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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 9 — Apr. 28, 2008
  • pp: 6646–6651
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Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths

S. Pitois, J. Fatome, and G. Millot  »View Author Affiliations


Optics Express, Vol. 16, Issue 9, pp. 6646-6651 (2008)
http://dx.doi.org/10.1364/OE.16.006646


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Abstract

In this work, we report the experimental observation of a polarization attraction process which can occur in optical fibers at telecommunication wavelengths. More precisely, we have numerically and experimentally shown that a polarization attractor, based on the injection of two counter-propagating waves around 1.55µm into a 2-m long high nonlinear fiber, can transform any input polarization state into a unique well-defined output polarization state.

© 2008 Optical Society of America

1. Introduction

2. Experimental device

Fig. 1. Experimental set-up. HNLF : Highly Nonlinear Fiber, λ/4 : quaterwave-plate, Pol : Polarizer.

At one end of the fiber, we analyzed the polarization of the signal beam in the circular basis by means of a quarter-wave plate followed by a linear polarizer (Pol 2). Finally, the polarization controller PC1 was adjusted so that the polarization of the pump beam was as circular as possible whereas the signal was not fixed to a particular state and consequently possess an arbitrary polarization.

3. Theoretical evidences of the polarization attraction process

A system of two counter-propagating waves with arbitrary polarizations and propagating in an isotropic optical fiber can be described using the following nonlinear coupled equations:

ut+vguz=i23vgγ[(u2+2v2)u+(2u¯2+2v¯2)u+2u¯v¯*v]
vt+vgvz=i23vgγ[(v2+2u2)v+(2u¯2+2v¯2)v+2v¯u¯*u]
u¯tvgu¯z=i23vgγ[(u¯2+2v¯2)u¯+(2u2+2v2)u¯+2uv*v¯]
v¯tvgv¯z=i23vgγ[(v¯2+2u¯2)v¯+(2u2+2v2)v¯+2vu*u¯]
(1)

In these equations, u and ν are the amplitudes of the left and right circular components of the forward (pump) wave whereas and ν¯ represent the amplitudes of the left and right circular components of the backward wave (signal). γ is the usual nonlinear Kerr coefficient and vg is the group-velocity of light in the fiber. In the following, we will take γ=0.022 m-1W-1 which corresponds to the experimental value of our HNLF. The first four terms on the right-hand sides of Eqs. (1) describe nonlinear phase modulations whereas the last term describes a resonant four-wave interaction responsible for energy exchanges between the two circular components of each wave. We would like to point out that both the total energy of each wave and the total energy along each polarization are conserved during the nonlinear interaction. A detailed theoretical description of the attraction process that takes place in the optical system described by Eqs. (1) is given in Ref [12

12. S. Pitois, A. Picozzi, G. Millot, H.R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88–94 (2005). [CrossRef]

] and one of the main results is that the circular polarization pump acts as an attractor for the signal polarization. Let us emphasize that this irreversible attraction process occurs thanks to two essential physical ingredients: the backward configuration of the interaction and the existence of a stable eigenmode of the system. Indeed, the counter-propagating configuration allows the signal polarization fluctuations to be continuously washed out from the system thanks to the transfer of polarization entropy between pump and signal waves. On the contrary, in the usual co-propagating geometry, the four-wave interaction is characterized by periodic analytical solutions describing a reversible exchange of energy between the waves, so that the forward configuration cannot support the existence of an attraction process. The second essential physical ingredient is the existence of a stable eigenmode of the equations governing the wave interaction. In the case of an isotropic fiber, this stable eigenmode consists of a mutual arrangement in which the two waves have identical circular polarizations. Accordingly, when one of the waves is injected into the nonlinear medium along one component of this eigenmode, the counter-propagating wave is then inevitably attracted to the other component of this eigenmode, regardless of its initial polarization state.

In the following, we will focus our attention on some novel numerical and experimental evidences of this original effect. In order to simulate the attraction process, we have numerically integrated Eqs. (1) using a standard split-step Fourier method. Due to the specific nature of counter-propagating interactions, propagation was resolved in time, i.e. at each step; the propagation was carried out from t to t+dt. The initial condition was therefore given for any z at t=0. Finally, we have used super-Gaussian pulses close to the 10-ns experimental pulses, instead of continuous waves, to avoid any numerical problem at the window boundaries. Figure 2(a) represents a series of numerical results for a pump beam having an input circular polarization state and for input signals with different elliptical polarizations.

Fig. 2. Simulation results: (a) Evolution of the energy ratio contained in the right circular polarization (solid line) and in the left (dashed line) circular polarization as a function of the pump/signal power for different initial signal polarizations. (b) Evolution of the signal polarization state on the Poincaré sphere for four different input signal polarization states. The counter-propagating pump wave is injected with a right circular polarization (S2=1).

