We implemented and demonstrated the concept of universal Omnipolarizer as shown in Fig. 3, see the Methods section for additional details. The efficiency of the device was first characterized when operating in the discrete PBS mode. In this case the setup only involves an output reflective element (i.e., the configuration depicted in Fig. 2a), such as a Fiber Bragg Grating (FBG, used here with 95% of reflection, 5% of transmission) or an optical circulator plus a fiber coupler, or end fiber coating. The corresponding experimental results are provided in Fig. 4. The SOP of an initial On/Off Keying (OOK) 40-Gbit/s signal centred around 1564 nm was scrambled so that it spreads over the entire Poincaré sphere. As a result, its eye-diagram signal was completely closed beyond a linear polarizer.

Figure 3 Experimental set-up of the Omnipolarizer. The polarization state of an input 40-Gbit/s Return-to-Zero transmitter (Tx) is first randomly distributed onto the Poincaré sphere by means of a polarization scrambler. Next the signal is amplified by means of an Erbium doped fiber amplifier (EDFA) up to 27 dBm before injection into a 6.2-km long standard silica Non-Zero Dispersion-Shifted Fiber (NZ-DSF). After propagation, the signal is back-reflected by either a Fiber Bragg Grating (FBG) or an amplified reflective loop consisting of a circulator, a fiber coupler to collect the output signal and a second EDFA, respectively. At the receiver, the efficiency of the self-repolarization effect is evaluated onto the Poincaré sphere. Moreover, time-domain monitoring of the output SOP is obtained by means of eye-diagrams and BER measurements of the signal passing through a conventional linear polarizer. (see Methods for additional experimental details.) Full size image

Figure 4 Experimental results obtained in the digital PBS operation mode, in configuration with a FBG, when the input power was set to 27 dBm. Two orthogonal universal points of attraction are observed depending on the input signal SOP ellipticity. All initial SOPs initially situated in the northern (southern) hemisphere emerge from the fiber in the right (left) circular polarization, as in a discrete circular PBS. Full size image

When the input average power was increased up to 27 dBm, we could observe that the output SOP self-stabilized in two orthogonal points on the Poincaré sphere: light self-organized its SOP. Indeed, for a positive (negative) ellipticity of the input signal SOP (i.e., the red (blue) points in Fig. 4), the output signal SOP remained confined around the north (south) pole of the sphere, that is to say close to the right (left)-handed circular polarization. In order to quantify the quality of the attraction process, the residual fluctuations in the output SOP can be contained in a maximum circle-cap characterized by a solid angle of 0.42 sr for the north pole (0.68 sr for the south), corresponding to a maximum fluctuation of the ellipticity angle of 0.37 rad (0.47 rad) peak-to-peak or a solid angle of 0.10 sr (0.12 sr) in rms corresponding to a variation of the ellipticity angle of 0.18 rad (0.20 rad), respectively. This residual distribution around a small area is attributed to the fact that the process of self-organization asymptotically converges to the poles in the limit case of very long fibers or high input powers. Consequently, nearly orthogonal input SOPs are difficult to attract into a single output point. Moreover, it is important to note that the two output SOPs are universal, in the sense that they do not depend on either the input signal, the telecom fiber sample, the laboratory reference frame or any environmental changes. Indeed, we checked that straining the fiber does not influence the position and width of the output SOP distributions. Moreover, by means of an air-free quarter-wave plate/polarizer setup, we measured the absolute (i.e., in the fixed laboratory frame) value of the SOP which always remains in a circular state. As a result, in the configuration leading to two universal output SOPs the Omnipolarizer behaves as a discrete PBS. Indeed, in spite of the initial polarization scrambling, no intensity fluctuations can be observed in the eye-diagrams of the 40-Gbit/s output intensity profiles. Depending on its initial ellipticity, all of the 40-Gbit/s signal energy is digitally routed to either the right or left-circular SOP without any pulse splitting.

Next we tested the second configuration shown in Fig. 2b and 3, which involves the reflective loop set-up and allows the Omnipolarizer to operate in (or switch among) the two different regimes – a polarizer or a PBS. Namely, one or two points of SOP stabilization can be observed, depending on the amount of energy that returns back into the fiber upon reflection. An associated short movie, which can be found in the Supplementary Movie, illustrates well the evolution of the output SOP as a function of the average power of the reflected signal for an input power of 27 dBm. The transition between the two regimes may be clearly observed.

