Electromagnetic Fields and Photonics Group
All-optical control and stabilization of light polarization in optical fibers
Wherever the polarization properties of a light beam are of concern, polarizers and polarizing beam splitters (PBS) are indispensable devices in linear-, nonlinear- and quantum-optical schemes. By the very nature of their operation principle, transformation of incoming unpolarized or partially polarized beams through these devices introduces large intensity variations in the fully polarized outcoming beam(s). Such intensity fluctuations are often detrimental, particularly when light is post-processed by nonlinear crystals or other polarization-sensitive optic elements.
In the frame of a collaboration with our colleagues at the University of Bourgogne in France, we have recently demonstrated the unexpected capability of light to self-organize its own state-of-polarization, upon propagation in optical fibers, into universal and environmentally robust states, namely right and left circular polarizations. We experimentally validated a novel polarizing device - the Omnipolarizer, which is understood as a nonlinear dual-mode polarizing optical element capable of operating in two modes - as a digital PBS and as an ideal polarizer. Switching between the two modes of operation requires changing beam’s intensity.
Figure 1 | (a, b) Illustration of the lossy nature of a linear polarizer based on the rejection principle, as opposed to the Omnipolarizer. Three input pulses, with different initial polarization states are incident on a) the linear (or conventional) passive polarizer; b) the Omnipolarizer. In the first case, we observe strong output intensity variations due to the rejection principle. In the second case all three pulses pass through with no degradation. In both cases the outcoming pulses are vertically polarized. (c, d) Illustration of the continuous splitting principle of the linear (or conventional) PBS, as opposed to the discrete splitting principle of the Omnipolarizer. Three pulses, with different initial polarization states are incident on c) the linear PBS; d) the Omnipolarizer. In the first case, pulse splitting and intensity variations are observed on each axis of the PBS. In the second case, no splitting is observed: all energy is routed to either one or another channel, simply depending on the initial polarization ellipticity of the pulse. Note that this figure only serves for illustrative purposes. Indeed, the Omnipolarizer splits mutually orthogonal circular (and not linear, as shown in the figure) polarizations.
Figure 2 | Schematics and principle of the Omnipolarizer. (a) Passive setup: the light beam interacts nonlinearly in an optical fiber with its backward replica, obtained by inserting a partially reflecting mirror. The device behaves as a discrete PBS. Depending on its initial ellipticity, the input signal is digitally routed towards one or the other pole of the Poincaré sphere, corresponding to circular polarization states. (b) Active setup: the back-reflected signal is amplified in a reflective fiber loop (circulator&lifier). The Omnipolarizer can switch between the PBS and polarizer modes depending on the back-reflected power. In the polarizer mode, all the input SOPs remain trapped around a small spot on the Poincaré sphere.
Polarization effects in coherent 100 Gbit/s transmission systems
In current 100 Gbit/s transmission systems employing polarization division multiplexing (PDM) and the quadrature phase shift keying (QPSK) modulation, compensation of the link chromatic-dispersion (CD) and polarization mode dispersion (PMD) is achieved by digital signal processing (DSP) at the coherent receiver. Other transmission impairments result from the fiber nonlinearity, i.e., self-phase modulation (SPM), cross-phase modulation (XPM) and cross polarization modulation (XPolM) among wavelength division multiplexing (WDM) channels.
Numerical simulations and experiments have shown that, in the case of dispersion-managed (DM) systems, nonlinear penalties in both single-channel and WDM 112 Gbit/s PDM-QPSK transmissions may be mitigated by introducing a moderate amount of fiber PMD. However, since CD can be fully compensated at the receiver, it is convenient to eliminate in-line CD compensating fibers. Moreover, in non-DM systems, large dispersive signal spreading strongly reduces the impact of nonlinearities.
Yet, in spite of the use of DSP for the compensation of the average PMD, the statistical nature of PMD-induced bite-error-rate (BER) degradation requires the full knowledge of the associated probability density function (PDF). In particular, the knowledge of the tail of the BER-PDF is necessary in order to compute the PMD-induced outage probability (OP).
The OP is associated with the presence of rare events, and its computation by means of conventional Monte Carlo simulation techniques is a prohibitive task. Hence the statistical distribution of PMD-induced errors in 112 Gbit/s PDM-QPSK transmission systems with coherent receivers and DSP remains to date largely unexplored.
Recent studies have compared the performance of different electronic PMD equalizers by computing the residual OP by means of the multicanonical Monte Carlo (MMC) technique. The iterative nature of the MMC approach required intensive parallel computing, and was limited to studying the performance of a simple PMD emulator involving 30 birefringent waveplates.
In our research, we applied first the importance-sampling (IS) technique to the estimation of the PDF of the output Q factor in the presence of fiber nonlinearity, CD and PMD in nonreturn-to-zero (NRZ) on-off keying (OOK) systems. Recently, we extended the use of the IS technique to the case of PDM-QPSK coherent transmissions, which enabled us to directly compute the PMD-induced OP in a realistic system setup involving CD, amplified spontaneous emission (ASE) noise, and fiber nonlinearity.
Figure showing the estimated PDF of the output Q factor of central 112 Gbit/s PDM QPSK channel without or with two NRZ-OOK side channels, for different average DGD values.