For each input signal polarization, we have plotted in Fig. 2(a) the evolution of the output polarization state of the signal as a function of the pump and signal powers injected into the fiber. In order to represent the signal polarization in the circular basis (|u|2, |v|2), we have calculated the ratio of signal energy contained in the right circular polarization state (solid line) and in the left circular state (dashed line), respectively. We can clearly see in Fig. 2(a) that, any input signal polarization is attracted towards the right circular polarization imposed by the input pump polarization state. Even for the worst configurations, especially when the signal polarization is close to the left circular state, we can notice that more than 80% of the energy is repolarized towards the pump polarization state. Figure 2(b) completes the illustration of this attraction phenomenon by showing on the Poincaré sphere the evolution of the signal polarization state during its propagation through the optical fiber for four different input states. Let us recall that the Stokes vectors (S1, S2, S3) used to represent any polarization state on the Poincaré sphere are defined by: S1=iu*v - iuv*, S2=|u|2-|v|2 and S3=u*v+uv*. In our simulations, the Stokes vectors have been normalized with respect to S0=|u|2+|v|2, so that the radius of the Poincaré sphere is equal to unity. In Fig. 2(b), we have represented the evolution of the polarization state of the central part of the 10-ns signal pulse when a counter-propagating circularly-polarized pump beam (S2=1) is injected into the fiber. Pump and signal input peak powers were fixed to 100 W. As can be seen, any input signal polarization converges asymptotically towards the right circular polarization state of the pump (S2=1). Consequently, if the output signals are projected along the right-circular polarization by means of a polarizer, the resulting signal has a constant intensity, independently of the input polarization. This important repolarization capability underlines the great potential of the polarization attraction for various telecommunication applications.

4. Experimental results and telecommunication applications

Experimental evidences of this polarization attraction effect are shown in Fig. 3. In a same way that in the numerical simulations represented in Fig. 2(a), we have experimentally measured the ratio of the signal energy contained in the right circular polarization component (solid line) and in the left circular component (dashed line) for different input polarization states (circles, triangles, squares and crosses) as a function of the input power and for a pump wave with a fixed right quasi-circular polarization (indeed, we have evaluated that the ratio of pump energy contained in the right circular polarization was 90%). These results are presented in Fig. 3(a). As can be seen, when power increases, all input signal polarizations asymptotically converge to the same output polarization corresponding to the pump state (not perfectly right circular), and this independently of their initial states. These experimental results are in good agreement with theoretical predictions of Fig. 2(a), thus proving the efficiency of the attraction process.

Fig. 3. (a). Experimental evolution of the energy ratio contained in the right (solid line) and in the left (dashed line) circular polarization as a function of the pump/signal power for four different initial signal polarization states. Output scrambled signal at P=1 W (b) and at P=45W (c).

Fig. 4. Output pump (a1) and signal (a2) for P=1 W after scrambling of the input signal polarization. Output pump (a3) and signal (a4) for P=45 W after scrambling of the input signal polarization. (b1), (b2), (b3) and (b4) are numerical simulations corresponding Figs. (a1), (a2), (a3) and (a4), respectively.

5. Conclusions

In this work, we have reported the experimental observation and numerical modelling of a polarization attraction process in the usual telecommunication band around 1.55 µm. This attraction phenomenon was observed between two counter-propagating 10-ns waves injected into a 2-m long standard HNLF. We have also pointed out an experimental evidence of a striking polarization fluctuations exchange process occurring between the pump and the signal waves. We strongly believe that this universal repolarizer which is lossless, instantaneous and which can be coupled with Raman amplification [11

11. S. Pitois, A. Sauter, and G. Millot, “Simultaneous achievement of polarization attraction and Raman amplification in isotropic optical fibers,” Opt. Lett. 29, 599–601 (2004). [CrossRef] [PubMed]

] could therefore constitute a powerful tool to combat detrimental polarization effects in telecommunication and signal processing systems, for example to combat the polarization sensitivity of certain devices like non linear optical loop mirror or coherent detection or to combat the impairments of PMD which strongly limits the transmission distance in optical fibers-based telecommunication lines at very high bit rates. Nethertheless, we would like to emphasize that a critical challenge in the present system here is that high powers are required so that cw waves can actually not be used. We believe that in the future, very-highly nonlinear fibers, such as chalcogenide or bismuth fibers could be used so that the required powers could be compatible with usual telecommunication parameters.

Acknowledgment

We would like to acknowledge financial support of the Agence National de la Recherche (FUTUR project), the GDR PhoNoMi2 and the Conseil Regional de Bourgogne.

References and links

1.

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, “2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror,” IEEE Photon. Technol. Lett. 19 (3), pp. 146–148 (2007). [CrossRef]

2.

