J. Lightwave Technol. 19,1502-1512 (2001).
[CrossRef]

Genack, A. Z.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, "Chiral fiber gratings," Science 305, 74-76 (2004).
[CrossRef] [PubMed]

Griggio, P.

Jain, R.

Jung, J.

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

Kazami, H.

H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).

Kim, J.

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

Kogure, T.

Kopp, V. I.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, "Chiral fiber gratings," Science 305, 74-76 (2004).
[CrossRef] [PubMed]

Lassing, H. S.

H. S. Lassing, A. M. Oomens, R. Woltjer, P. C. T. van der Laan, and G. G. Woizak, "Development of a magneto-optic current sensor for high, pulsed currents," Rev. Sci. Instrum. 57,851-854 (1986).
[CrossRef]

Lee, B. H.

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

Li, M. J.

Li, M.-J.

Lin, Q.

Marks, B. S.

A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks, and C. R. Menyuk, "An analytical formula for the mean differential group delay of randomly-birefringent spun fibers," J. Lightwave Technol. 21,1635-1643 (2003).
[CrossRef]

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, "Influence of the model for random birefringence on the differential group delay of periodically spun fibers," IEEE Photon. Technol. Lett. 15,819-821 (2003).
[CrossRef]

Matsushita, S.

H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).

Matsuura, H.

H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).

Menyuk, C. R.

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, "Influence of the model for random birefringence on the differential group delay of periodically spun fibers," IEEE Photon. Technol. Lett. 15,819-821 (2003).
[CrossRef]

A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks, and C. R. Menyuk, "An analytical formula for the mean differential group delay of randomly-birefringent spun fibers," J. Lightwave Technol. 21,1635-1643 (2003).
[CrossRef]

Mizuochi, T.

Motoshima, K.

Murase, T.

H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).

Namiki, S.

H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).

Neugroschl, D.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, "Chiral fiber gratings," Science 305, 74-76 (2004).
[CrossRef] [PubMed]

Nolan, D. A.

Nouchi, P.

Oh, K.

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

Oomens, A. M.

H. S. Lassing, A. M. Oomens, R. Woltjer, P. C. T. van der Laan, and G. G. Woizak, "Development of a magneto-optic current sensor for high, pulsed currents," Rev. Sci. Instrum. 57,851-854 (1986).
[CrossRef]

Paek, U. C.

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

Palmieri, L.

E. Bettini, A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Backward Raman Amplification in Unidirectionally Spun Fibers," IEEE Photon. Technol. Lett. 20,27-29 (2008).
[CrossRef]

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

A. Galtarossa, L. Palmieri, A. Pizzinat, and L. Schenato, "Polarization properties of randomly-birefringent spun fibers," Opt. Fiber Technol. 12,205-216 (2006).
[CrossRef]

A. Galtarossa, L. Palmieri, and D. Sarchi, "Measure of spin period in randomly-birefringent low-PMD fibers," IEEE Photon. Technol. Lett. 16,1131-1133 (2004).
[CrossRef]

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, "Influence of the model for random birefringence on the differential group delay of periodically spun fibers," IEEE Photon. Technol. Lett. 15,819-821 (2003).
[CrossRef]

A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks, and C. R. Menyuk, "An analytical formula for the mean differential group delay of randomly-birefringent spun fibers," J. Lightwave Technol. 21,1635-1643 (2003).
[CrossRef]

A. Galtarossa, P. Griggio, A. Pizzinat, and L. Palmieri, "Calculation of mean differential group delay of periodically spun randomly birefringent fibers," Opt. Lett. 27,692-694 (2002).
[CrossRef]

A. Galtarossa, L. Palmieri, and A. Pizzinat, "Optimized spinning design for low PMD fibers: an analytical approach," J. Lightwave Technol. 19,1502-1512 (2001).
[CrossRef]

Payne, D. N.

Pizzinat, A.

