## Demonstration of polarization pulling using a fiber-optic parametric amplifier |

Optics Express, Vol. 20, Issue 24, pp. 27248-27253 (2012)

http://dx.doi.org/10.1364/OE.20.027248

Acrobat PDF (2321 KB)

### Abstract

We report the observation of all-optical polarization pulling of an initially polarization-scrambled signal using parametric amplification in a highly nonlinear optical fiber. Broadband polarization pulling has been achieved both for the signal and idler waves with up to 25 dB gain using the strong polarization sensitivity of parametric amplifiers. We further derive the probability distribution function for the final polarization state, assuming a randomly polarized initial state, and we show that it agrees well with the experiments.

© 2012 OSA

## 1. Introduction

7. M. E. Marhic, *Fiber Optical Parametric Amplifiers, Oscillators and Related Devices* (Cambridge University Press, Cambridge2007). [CrossRef]

10. Q. Lin and G. P. Agrawal, “Vector theory of four-wave mixing: polarization effects in fiber-optic parameteric amplifiers,” J. Opt. Soc. Am. B **21**, 1216–1224 (2004). [CrossRef]

8. J. F. L. Freitas, C. J. S. de Matos, M. B. Costa e Silva, and A. S. L. Gomes, “Impact of phase modulation and parametric gain on signal polarization in an anomalously dispersive optical fiber,” J. Opt. Soc. Am. B **24**(7), 1469–1474 (2007). [CrossRef]

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

7. M. E. Marhic, *Fiber Optical Parametric Amplifiers, Oscillators and Related Devices* (Cambridge University Press, Cambridge2007). [CrossRef]

7. M. E. Marhic, *Fiber Optical Parametric Amplifiers, Oscillators and Related Devices* (Cambridge University Press, Cambridge2007). [CrossRef]

*Fiber Optical Parametric Amplifiers, Oscillators and Related Devices* (Cambridge University Press, Cambridge2007). [CrossRef]

## 2. Experimental setup

_{3}-based phase modulator driven by a 2

^{23}–1 pseudorandom bit sequence at a fundamental frequency of 3 GHz in order to suppress stimulated Brillouin scattering while keeping a constant CW power. Using a high-resolution optical spectrum analyzer, we measured the broadened pump linewidth to be

*Δν*≈ 3 GHz. The output was launched into a high-power erbium-doped fiber amplifier (33 dBm). A 1 nm-band-pass filter then followed to reduce the amplified spontaneous emission and to keep the pump optical signal-to-noise ratio (OSNR) as high as possible [11

_{p}11. A. Durécu-Legrand, C. Simmoneau, D. Bayart, A. Mussot, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump OSNR on noise figure for fiber-optical parametric amplifiers,” IEEE Photon. Technol. Lett. **17**(6), 1178–1180 (2005). [CrossRef]

*G*between the maximum and minimum gains for a signal SOP parallel and orthogonal to the pump. These measurements will serve in the following for our theoretical modeling of polarization pulling.

## 3. Experimental results

2. J. Fatome, P. Morin, S. Pitois, and G. Millot, “Light-by-Light Polarization Control of 10-Gb/s RZ and NRZ Telecommunication Signals,” IEEE J. Sel. Top. Quant. Electron. **18**(2), 621–628 (2012). [CrossRef]

*S*are the normalized Stokes parameters on the Poincaré sphere, transformed linearly so that the SOP of the pump wave is aligned with the

_{i}*S*

_{3}axis. The gain spectra are also plotted in Fig. 2(c) with the parametric gain, the differential gain

*G*and the signal OSNR in insets.

4. 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]

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

*S*

_{3}-axis corresponds to the barycenter of the signal SOP measurements. The largest signal DOP is reached for the maximum parametric gain of 25 dB and a PDG of 19 dB in the undepleted pump regime while the OSNR is 22 dB. Figure 2(b) also shows that the idler SOP is pulled towards the pump with a better efficiency than the signal. This effect occurs because the idler wave is generated with a SOP that matches with the pump only due to the strict scalar phase-matching conditions [12

12. 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]

11. A. Durécu-Legrand, C. Simmoneau, D. Bayart, A. Mussot, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump OSNR on noise figure for fiber-optical parametric amplifiers,” IEEE Photon. Technol. Lett. **17**(6), 1178–1180 (2005). [CrossRef]

13. A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express **16**(26), 21692–21707 (2008). [CrossRef] [PubMed]

## 4. Theoretical model

**u**

_{in}=

*c*

_{+}

**u**

_{+}+

*c*

_{−}

**u**

_{−}, where

**u**

_{+}and

**u**

_{−}are unit Jones vectors that are aligned with the directions of maximum and minimum gain and are orthogonal [14

14. C. R. Menyuk, D. Wang, and A. N. Pilipetskii, “Repolarization of polarization-scrambled optical signals due to polarization dependent loss,” IEEE Photon. Technol. Lett. **9**(9), 1247–1249 (1997). [CrossRef]

