Abstract

We proposed a theoretical model to investigate the polarization pulling effect in bi-directionally pumped degenerate Raman assisted fiber optical parameter amplifiers (RA-FOPAs) using randomly birefringent fibers. The contributions of chromatic dispersion, polarization mode dispersion (PMD), Raman gain, and nonlinear effects to the phase matching in RA-FOPAs are investigated. We characterize four different states of polarization pulling in RA-FOPAs. We found that broadband polarization attraction can be obtained in the optimum phase-matching state of the bi-directionally pumped RA-FOPAs when the parametric pump power is chosen to avoid deep saturation of the Raman gain.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  12. V. V. Kozlov, J. Nuño, J. D. Ania-Castañón, and S. Wabnitz, “Analytic theory of fiber-optic Raman polarizers,” Opt. Express 20(24), 27242–27247 (2012).
    [Crossref] [PubMed]
  13. F. Chiarello, L. Ursini, L. Palmieri, and M. Santagiustina, “Polarization attraction in counter propagating fiber Raman amplifiers,” IEEE Photonics Technol. Lett. 23(20), 1457–1459 (2011).
    [Crossref]
  14. F. Chiarello, L. Palmieri, M. Santagiustina, R. Gamatham, and A. Galtarossa, “Experimental characterization of the counter-propagating Raman polarization attraction,” Opt. Express 20(23), 26050–26055 (2012).
    [Crossref] [PubMed]
  15. V. V. Kozlov, J. Nuño, J. D. Ania-Castañón, and S. Wabnitz, Trapping Polarization of Light in Nonlinear Optical Fibers: An Ideal Raman Polarizer (Springer Berlin Heidelberg, 2012).
  16. Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19(27), 25873–25880 (2011).
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    [Crossref] [PubMed]
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    [Crossref]
  23. S. H. Wang, L. Xu, P. K. A. Wai, and H. Y. Tam, “Optimization of Raman-assisted fiber optical parametric amplifier gain,” J. Lightwave Technol. 29(8), 1172–1181 (2011).
    [Crossref]
  24. X. Guo and C. Shu, “Cross-gain modulation suppression in a Raman-assisted fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 26(13), 1360–1363 (2014).
    [Crossref]
  25. A. Redyuk, M. F. C. Stephens, and N. J. Doran, “Suppression of WDM four-wave mixing crosstalk in fibre optic parametric amplifier using Raman-assisted pumping,” Opt. Express 23(21), 27240–27249 (2015).
    [Crossref] [PubMed]
  26. X. Guo, X. Fu, and C. Shu, “Control of saturation characteristics in a fiber optical parametric amplifier by Raman amplification,” in Conference on Lasers and Electro-Optics, 2014 OSA Technical Digest Series (Optical Society of America, 2014), paper JTu4A.64.
    [Crossref]
  27. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).
  28. P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
    [Crossref]
  29. V. V. Kozlov and S. Wabnitz, “Suppression of relative intensity noise in fiber-optic Raman polarizers,” IEEE Photonics Technol. Lett. 23(15), 1088–1090 (2011).
    [Crossref]

2015 (2)

2014 (2)

G. Millot and S. Wabnitz, “Nonlinear polarization effects in optical fibers: polarization attraction and modulation instability,” J. Opt. Soc. Am. B 31(11), 2754–2768 (2014).
[Crossref]

X. Guo and C. Shu, “Cross-gain modulation suppression in a Raman-assisted fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 26(13), 1360–1363 (2014).
[Crossref]

2012 (6)

2011 (6)

2010 (2)

M. Santagiustina and L. Schenato, “Single-pump parametric amplification in randomly birefringent fibers,” IEEE Photonics Technol. Lett. 22(2), 73–75 (2010).
[Crossref]

V. V. Kozlov, J. Nuño, J. D. Ania-Castañón, and S. Wabnitz, “Theory of fiber optic Raman polarizers,” Opt. Lett. 35(23), 3970–3972 (2010).
[Crossref] [PubMed]

2009 (2)

2005 (1)

J. F. L. Freitas, M. B. Costa e Silva, S. R. Lüthi, and A. S. L. Gomes, “Raman enhanced parametric amplifier based S-C band wavelength converter: Experiment and simulations,” Opt. Commun. 255(4-6), 314–318 (2005).
[Crossref]

2004 (2)

2003 (1)

2001 (1)

1996 (1)

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
[Crossref]

Agrawal, G. P.

