Abstract

A comprehensive theoretical model to investigate phase matching in degenerate polarized fiber optical parametric amplifiers (FOPAs) in randomly birefringent fibers is developed. We show that in the small signal region, simulation results from the proposed model agree well with the experimental results. It was also shown that four waves mixing (FWM) effect could compensate polarization mode dispersion (PMD) induced phase mismatch. Similar to counter-propagating fiber Raman amplifiers (FRAs), the degree of polarization of FOPAs approaches unity exponentially with the gain but at a larger rate 1/Γ. Thus larger polarization-pulling can be achieved in FOPAs than the counter-propagating FRAs for the same gain.

© 2015 Optical Society of America

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Corrections

Shao Hao Wang and P. K. A. Wai, "Polarized fiber optical parametric amplification in randomly birefringent fibers: erratum," Opt. Express 25, 21265-21266 (2017)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-25-18-21265

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References

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  2. T. Torounidis, P. A. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70-db gain,” IEEE Photonics Technol. Lett. 18(10), 1194–1196 (2006).
    [Crossref]
  3. K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 14(7), 911–913 (2002).
    [Crossref]
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    [Crossref]
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    [Crossref]
  10. M. Guasoni, V. V. Kozlov, and S. Wabnitz, “Theory of polarization attraction in parametric amplifiers based on telecommunication fibers,” J. Opt. Soc. Am. B 39(10), 2710–2720 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  19. 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]
  20. 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]
  21. C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22(19), 1029–1030 (1986).
    [Crossref]
  22. G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Lightwave Technol. 8(4), 824–838 (1991).
  23. P. K. A. Wai and C. R. Menyak, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14(2), 148–157 (1996).
    [Crossref]

2014 (1)

2012 (5)

2011 (4)

2010 (1)

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

2009 (2)

2006 (1)

T. Torounidis, P. A. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70-db gain,” IEEE Photonics Technol. Lett. 18(10), 1194–1196 (2006).
[Crossref]

2004 (3)

2002 (1)

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 14(7), 911–913 (2002).
[Crossref]

1996 (1)

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

1991 (1)

G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Lightwave Technol. 8(4), 824–838 (1991).

1986 (1)

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22(19), 1029–1030 (1986).
[Crossref]

Agrawal, G. P.

Andrekson, P. A.

T. Torounidis, P. A. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70-db gain,” IEEE Photonics Technol. Lett. 18(10), 1194–1196 (2006).
[Crossref]

Ania-Castañón, J. D.

Cappellini, G.

G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Lightwave Technol. 8(4), 824–838 (1991).

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.

Eyal, A.

Fatome, J.

Ferrario, M.

Galtarossa, A.

Gamatham, R.

Guasoni, M.

M. Guasoni, V. V. Kozlov, and S. Wabnitz, “Theory of polarization attraction in parametric amplifiers based on telecommunication fibers,” J. Opt. Soc. Am. B 39(10), 2710–2720 (2012).
[Crossref]

M. Guasoni and S. Wabnitz, “Nonlinear polarizers based on four-wave mixing in high-birefringence optical fibers,” J. Opt. Soc. Am. B 29(6), 1511–1520 (2012).
[Crossref]

Jopson, R.

Kanaev, A.

Kazovsky, L. G.

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 14(7), 911–913 (2002).
[Crossref]

Kogelnik, H.

Kozlov, V. V.

Lantz, E.

Lin, Q.

Maillotte, H.

Marazzi, L.

Marhic, M. E.

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 14(7), 911–913 (2002).
[Crossref]

Martelli, P.

Martinelli, M.

McKinstrie, C.

Menyak, C. R.

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

Menyuk, C. R.

Millot, G.

Morin, P.

Muga, N. J.

Nguyen, D. M.

Nuño, J.

Olsson, B.-E.

T. Torounidis, P. A. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70-db gain,” IEEE Photonics Technol. Lett. 18(10), 1194–1196 (2006).
[Crossref]

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.

Poole, C. D.

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22(19), 1029–1030 (1986).
[Crossref]

Primerov, N.

Radic, S.

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]

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.

Silva, N. A.

Stiller, B.

Sylvestre, T.

Tam, H. Y.

Thevenaz, L.

Torounidis, T.

T. Torounidis, P. A. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70-db gain,” IEEE Photonics Technol. Lett. 18(10), 1194–1196 (2006).
[Crossref]

Trillo, S.

G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Lightwave Technol. 8(4), 824–838 (1991).

Tur, M.

Uesaka, K.

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 14(7), 911–913 (2002).
[Crossref]

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.

Wagner, R. E.

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22(19), 1029–1030 (1986).
[Crossref]

Wai, P. K. A.

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]

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

Wang, S. H.

Wong, K. K. Y.

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 14(7), 911–913 (2002).
[Crossref]

Xu, L.

Zadok, A.