A. Galtarossa, L. Palmieri, A. Pizzinat, and L. Schenato, "Polarization properties of randomly-birefringent spun fibers," Opt. Fiber Technol. 12,205-216 (2006).
[CrossRef]

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, "Influence of the model for random birefringence on the differential group delay of periodically spun fibers," IEEE Photon. Technol. Lett. 15,819-821 (2003).
[CrossRef]

A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks, and C. R. Menyuk, "An analytical formula for the mean differential group delay of randomly-birefringent spun fibers," J. Lightwave Technol. 21,1635-1643 (2003).
[CrossRef]

A. Galtarossa, P. Griggio, A. Pizzinat, and L. Palmieri, "Calculation of mean differential group delay of periodically spun randomly birefringent fibers," Opt. Lett. 27,692-694 (2002).
[CrossRef]

A. Galtarossa, L. Palmieri, and A. Pizzinat, "Optimized spinning design for low PMD fibers: an analytical approach," J. Lightwave Technol. 19,1502-1512 (2001).
[CrossRef]

Popov, S.

S. Sergeyev, S. Popov, and A. T. Friberg, "Polarization dependent gain and gain fluctuations in a fiber Raman amplifier," J. Opt. A: Pure Appl. Opt. 9,1119-1122 (2007).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, "Modeling polarization-dependent gain in fiber Raman amplifiers with randomly varying birefringence," Opt. Commun. 262, 114-119 (2006).
[CrossRef]

S. Popov, S. Sergeyev, and A. T. Friberg, "The impact of pump polarization on the polarization dependence of the Raman gain due to the breaking of a fiber???s circular symmetry," J. Opt. A: Pure Appl. Opt. 6, S72-S76 (2004).
[CrossRef]

Ramskov-Hansen, J. J.

Santagiustina, M.

E. Bettini, A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Backward Raman Amplification in Unidirectionally Spun Fibers," IEEE Photon. Technol. Lett. 20,27-29 (2008).
[CrossRef]

Sarchi, D.

A. Galtarossa, L. Palmieri, and D. Sarchi, "Measure of spin period in randomly-birefringent low-PMD fibers," IEEE Photon. Technol. Lett. 16,1131-1133 (2004).
[CrossRef]

Schenato, L.

E. Bettini, A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Backward Raman Amplification in Unidirectionally Spun Fibers," IEEE Photon. Technol. Lett. 20,27-29 (2008).
[CrossRef]

A. Galtarossa, L. Palmieri, A. Pizzinat, and L. Schenato, "Polarization properties of randomly-birefringent spun fibers," Opt. Fiber Technol. 12,205-216 (2006).
[CrossRef]

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

Schuh, R. E.

Sergeyev, S.

S. Sergeyev, S. Popov, and A. T. Friberg, "Polarization dependent gain and gain fluctuations in a fiber Raman amplifier," J. Opt. A: Pure Appl. Opt. 9,1119-1122 (2007).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, "Modeling polarization-dependent gain in fiber Raman amplifiers with randomly varying birefringence," Opt. Commun. 262, 114-119 (2006).
[CrossRef]

S. Popov, S. Sergeyev, and A. T. Friberg, "The impact of pump polarization on the polarization dependence of the Raman gain due to the breaking of a fiber???s circular symmetry," J. Opt. A: Pure Appl. Opt. 6, S72-S76 (2004).
[CrossRef]

Shan, X.

Shiba, T.

H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).

Shimizu, K.

Siddiqui, A. S.

J. G. Ellison and A. S. Siddiqui, "Using polarimetric optical time domain reflectometry to extract spun fiber parameters," Proc. Inst. Electr. Eng.???Optoelectron. 148,176-182 (2001).
[CrossRef]

R. E. Schuh, X. Shan, and A. S. Siddiqui, "Polarization mode dispersion in spun fibers with different linear birefringence and spinning parameters," J. Lightwave Technol. 16,1583-1588 (1998).
[CrossRef]

Singer, J.

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, "Chiral fiber gratings," Science 305, 74-76 (2004).
[CrossRef] [PubMed]

Someda, C. G.