Ania-Castañón, J. D.

Chestnut, D. A.

Chiarello, F.

F. Chiarello, L. Palmieri, M. Santagiustina, R. Gamatham, and A. Galtarossa, “Experimental characterization of the counter-propagating Raman polarization attraction,” Opt. Express 20(23), 26050–26055 (2012).
[Crossref] [PubMed]

F. Chiarello, L. Ursini, L. Palmieri, and M. Santagiustina, “Polarization attraction in counter propagating fiber Raman amplifiers,” IEEE Photonics Technol. Lett. 23(20), 1457–1459 (2011).
[Crossref]

Chin, S.

Cirigliano, M.

Costa e Silva, M. B.

J. F. L. Freitas, M. B. Costa e Silva, S. R. Lüthi, and A. S. L. Gomes, “Raman enhanced parametric amplifier based S-C band wavelength converter: Experiment and simulations,” Opt. Commun. 255(4-6), 314–318 (2005).
[Crossref]

de Matos, C. J. S.

Doran, N. J.

Eyal, A.

Fatome, J.

Ferrario, M.

Freitas, J. F. L.

J. F. L. Freitas, M. B. Costa e Silva, S. R. Lüthi, and A. S. L. Gomes, “Raman enhanced parametric amplifier based S-C band wavelength converter: Experiment and simulations,” Opt. Commun. 255(4-6), 314–318 (2005).
[Crossref]

Galtarossa, A.

Gamatham, R.

Gomes, A. S. L.

J. F. L. Freitas, M. B. Costa e Silva, S. R. Lüthi, and A. S. L. Gomes, “Raman enhanced parametric amplifier based S-C band wavelength converter: Experiment and simulations,” Opt. Commun. 255(4-6), 314–318 (2005).
[Crossref]

Guasoni, M.

Guo, X.

X. Guo and C. Shu, “Cross-gain modulation suppression in a Raman-assisted fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 26(13), 1360–1363 (2014).
[Crossref]

Kozlov, V. V.

Lantz, E.

Lin, Q.

Lüthi, S. R.

J. F. L. Freitas, M. B. Costa e Silva, S. R. Lüthi, and A. S. L. Gomes, “Raman enhanced parametric amplifier based S-C band wavelength converter: Experiment and simulations,” Opt. Commun. 255(4-6), 314–318 (2005).
[Crossref]

Maillotte, H.

Marazzi, L.

Martelli, P.

Martinelli, M.

Menyuk, C. R.

B. Stiller, P. Morin, D. M. Nguyen, J. Fatome, S. Pitois, E. Lantz, H. Maillotte, C. R. Menyuk, and T. Sylvestre, “Demonstration of polarization pulling using a fiber-optic parametric amplifier,” Opt. Express 20(24), 27248–27253 (2012).
[Crossref] [PubMed]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
[Crossref]

Millot, G.

Morin, P.

Muga, N. J.

Nguyen, D. M.

Nuño, J.

Palmieri, L.

F. Chiarello, L. Palmieri, M. Santagiustina, R. Gamatham, and A. Galtarossa, “Experimental characterization of the counter-propagating Raman polarization attraction,” Opt. Express 20(23), 26050–26055 (2012).
[Crossref] [PubMed]

F. Chiarello, L. Ursini, L. Palmieri, and M. Santagiustina, “Polarization attraction in counter propagating fiber Raman amplifiers,” IEEE Photonics Technol. Lett. 23(20), 1457–1459 (2011).
[Crossref]

Pinto, A. N.

Pitois, S.

Primerov, N.

Redyuk, A.

Reeves-Hall, P. C.

Santagiustina, M.