*S*

_{3}-axis is aligned with the direction of maximum gain. We may usefully write

*c*

_{+}=

*A*cos(

*θ*/2)exp(

*iϕ*/2) and

*c*

_{−}=

*A*sin(

*θ*/2)exp(−

*iϕ*/2), where

*A*is the complex amplitude of the signal, while

*θ*and

*ϕ*are the angles of the Poincaré sphere polar coordinates. We may write

*θ*is the azimuthal angle for the Stokes vector of the input signal with respect to the direction of maximum gain. It will be useful to define

*μ*= cos

*θ*, so that a change in the spherical angle is given by

*d*Ω = sin

*θdθdϕ*=

*dμdϕ*. It then follows that

*c*

_{+}=

*A*[(1 +

*μ*)/2])

^{1/2}exp(

*iϕ*/2) and

*c*

_{−}=

*A*[(1 −

*μ*)/2])

^{1/2}exp(−

*iϕ*/2). We note that if the original signal is distributed uniformly over the Poincaré sphere, then the values of

*μ*will be uniformly distributed between −1 and 1.

*g*

_{+}and

*g*

_{−}are the maximum (parallel) and minimum (perpendicular) gains, respectively. The output value for

*μ*is given by where

*G*= exp[2(

*g*

_{+}−

*g*

_{−})

*L*] is the differential gain of the PDG. We note that when

*G*→ ∞, we find that

*μ*

_{out}→ 1, regardless of the value of

*μ*, so that the Stokes vector is pulled to the positive

*S*

_{3}-axis, as we would expect.

*μ*

_{out}. To do that, we first invert Eq. (3) to obtain The quantity

*μ*is uniformly distributed between −1 and 1, and we must have

*p*(

*μ*

_{out})

*dμ*

_{out}=

*p*(

*μ*)

*dμ*= (1/2)

*dμ*. We find the PDF as The corresponding cumulative distribution function is given by As expected, we find that

*μ*

_{out}= 1 when

*G*becomes large.

*S*

_{3}-component of the experimental data. We divide the interval from −1 to 1 into 21 bins with variable interval length Δ

*μ*=

_{i}*μ*

_{i}_{+1}−

*μ*,

_{i}*i*= 1, 21. The lengths of interval are chosen so that

*n*= 12 = 252/21 samples lie in each interval. In Fig. 3(a), we compare the predicted PDF from Eq. (5) to the histogram height

*n*/(

*N*Δ

*μ*), where

_{i}*N*= 252 is the total number of samples, which we plot at the mid-point of each interval,

*μ*= (

*μ*+

_{i}*μ*

_{i}_{+1})/2. In order to estimate the value of

*G*, we use MATLAB’s

`NLINFIT`function to carry out a nonlinear regression analysis, based on our estimate of the cumulative distribution function

*F*(

*μ*,

_{i}*G*) =

*N*/

_{i}*N*, where

*N*=

_{i}*ni*is the sum of the samples in all the histogram bins up to

*μ*=

*μ*. The expected error (standard deviation) ranges from 0.26 dB to 0.44 dB. We note that when no parametric gain is present, we observe a negative value of

_{i}*G*, indicating the presence of residual PDL that we attribute to the fiber couplers. As expected, an increase in the gain leads to a sharply peaked PDF in the neighborhood of

*μ*

_{out}= 1 in agreement with the experiments. The agreement between the fitted values of Fig. 3(a) and the experimental maximal gain is very good, but less in comparison to the PDG. A possible reason is that the value for the PDG is biased and actually higher, since the measurement requires an accurate alignment of the polarization and the spectra were not sufficiently stable to accurately measure the PDG. In order to confirm this assumption we plotted in Fig. 3(b) the signal SOP on the Poincaré sphere for the same values of

*G*as the maximal gain in Fig. 2 using Eq. (3) for

*S*

_{3}and the corresponding ones for

*S*

_{1}and

*S*

_{2}. As can be seen, the signal polarization is pulled towards the

*S*

_{3}-axis with increasing

*G*. The theoretical results agree well with the experimental results in Fig. 2. However, this also confirms that the PDG in our experiment is actually higher and close to the maximal gain since the orthogonal parametric gain should be theoretically zero.