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

Sugihara, T.

Tokura, T.

Tsuyuki, M.

H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).

Ursini, L.

E. Bettini, A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Backward Raman Amplification in Unidirectionally Spun Fibers," IEEE Photon. Technol. Lett. 20,27-29 (2008).
[CrossRef]

van der Laan, P. C. T.

H. S. Lassing, A. M. Oomens, R. Woltjer, P. C. T. van der Laan, and G. G. Woizak, "Development of a magneto-optic current sensor for high, pulsed currents," Rev. Sci. Instrum. 57,851-854 (1986).
[CrossRef]

Wang, Y.

Y. Wang and Ch.-Q. Xu, "Spun FBG sensors with low polarization dependence under transverse force," IEEE Photon. Technol. Lett. 19,477-479 (2007).
[CrossRef]

Woizak, G. G.

H. S. Lassing, A. M. Oomens, R. Woltjer, P. C. T. van der Laan, and G. G. Woizak, "Development of a magneto-optic current sensor for high, pulsed currents," Rev. Sci. Instrum. 57,851-854 (1986).
[CrossRef]

Woltjer, R.

H. S. Lassing, A. M. Oomens, R. Woltjer, P. C. T. van der Laan, and G. G. Woizak, "Development of a magneto-optic current sensor for high, pulsed currents," Rev. Sci. Instrum. 57,851-854 (1986).
[CrossRef]

Xu, Ch.-Q.

Y. Wang and Ch.-Q. Xu, "Spun FBG sensors with low polarization dependence under transverse force," IEEE Photon. Technol. Lett. 19,477-479 (2007).
[CrossRef]

Yamamoto, K.

H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).

Zhu, X.

Appl. Opt. (1)

Furakawa Review (1)

H. Kazami, S. Matsushita, Y. Emori, T. Murase, M. Tsuyuki, K. Yamamoto, H. Matsuura, S. Namiki, and T. Shiba, "Development of a crystal-type depolarizer," Furakawa Review 23, 44-47 (2003).

IEEE Photon. Technol. Lett. (4)

A. Galtarossa, L. Palmieri, and D. Sarchi, "Measure of spin period in randomly-birefringent low-PMD fibers," IEEE Photon. Technol. Lett. 16,1131-1133 (2004).
[CrossRef]

E. Bettini, A. Galtarossa, L. Palmieri, M. Santagiustina, L. Schenato, and L. Ursini, "Polarized Backward Raman Amplification in Unidirectionally Spun Fibers," IEEE Photon. Technol. Lett. 20,27-29 (2008).
[CrossRef]

Y. Wang and Ch.-Q. Xu, "Spun FBG sensors with low polarization dependence under transverse force," IEEE Photon. Technol. Lett. 19,477-479 (2007).
[CrossRef]

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, "Influence of the model for random birefringence on the differential group delay of periodically spun fibers," IEEE Photon. Technol. Lett. 15,819-821 (2003).
[CrossRef]

J. Lightwave Technol. (5)

J. Opt. A: Pure Appl. Opt. (2)

S. Sergeyev, S. Popov, and A. T. Friberg, "Polarization dependent gain and gain fluctuations in a fiber Raman amplifier," J. Opt. A: Pure Appl. Opt. 9,1119-1122 (2007).
[CrossRef]

S. Popov, S. Sergeyev, and A. T. Friberg, "The impact of pump polarization on the polarization dependence of the Raman gain due to the breaking of a fiber???s circular symmetry," J. Opt. A: Pure Appl. Opt. 6, S72-S76 (2004).
[CrossRef]

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

Opt. Commun. (1)

S. Sergeyev, S. Popov, and A. T. Friberg, "Modeling polarization-dependent gain in fiber Raman amplifiers with randomly varying birefringence," Opt. Commun. 262, 114-119 (2006).
[CrossRef]

Opt. Express (1)

Opt. Fiber Technol. (2)