F. Chiarello, L. Palmieri, M. Santagiustina, R. Gamatham, and A. Galtarossa, “Experimental characterization of the counter-propagating Raman polarization attraction,” Opt. Express 20(23), 26050–26055 (2012).
[Crossref] [PubMed]

F. Chiarello, L. Ursini, L. Palmieri, and M. Santagiustina, “Polarization attraction in counter propagating fiber Raman amplifiers,” IEEE Photonics Technol. Lett. 23(20), 1457–1459 (2011).
[Crossref]

M. Santagiustina and L. Schenato, “Single-pump parametric amplification in randomly birefringent fibers,” IEEE Photonics Technol. Lett. 22(2), 73–75 (2010).
[Crossref]

Sauter, A.

Schenato, L.

M. Santagiustina and L. Schenato, “Single-pump parametric amplification in randomly birefringent fibers,” IEEE Photonics Technol. Lett. 22(2), 73–75 (2010).
[Crossref]

Shmilovitch, Z.

Shu, C.

X. Guo and C. Shu, “Cross-gain modulation suppression in a Raman-assisted fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 26(13), 1360–1363 (2014).
[Crossref]

Silva, N. A.

Stephens, M. F. C.

Stiller, B.

Sylvestre, T.

Tam, H. Y.

Taylor, J. R.

Thevenaz, L.

Tur, M.

Ursini, L.

F. Chiarello, L. Ursini, L. Palmieri, and M. Santagiustina, “Polarization attraction in counter propagating fiber Raman amplifiers,” IEEE Photonics Technol. Lett. 23(20), 1457–1459 (2011).
[Crossref]

Wabnitz, S.

Wai, P. K. A.

Wang, S. H.

Xu, L.

Xu, X.

Zadok, A.

IEEE Photonics Technol. Lett. (4)

M. Santagiustina and L. Schenato, “Single-pump parametric amplification in randomly birefringent fibers,” IEEE Photonics Technol. Lett. 22(2), 73–75 (2010).
[Crossref]

F. Chiarello, L. Ursini, L. Palmieri, and M. Santagiustina, “Polarization attraction in counter propagating fiber Raman amplifiers,” IEEE Photonics Technol. Lett. 23(20), 1457–1459 (2011).
[Crossref]

V. V. Kozlov and S. Wabnitz, “Suppression of relative intensity noise in fiber-optic Raman polarizers,” IEEE Photonics Technol. Lett. 23(15), 1088–1090 (2011).
[Crossref]

X. Guo and C. Shu, “Cross-gain modulation suppression in a Raman-assisted fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 26(13), 1360–1363 (2014).
[Crossref]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. B (6)

Opt. Commun. (1)

J. F. L. Freitas, M. B. Costa e Silva, S. R. Lüthi, and A. S. L. Gomes, “Raman enhanced parametric amplifier based S-C band wavelength converter: Experiment and simulations,” Opt. Commun. 255(4-6), 314–318 (2005).
[Crossref]

Opt. Express (7)

F. Chiarello, L. Palmieri, M. Santagiustina, R. Gamatham, and A. Galtarossa, “Experimental characterization of the counter-propagating Raman polarization attraction,” Opt. Express 20(23), 26050–26055 (2012).
[Crossref] [PubMed]

V. V. Kozlov, J. Nuño, J. D. Ania-Castañón, and S. Wabnitz, “Analytic theory of fiber-optic Raman polarizers,” Opt. Express 20(24), 27242–27247 (2012).
[Crossref] [PubMed]

B. Stiller, P. Morin, D. M. Nguyen, J. Fatome, S. Pitois, E. Lantz, H. Maillotte, C. R. Menyuk, and T. Sylvestre, “Demonstration of polarization pulling using a fiber-optic parametric amplifier,” Opt. Express 20(24), 27248–27253 (2012).
[Crossref] [PubMed]

M. Martinelli, M. Cirigliano, M. Ferrario, L. Marazzi, and P. Martelli, “Evidence of Raman-induced polarization pulling,” Opt. Express 17(2), 947–955 (2009).
[Crossref] [PubMed]