Sonia Boscolo, Sergei K. Turitsyn, and Keith J. Blow, “Nonlinear loop mirror-based all-optical signal processing in fiber-optic communications,” Opt. Fiber Technol. Available online 17 March 2008.

3.

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16, 753–791 (2008). [CrossRef] [PubMed]

4.

E. Ciaramella, F. Curti, and S. Trillo, “All-optical signal reshaping by means of four-wave mixing in optical fibers,” IEEE Photon. Technol. Lett. 13, 142–144 (2001). [CrossRef]

5.

P. Honzatko, A. Kumpera, and P. Skoda, “Effects of polarization dependent gain and dynamic birefringence of the SOA on the performance of the ultrafast nonlinear interferometer gate,” Opt. Express 15, 2541–2547 (2007). [CrossRef] [PubMed]

6.

Y. Takahashi, A. Neogi, and H. Kawaguchi, “Polarization dependent nonlinear gain in semiconductor optical amplifiers,” J. Quantum Electron. 34, 1660–1672, (1998). [CrossRef]

7.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers”, PNAS 97, 4541–4550 (2000). [CrossRef] [PubMed]

8.

J. Garnier, J. Fatome, and G. Le Meur, “Statistical analysis of pulse propagation driven by polarization-mode dispersion,” J. Opt. Soc. Am. B 19, 1968–1977 (2002). [CrossRef]

9.

E. Heebner, R. S. Bennink, R. W. Boyd, and R. A. Fisher, “Conversion of unpolarized light to polarized light with greater than 50% efficiency by photorefractive two-beam coupling,” Opt. Lett. 25, 257–259 (2000). [CrossRef]

10.

S. Pitois, G. Millot, and S. Wabnitz, “Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments,” J. Opt. Soc. Am. B 18, 432–443 (2001). [CrossRef]

11.

S. Pitois, A. Sauter, and G. Millot, “Simultaneous achievement of polarization attraction and Raman amplification in isotropic optical fibers,” Opt. Lett. 29, 599–601 (2004). [CrossRef] [PubMed]

12.

S. Pitois, A. Picozzi, G. Millot, H.R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88–94 (2005). [CrossRef]

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(230.4320) Optical devices : Nonlinear optical devices

ToC Category:
Nonlinear Optics

History
Original Manuscript: January 22, 2008
Revised Manuscript: March 27, 2008
Manuscript Accepted: March 28, 2008
Published: April 25, 2008

Citation
S. Pitois, J. Fatome, and G. Millot, "Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths," Opt. Express 16, 6646-6651 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6646


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References

  1. K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007). [CrossRef]
  2. S. Boscolo, S. K. Turitsyn, and K. J. Blow, "Nonlinear loop mirror-based all-optical signal processing in fiber-optic communications," Opt. Fiber Technol. Available online 17 March 2008.
  3. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in optical fiber systems, " Opt. Express 16, 753-791 (2008). [CrossRef] [PubMed]
  4. E. Ciaramella, F. Curti, and S. Trillo, "All-optical signal reshaping by means of four-wave mixing in optical fibers," IEEE Photon. Technol. Lett. 13, 142-144 (2001). [CrossRef]
  5. P. Honzatko, A. Kumpera, and P. Skoda, "Effects of polarization dependent gain and dynamic birefringence of the SOA on the performance of the ultrafast nonlinear interferometer gate, " Opt. Express 15, 2541-2547 (2007). [CrossRef] [PubMed]
  6. Y. Takahashi, A. Neogi, and H. Kawaguchi, "Polarization dependent nonlinear gain in semiconductor optical amplifiers," J. Quantum Electron. 34, 1660-1672 (1998). [CrossRef]
  7. J. P. Gordon and H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," PNAS 97, 4541-4550 (2000). [CrossRef] [PubMed]
  8. J. Garnier, J. Fatome, and G. Le Meur, "Statistical analysis of pulse propagation driven by polarization-mode dispersion," J. Opt. Soc. Am. B 19, 1968-1977 (2002). [CrossRef]
  9. E. Heebner, R. S. Bennink, R. W. Boyd, and R. A. Fisher, "Conversion of unpolarized light to polarized light with greater than 50% efficiency by photorefractive two-beam coupling," Opt. Lett. 25, 257-259 (2000). [CrossRef]
  10. S. Pitois, G. Millot, and S. Wabnitz, "Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments, " J. Opt. Soc. Am. B 18, 432-443 (2001). [CrossRef]
  11. S. Pitois, A. Sauter, and G. Millot, "Simultaneous achievement of polarization attraction and Raman amplification in isotropic optical fibers," Opt. Lett. 29, 599-601 (2004). [CrossRef] [PubMed]
  12. S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, "Polarization and modal attractors in conservative counterpropagating four-wave interaction," Europhys. Lett. 70, 88-94 (2005). [CrossRef]

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