A. Galtarossa, L. Palmieri, A. Pizzinat, and L. Schenato, "Polarization properties of randomly-birefringent spun fibers," Opt. Fiber Technol. 12,205-216 (2006).
[CrossRef]

A. Galtarossa, J. Jung, J. Kim, B. H. Lee, K. Oh, U. C. Paek, L. Palmieri, A. Pizzinat, L. Schenato and C. G. Someda, "Low polarization mode dispersion measurements in ad hoc drawn spun fibers," Opt. Fiber Technol. 12,323-327 (2006).
[CrossRef]

Opt. Lett. (4)

Optoelectron. (1)

J. G. Ellison and A. S. Siddiqui, "Using polarimetric optical time domain reflectometry to extract spun fiber parameters," Proc. Inst. Electr. Eng.???Optoelectron. 148,176-182 (2001).
[CrossRef]

Rev. Sci. Instrum. (1)

H. S. Lassing, A. M. Oomens, R. Woltjer, P. C. T. van der Laan, and G. G. Woizak, "Development of a magneto-optic current sensor for high, pulsed currents," Rev. Sci. Instrum. 57,851-854 (1986).
[CrossRef]

Science (1)

V. I. Kopp, V. M. Churikov, J. Singer, N. Chao, D. Neugroschl, and A. Z. Genack, "Chiral fiber gratings," Science 305, 74-76 (2004).
[CrossRef] [PubMed]

Other (3)

A. Hart, R. G. Huff, and K. L. Walker, "Method of making a fiber having low polarization mode dispersion due to a permanent spin," U.S. Patent 5298047 (1994).

P. E. Blaszyk, W. R. Christoff, D. E. Gallagher, R. M. Hawk, and W. J. Kiefer, "Method and apparatus for introducing controlled spin in optical fibers," U.S. Patent 6324873 B1 (2001).

M. N. Islam, C. DeWilde, and A. Kuditcher, "Wideband Raman amplifiers," in Raman Amplifiers for Telecommunications2: Sub-Systems and Systems, ed. Islam, M. N. (Springer, 2004), pp. 445-490.

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Figures (4)

Fig. 1.
Fig. 1.

Drawing the spun fiber with controlled spin parameters. A unidirectional periodic spin profile of A(z)=A 0 sin(2π f 0 z) with amplitude A 0 and frequency f 0 is optimal for strong PMD suppression [9-20].

Fig. 2.
Fig. 2.

Optical pulse distortion in terms of the differential group delay (DGD, caused by polarization mode dispersion PMD) and the polarization dependent gain (PDG) in a Raman fiber amplifier with a fixed birefringence, e.g., a polarization maintaining (PM) fiber. (a) Pump electric-field vector is oriented along a birefringence axis, (b) pump field is equally shared between the two orthogonal states of polarization.

Fig. 3.
Fig. 3.

Evolution of the pump (p) and signal (s) states of polarization on the Poincaré sphere, as well as the rotation of the local birefringence vector w. Vectors p and s rotates around the local axis w with the rates b p and b s, while vector w rotates randomly in the equatorial plane at the rate σ=L c -1/2 (L c is the correlation length). (a) Initial orientations of the Stokes components for maximum PDG: pump polarization p=(1, 0, 0), signal polarizations s max=(1, 0, 0) giving maximum Raman gain, and s min=(-1, 0, 0) giving the minimum gain. (b) Initial orientations of the Stokes components for minimum PDG: pump polarization p=(0, 0, 1), signal polarizations s max=(0, 1, 0) giving maximum Raman gain, and s min=(0, -1, 0) giving the minimum gain. These orientations correspond to the minimum polarization dependent gain for the case of oscillatory behavior of the pump to signal SOP projection, i.e. when b p-b s is much higher than de-correlation rate L c-1.

Fig. 4.
Fig. 4.