A. Redyuk, M. F. C. Stephens, and N. J. Doran, “Suppression of WDM four-wave mixing crosstalk in fibre optic parametric amplifier using Raman-assisted pumping,” Opt. Express 23(21), 27240–27249 (2015).
[Crossref] [PubMed]

S. H. Wang, X. Xu, and P. K. A. Wai, “Polarized fiber optical parametric amplification in randomly birefringent fibers,” Opt. Express 23(25), 32747–32758 (2015).
[Crossref] [PubMed]

Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19(27), 25873–25880 (2011).
[Crossref] [PubMed]

Opt. Lett. (4)

Other (3)

X. Guo, X. Fu, and C. Shu, “Control of saturation characteristics in a fiber optical parametric amplifier by Raman amplification,” in Conference on Lasers and Electro-Optics, 2014 OSA Technical Digest Series (Optical Society of America, 2014), paper JTu4A.64.
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

V. V. Kozlov, J. Nuño, J. D. Ania-Castañón, and S. Wabnitz, Trapping Polarization of Light in Nonlinear Optical Fibers: An Ideal Raman Polarizer (Springer Berlin Heidelberg, 2012).

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Figures (9)

Fig. 1
Fig. 1

The maximum gains with different DPMD versus the signal detuning for the RA-FOPAs using (a) HNLF1 with the Raman pump at 1.17 W and parametric pump at 128 mW, and (b) HNLF2 with the Raman pump 1.15 W and the parametric pump at 148 mW. The corresponding experimental data (solid circles) of [23] and [24] are also shown for comparison.

Fig. 2
Fig. 2

Comparison of the (a) global maximum gains and (b) mean gains as a function of the signal detuning and (c) the relationship between the mean gain and output DOPs of RA-FOPAs using pumps with different initial SOPs conditions. The parameters are the same as that used in Fig. 1(b) for DPMD = 0.04 ps/km1/2.

Fig. 3
Fig. 3

The (a) average gains, (b) average conversion efficiencies, (c) mean signal output DOPG, and (d) mean idler output DOPCE of the RA-FOPAs using HNLF2 with DPMD = 0.02 (triangles), 0.04 (circles), and 0.06 ps/km1/2 (squares) versus signal detuning. The corresponding standard deviations of the (e) average gains, (f) mean signal output DOPG, (g) average conversion efficiencies, and (h) mean idler output DOPCE are also shown, respectively.

Fig. 4
Fig. 4

The mean DOPG as a function of the mean gain over the gain band of the RA-FOPAs using HNLF1 when the Raman pump powers are (a) 1.17, (b) 0.8, and (c) 0.6 W, respectively. The symbols represent the simulation results when parametric pump powers vary from 2 to 200 mW. Here, the PMD coefficient DPMD equals to 0.02 ps/km1/2. The interpolation functions for co-propagating FOPAs (Γ = 6.2 [9]), counter-propagating FRAs (Γ = 10.2 [13]), and optimum bi-directionally pumped RA-FOPAs (Γ = 8.5) are also shown.

Fig. 5
Fig. 5

(a) The mean gains (open symbols), the global maximum gains (solid symbols), and the standard deviations of the gains (gray symbols) at the gain peak of the RA-FOPAs as a function of the input parametric pump power for the RA-FOPAs in Figs. 4(a)-(c) when the Raman pump powers are 1.17, 0.8, and 0.6 W, respectively. (b) The mean DOPs (gray symbols) and corresponding standard deviations of DOPs (open symbols) of Fig. 5(a).

Fig. 6
Fig. 6

(a) The mean output DOPP of the parametric pump with 100 different input SOPs (as mentioned in Step I, Sec. 3.1) over the 100 fiber realizations as a function of input parametric pump powers when the Raman pump powers are 1.17, 0.8, and 0.6 W, respectively. (b) The corresponding average output powers as a function of input parametric pump powers. (c) The corresponding mean output DOPP of the parametric pump as a function of average Raman gain to the parametric pumps.