Electron. Lett. (1)

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22(19), 1029–1030 (1986).
[Crossref]

IEEE Photonics Technol. Lett. (4)

T. Torounidis, P. A. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70-db gain,” IEEE Photonics Technol. Lett. 18(10), 1194–1196 (2006).
[Crossref]

K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent two-pump fiber optical parametric amplifier,” IEEE Photonics Technol. Lett. 14(7), 911–913 (2002).
[Crossref]

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]

J. Lightwave Technol. (4)

N. A. Silva, N. J. Muga, and A. N. Pinto, “Influence of the stimulated Raman scattering on the four-wave mixing process in birefringent fibers,” J. Lightwave Technol. 27(22), 4979–4988 (2009).
[Crossref]

G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Lightwave Technol. 8(4), 824–838 (1991).

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

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]

J. Opt. Soc. Am. B (5)

Opt. Express (6)

Opt. Lett. (1)

Other (2)

M. E. Marhic, Fiber optical parametric amplifiers, oscillators and related devices, (Cambridge University, 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 (7)

Fig. 1
Fig. 1 DOPs as a function of the maximum gain of the signal in HNLF1 in the fiber realization with maximum gain. Experimental results (solid diamonds) in [4] are also shown for comparison. The simulated data (open symbols) are obtained when input pump powers equal to 27.3 (triangles), 28.4 (circles), and 29.7 dBm (squares), respectively.
Fig. 2
Fig. 2 (a) Maximum gains of the FOPAs using fibers with different DPMD versus the signal detuning. The experimental data (solid circles) of [20] are also shown for comparison. (b) The maximum gains and mean DOPs as a function of DPMD when Δυ = 0.7 THz. In both figures, the parameters are the same as HNLF2 except for DPMD.
Fig. 3
Fig. 3 (a) Average gains, (b) mean signal output DOPG, (c) average conversion efficiencies, and (d) mean idler output DOPCE of the FOPAs using HNLF2 with different DPMD versus signal detuning.
Fig. 4
Fig. 4 Corresponding standard deviations of (a) average gains, (b) mean signal output DOPG, (c) average conversion efficiencies, and (d) mean idler output DOPCE of Fig. 3.
Fig. 5
Fig. 5 Corresponding average gains, average conversion efficiencies, mean DOPG, and mean DOPCE of Fig. 3(a)-(d) as functions of DPMD when the detuning Δυ equals to 0.7 THz.
Fig. 6
Fig. 6 Evolutions of the mean Θ(z) and standard deviations std(Θ(z)) of the phase combination Θ along the HNLF1 at the frequencies of the parametric gain peak.
Fig. 7
Fig. 7 Mean DOP as a function of the average gain over the gain band of FOPAs using HNLF1 and HNLF2. The interpolation functions for FOPAs and counter-propagating FRAs are also shown.

Tables (2)

Tables Icon

Table 1 The Parameters of the Fibers Used in the Experiments [4, 20]

Tables Icon

Table 2 Measured and simulated results of GMAX, DOPG, and DOPCE.

Equations (10)

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d P ¯ dz =α P ¯ +( ω p b ¯ + W ¯ p )× P ¯ + K ¯ ,
d S ¯ dz =α S ¯ +( ω s b ¯ + W ¯ s )× S ¯ + M ¯ ,
d D ¯ dz =α D ¯ +( 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+ C xxxx + C xxyy + C yyxx + C xyxy + C yxxy ,
K ¯ =( K 1 K 2 K 3 )= 4γ 3 ( 3 V xxxx V yyxx + V xxyy +3 V yyyy V yxxx V xyxx V yxyy V xyyy 4 V xxxy 4 V yyxy U yxxx + U xyxx U yxyy U xyyy 2 U xxxy +2 U yyxy ),
M ¯ =( M 1 M 2 M 3 )= 2γ 3 ( 3 V xxxx V yyxx + V xxyy 3 V yyyy +2 V xyxy 2 V yxxy 3 V yxxx + V xyxx + V yxyy +3 V xyyy +2 V xxxy +2 V yyxy 3 U yxxx + U xyxx U yxyy +3 U xyyy +2 U xxxy 2 U yyxy ),
N ¯ =( N 1 N 2 N 3 )= 2γ 3 ( 3 V xxxx V yyxx + V xxyy 3 V yyyy 2 V xyxy +2 V yxxy V yxxx +3 V xyxx +3 V yxyy + V xyyy +2 V xxxy +2 V yyxy U yxxx 3 U xyxx +3 U yxyy U xyyy +2 U xxxy 2 U yyxy ),
Q= γ 3 [ 2( 2 P 0 S 0 D 0 )+(2 P 1 S 1 D 1 )( 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 ) ].
d P ¯ dz =α P ¯ +( ω p b ¯ + W ¯ p )× P ¯ .
DOP=1exp[ G on-off ( dB ) /Γ ].

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