(a). Maximum (thick solid and dotted lines) and minimum (thin solid and dotted lines) polarization dependent gain (PDG) as a function of the spinning amplitude A0 for two-section (solid line) and periodically spun (dotted line) fibers. Approximate values for maxim PDG: dashed line and minimum PDG dash-dotted line (Eq. (2)). (b) SIRF as a function of the spinning amplitude A0 for periodically spun (solid line), two-section (dash-dotted line) fibers, and for fibers with the frequency modulated (dotted line) and exponentially varying (dashed line) spin rates. (c) Evolution of the signal to pump SOP <x> for the case of two-section (solid and dotted line) and periodically spun (circles) fibers. Minimum PDG: dotted line, open circles; maximum PDG: solid line, closed circles. Projection for the maximum gain: thick solid line, thick dotted line and thick circles; for the minimum gain: thin solid line, thin dotted line and thin circles. (d) Maximum (thick solid and dotted lines) and minimum (thin solid and dotted lines) polarization dependent gain (PDG) as a function of the spinning amplitude A0 for the fibers with exponentially varying (solid line) and frequency modulated (dotted line) spin rates. Parameters: the pump SOP for minimum PDG is (0,0,1), the pump SOP for maximum PDG is (1,0,0), foLb,s=3, Lb,s=8.17 m, L 1 5 T 2 = ( 5 π L c ) 4 ε 3 2 1 4 = 259 m , L2=10 km, Lc=30 m, Ω=1/Lb,s, αp=0.27 dB/km, Dp=0.2 ps·km-1/2, λp=1460 nm, λs=1550 nm, g=1.8 W-1km-1, and P=1 W.

Equations (22)

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PDG = 10 log ( S 0 max S 0 min ) = 10 log ( 1 + g P in 2 0 L exp ( α p z ) x max dz 1 + g P in 2 0 L exp ( α p z ) x min dz ) ,
PDG max = 10 ε 1 ( 1 + 2 ε 3 2 ) ln ( 10 ) ( ε 2 ( ε 2 + 1 2 ) + ε 3 2 ) , PDG max = 20 ε 1 ε 3 ln ( 10 ) ( ε 2 ( ε 2 + 1 2 ) + ε 3 2 ) ,
A ( z ) = A 0 sin ( 2 π f 0 z ) ,
SIRF = Δ τ 2 ( L ) Δ τ un 2 ( L ) ,
Δ τ un 2 ( L ) = 2 [ λ ( L b c ) ] L c [ exp ( L L c ) + L L c 1 ] ,
SIRF | A 0 1.2 [ ( L c L ) ( exp ( L 1 L c ) 1 ) + L 1 L ] ,
ds 0 dz = g 2 P 0 ( z ) ( p ̂ · s )
d s dz = g 2 P 0 ( z ) s 0 p ̂ + W s × s .
η d p ̂ dz = W p × p ̂
d Ω dz = W s ω + W s × Ω
R 3 ( γ ) = ( cos γ sin γ 0 sin γ cos γ 0 0 0 1 ) .
d ϕ dz = β ( z ) , β ( z ) = 0 , β ( z ) β ( z ) = σ 2 δ ( z z ) ,
d s 0 dz = ε 1 exp ( ε 2 z ) x
d x dz = ε 1 exp ( ε 2 z ) s 0 ε 3 y .
d y dz = ε 3 [ x p ˜ 1 ( 0 ) s ˜ 1 ( 0 ) exp ( z ) ] 2 α ( z ) L c u y 2
d u dz = 2 α ( z ) L c y u 2
d SIRF 2 dz = ε 4 Ω ̂ 1
d Ω ̂ 1 dz = Ω ̂ 1 + 2 α ( z ) L c Ω ̂ 2 + 1 ,
d Ω ̂ 2 dz = 2 α ( z ) L c Ω ̂ 1 Ω ̂ 2 ε 5 Ω ̂ 3
d Ω ̂ 3 dz = ε 5 Ω ̂ 2
α FM ( z ) = 2 π f 0 A 0 cos { 2 π [ f 0 z + f m cos ( 2 π Ω z ) ] } .
α EXV ( z ) = 2 A 0 π f 0 cos ( 2 π f 0 z ) [ 1 exp ( z L 1 ) ]

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