Fig. 7
Fig. 7

(a) The relationships of the mean DOP and the mean gain at the gain peak of the RA-FOPAs when the Raman pump powers are 1.17 (squares), 0.8 (circles), and 0.6 W (triangles), respectively. (b) The four different operating states, FRAs, RA-FOPAs, deep saturation of the FRAs, and FOPAs of the RA-FOPAs when PR = 0.8 W. The numbers in the parentheses refer to different parametric pump powers as shown in the legend of Fig. 4. Selected data points with different pump combinations are also shown for Fig. 8.

Fig. 8
Fig. 8

Simulated output SOPs of the signal (top row) and the idler waves (bottom row) in the realizations with the global maximum gain for different pump combinations, (a) PR = 0.6 W, PP = 2 mW, (b) PR = 0.8 W, PP = 80 mW, (c) PR = 0.8 W, PP = 128 mW, (d) PR = 0.6 W, PP = 160 mW, as shown in Fig. 6(a). The SOPs are normalized by the maximum S0(L) and D0(L). Most of the data points thus are inside instead of on the surface of the Poincare sphere. The output SOPs of the parametric pump are also shown in black solid diamonds. The input SOP of the Raman pump is fixed at (1, 0, 0). The details of the corresponding results are shown in Table 2.

Figure 9
Figure 9

The output DOPG as a function of the mean gains of the RA-FOPAs using 100 different fiber realizations (open circles) for the four pump combinations shown in Table 2. The data points of the corresponding realizations shown in Figs. 8(a)-8(d) are also shown in solid diamonds.

Tables (2)

Tables Icon

Table 1 Parameters of the Fibers Used in the RA-FOPA Experiments [23,24]

Tables Icon

Table 2 Corresponding Simulation Results of Fig. 8

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

d R ¯ dz = α R R ¯ + g R Ω 2 ω R ω p [ P 0 R ¯ + R 0 P ¯ +μ( 3 P 0 R ¯ + R 0 P ¯ 2 R 0 P ¯ 3 ) ]( M ¯ ω R b ¯ + W ¯ R )× R ¯ ,
d P ¯ dz = α p P ¯ + g R Ω 2 [ R 0 P ¯ + P 0 P ¯ +μ( 3 R 0 P ¯ + P 0 R ¯ 2 P 0 R 3 ¯ ) ]+( ω p b ¯ + W p ¯ )× P ¯ + K ¯ ,
d S ¯ dz = α p S ¯ + g R ΩΛ 2 [ R 0 S ¯ + S 0 R ¯ +μ( 3 R 0 S ¯ + S 0 R ¯ 2 S 0 R ¯ 3 ) ]+( ω s b ¯ + W ¯ s )× S ¯ + M ¯ ,
d D ¯ dz = α p D ¯ + g R Ω+Λ 2 [ R 0 D ¯ + D 0 R ¯ +μ( 3 R 0 D ¯ + D 0 R ¯ 2 D 0 R ¯ 3 ) ]+( ω i b ¯ + W ¯ i )× D ¯ + N ¯ ,
dΘ dz =Δk+ b 2 4 ( 2 ω p P 2 I px ω s S 2 I sx ω i D 2 I ix )+Q+U+ C xxxx + C xxyy + C yyxx + C xyxy + C yxxy ,
Q= γ 3 [ 2( 2 P 0 S 0 D 0 )+(2 P 1 S 1 D 1 ) ( R 2 + P 2 + S 2 + D 2 )( 2 P 2 I px S 2 I sx D 2 I ix )+( P 2 2 I px S 2 2 2 I sx D 2 2 2 I ix ) ].
U= g R Ω 4 [ ( 1+μ ) R 2 ( S 3 I sx + D 3 I ix 2 P 3 I px )+(1μ) R 3 ( 2 P 2 I px S 2 I sx D 2 I ix ) ],
d P dz = α p P + g R Ω 2 [ R 0 P + P 0 R +μ( 3 R 0 P + P 0 R 2 P 0 R 3 ) ]+( ω p b + W p )× P .
DO P G =1exp[ G on-off ( dB ) /Γ ]

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