The 40-Gbit/s experimental results obtained for the Omnipolarizer in polarizer mode are summarized in Fig. 5. When the back-reflected signal was amplified by means of the reflective loop configuration of Fig. 3 so that its power was just beyond the input power (i.e., when the power of the back-reflected signal was increased up to 28 dBm), a single point of stabilization survived: all of the output SOPs remained localized around a small area of the Poincaré sphere (see Fig. 5) contained in a circle-cap characterized by a solid angle of 0.28 sr, corresponding to a maximum fluctuation of the ellipticity angle of 0.30 rad peak-to-peak or a solid angle of 0.06 sr in rms corresponding to a variation of the ellipticity angle of 0.14 rad. As in the previous PBS case, we would like to notice that since all the input SOPs converge asymptotically to the pole of the sphere, a large number of nonlinear lengths would be theoretically required to reduce this small area to a single point, which is hardly possible in practice. Note that the finite size of the SOP spot can also be interpreted theoretically by the fact that the singularities lie on the boundary of the energy-momentum diagram (see Fig. 2 of the supplementary materials), so that convergence to the singularities cannot take place in an isotropic way, which limits the efficiency of the attraction process27. We remark that the polarization controller inserted into the reflective loop of Fig. 3 can be used to tune the point of attraction on the Poincaré sphere and thus to select a specific output SOP on demand. Consequently, whatever the initial SOP, the output polarization of the 40-Gbit/s signal remains trapped close to a single SOP and the output eye-diagram is completely open behind a polarizer. In other words, a negligible polarization-dependent loss is obtained from the Omnipolarizer, indicating that the self-polarization process operates in its full strength, free from RIN. More importantly, the corresponding bit-error-rate (BER) measurements (also presented in Fig. 5) show that, in spite of the initial polarization scrambling process, the Omnipolarizer enables clean error-free data recovery behind a polarization dependent component. This completes the demonstration of the powerful SOP stabilization which is achieved by the device.

Figure 5 Experimental results obtained in the polarizer mode when the back-reflected signal power is amplified (28 dBm) just beyond the input one (27 dBm), in a configuration with a reflective loop (Fig.2b). A unique point of stabilization was observed on the Poincaré sphere, i.e. the device operates as a polarizer. Fig. 5 illustrates the experimental eye-diagram of the 40-Gbit/s signal at the input and output of the device through a polarizer. The SOP of the signal is aligned with the polarizer in order to transfer all polarization fluctuations into the intensity domain. We also show BER measurements obtained at the input and output of the Omnipolarizer in the presence of polarization scrambling. Full size image

Theoretical analysis

From a theoretical point of view, the description of the previously discussed self-polarization phenomenon can be established on the analysis of the spatio-temporal evolution of counter-propagating beams (the propagating signal and its own reflective replica) in a standard randomly birefringent telecom fiber, whose dynamics can be modelled by a set of 2 coupled equations25:

where z is the spatial coordinate along the fiber, v is the group-velocity, is the nonlinear Kerr coefficient, × denotes the vector product and I is a diagonal matrix with coefficients (−1,−1,1)25. The SOPs of the forward and backward beams are described by the Stokes vectors and . In spite of its apparent simplicity, model (1) captures all of the essential properties of the Omnipolarizer: excellent quantitative agreement with the experimental results is obtained without using adjustable parameters (see the theoretical supplementary material). In particular, the simulations of Eq. (1) confirm the existence of either one or two points of self-organization for the SOP on the poles of the Poincaré sphere (see Figs. 6a–c). The self-organisation mechanism can be qualitatively understood as follows. Because of statistical averaging over its random linear birefringence distribution, the fiber does not favour any particular polarization direction. For instance, this argument indicates that the SOPs of the two beams cannot relax towards, e.g., a linear state, because such a relaxation would violate the symmetry properties of the fiber. In this respect, the left and right circular SOPs are the only ones which satisfy the requirements imposed by the characteristics of the optical fiber. In its passive configuration, the two circular SOPs are completely symmetric, hence the fiber exhibits two distinct points of attraction for the beam SOPs. The switching between the two modes of operation results from the symmetry-breaking induced by the boundary conditions inherent to the active configuration. More precisely, suppose that the energy of the transmitted signal remains larger than its backward replica (i.e., when a FBG only is used in the configuration of Fig. 2a). In this case the numerical simulations confirm well the experimental observation that, depending on the initial ellipticity of the input SOP, the output SOP self-stabilizes in either one or another of the two poles of the Poincaré sphere (see Fig. 6a). In this situation, the Omnipolarizer acts as a digital PBS, just as in the experimental observations of Fig. 4. On the other hand, whenever the energy of the back-reflected signal becomes equal or slightly larger than the transmitted signal energy, by means of an additional gain as in Fig. 2b, the solutions of Eqs. (1) confirm the experimental findings of Fig. 5 that the Omnipolarizer acts as lossless polarizer (see Fig. 6b). In this case, irrespective of the initial SOP at the input of the device, one obtains at the Omnipolarizer output a unique polarization state without any residual polarization depending loss. It can be shown that the selection of either the right or left circular SOP is determined by the angle of polarization rotation in the reflection process. Such angle is at the origin of the symmetry breaking between the two circular SOP and it can be adjusted experimentally thanks to the polarization controller. More precisely, if one only considers a polarization rotation around the vertical axis of the Poincaré sphere, then a positive (negative) rotation angle favors the left (right) circular SOP. This result can be interpreted intuitively, since a positive angle turns the polarization state in the same sense as the left circular polarization state, which thus favors the attraction process toward this particular SOP (see the theoretical supplementary material).

Figure 6 (a) Theoretical Poincaré representation obtained by numerically solving the spatio-temporal SOP evolution defined by Eq. (1) in the same configuration as in Fig. 2a involving two output SOP attraction points. To simulate the experiments, we considered a set of 64 different input signal SOPs, uniformly distributed over the Poincaré sphere (blue and green points). The red dots represent output SOPs. The input SOP ellipticity determines the two basins of attraction of the Omnipolarizer: green (blue) dots are attracted to the north (south) pole of the Poincaré sphere. (b)Same as in (a), but in the configuration of Fig. 2b involving a single output SOP attraction point (see the theoretical supplement material for details on the parameters used in the numerical computations). (c) Reduced phase-space representation of the stationary states of the system (1), where the Hamiltonian H = γ(S x J x + S y J y − S z J z ) and K z = S z −J z are conserved quantities. Each point of the phase-space diagram (H, K z ) refers to a torus. The final points of the numerical simulations of Eqs. (1) are represented by green crosses. The small insert is a zoom near the singular point (H = −γ, K z = 0: red point), which reveals that the SOP is attracted towards this point. The parameter γ has been fixed to 1 in the numerical computations. Full size image

In addition to this qualitative understanding, the physical mechanism underlying the observed self-polarization phenomenon can be described in terms of mathematical techniques associated with Hamiltonian geometric singularities28 (see the theoretical supplemental). Such singularities are topological structures that are also known as singular tori: these can be viewed as a two-dimensional extension of the concept of separatrix, which is a well-known property of basic one-dimensional physical systems (e.g., a pendulum). It can be shown that singular tori play the role of attractors for the SOP as described by Eqs. (1)29,30. This is schematically illustrated in Fig. 6c, which provides a phase-space representation of the system: The numerical simulations show that the SOP converges toward the singular torus, i.e. the red point in Fig. 6c. The singular torus for the present model can be represented as a sphere, an object which is topologically singular in the sense that it cannot be transformed into a regular torus by means of continuous deformations.

We briefly illustrate here the results for the passive configuration of the Omnipolarizer and refer the reader to the Supplemental for details. The numerical simulations of Eqs. (1) reveal that, irrespective of the initial conditions, the spatiotemporal dynamics exhibit a relaxation toward a stationary state. This can be understood intuitively by remarking that light reflection on the mirror introduces a supplementary condition for the polarizations states of the forward and reflected waves: S(L,t) − J(L,t) = 0 at any time t. This condition may be viewed as a temporal fixed point on the mirror at z = L. Then the physical picture that one may have in mind is that the system gradually extends this stationary behaviour from the mirror toward the whole fiber. This relaxation process is possible thanks to the reflected wave, which can evacuate the fluctuations of the waves throughout the free boundary condition at z = 0. In this way the counter-propagating waves relax toward an inhomogeneous stationary state in which their SOPs keep a fixed constant value for any z.