## 5. Conclusion

## Acknowledgments

## References and links

1. | S. Pitois, J. Fatome, and G. Millot, “Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths,” Opt. Express |

2. | J. Fatome, P. Morin, S. Pitois, and G. Millot, “Light-by-Light Polarization Control of 10-Gb/s RZ and NRZ Telecommunication Signals,” IEEE J. Sel. Top. Quant. Electron. |

3. | V. V. Kozlov, J. Nuno, and S. Wabnitz, “Theory of lossless polarization attraction in telecommunication fibers,” J. Opt. Soc. Am. B |

4. | M. Martinelli, M. Cirigliano, M. Ferrario, L. Marazzi, and P. Martelli, “Evidence of Raman-induced polarization pulling,” Opt. Express |

5. | L. Ursini, M. Santagiustina, and L. Palmieri, “Raman Nonlinear Polarization Pulling in the Pump Depleted Regime in Randomly Birefringent Fibers,” IEEE Photon. Technol. Lett. |

6. | Z. Shmilovitch, N. Primerov, A. Zadok, A. Sanghoon Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express |

7. | M. E. Marhic, |

8. | J. F. L. Freitas, C. J. S. de Matos, M. B. Costa e Silva, and A. S. L. Gomes, “Impact of phase modulation and parametric gain on signal polarization in an anomalously dispersive optical fiber,” J. Opt. Soc. Am. B |

9. | M. Guasoni and S. Wabnitz, “Nonlinear polarizers based on four-wave mixing in high-birefringence optical fibers,” J. Opt. Soc. Am. B |

10. | Q. Lin and G. P. Agrawal, “Vector theory of four-wave mixing: polarization effects in fiber-optic parameteric amplifiers,” J. Opt. Soc. Am. B |

11. | A. Durécu-Legrand, C. Simmoneau, D. Bayart, A. Mussot, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump OSNR on noise figure for fiber-optical parametric amplifiers,” IEEE Photon. Technol. Lett. |

12. | 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. |

13. | A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express |

14. | C. R. Menyuk, D. Wang, and A. N. Pilipetskii, “Repolarization of polarization-scrambled optical signals due to polarization dependent loss,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

(230.5440) Optical devices : Polarization-selective devices

**ToC Category:**

Polarization Control and Vector Solitons

**History**

Original Manuscript: June 22, 2012

Revised Manuscript: August 13, 2012

Manuscript Accepted: August 14, 2012

Published: November 19, 2012

**Virtual Issues**

Nonlinear Photonics (2012) *Optics Express*

**Citation**

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**, 27248-27253 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-27248

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### References

- S. Pitois, J. Fatome, and G. Millot, “Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths,” Opt. Express16(9), 6646–6651 (2008). [CrossRef] [PubMed]
- J. Fatome, P. Morin, S. Pitois, and G. Millot, “Light-by-Light Polarization Control of 10-Gb/s RZ and NRZ Telecommunication Signals,” IEEE J. Sel. Top. Quant. Electron.18(2), 621–628 (2012). [CrossRef]
- V. V. Kozlov, J. Nuno, and S. Wabnitz, “Theory of lossless polarization attraction in telecommunication fibers,” J. Opt. Soc. Am. B28(1), 100–108 (2011). [CrossRef]
- M. Martinelli, M. Cirigliano, M. Ferrario, L. Marazzi, and P. Martelli, “Evidence of Raman-induced polarization pulling,” Opt. Express17(2), 947–955 (2009). [CrossRef] [PubMed]
- L. Ursini, M. Santagiustina, and L. Palmieri, “Raman Nonlinear Polarization Pulling in the Pump Depleted Regime in Randomly Birefringent Fibers,” IEEE Photon. Technol. Lett.23(4), 1041–1135 (2011). [CrossRef]
- Z. Shmilovitch, N. Primerov, A. Zadok, A. Sanghoon Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express19, 25873–25880 (2011). [CrossRef]
- M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge University Press, Cambridge2007). [CrossRef]
- J. F. L. Freitas, C. J. S. de Matos, M. B. Costa e Silva, and A. S. L. Gomes, “Impact of phase modulation and parametric gain on signal polarization in an anomalously dispersive optical fiber,” J. Opt. Soc. Am. B24(7), 1469–1474 (2007). [CrossRef]
- M. Guasoni and S. Wabnitz, “Nonlinear polarizers based on four-wave mixing in high-birefringence optical fibers,” J. Opt. Soc. Am. B29, 1511–1520 (2012). [CrossRef]
- Q. Lin and G. P. Agrawal, “Vector theory of four-wave mixing: polarization effects in fiber-optic parameteric amplifiers,” J. Opt. Soc. Am. B21, 1216–1224 (2004). [CrossRef]
- A. Durécu-Legrand, C. Simmoneau, D. Bayart, A. Mussot, T. Sylvestre, E. Lantz, and H. Maillotte, “Impact of pump OSNR on noise figure for fiber-optical parametric amplifiers,” IEEE Photon. Technol. Lett.17(6), 1178–1180 (2005). [CrossRef]
- 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]
- A. Zadok, E. Zilka, A. Eyal, L. Thevenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express16(26), 21692–21707 (2008). [CrossRef] [PubMed]
- C. R. Menyuk, D. Wang, and A. N. Pilipetskii, “Repolarization of polarization-scrambled optical signals due to polarization dependent loss,” IEEE Photon. Technol. Lett.9(9), 1247–1249 (1997). [CrossRef]

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