Polarization-dependent nonlinear effects in coherent detection systems

Abstract

In the last decades the demand for data capacity has increased exponentially. Optical Coherent Detection, firstly proposed at the end of the 1980s to improve receiver sensitivity, has proved as one of the most powerful techniques to increase the optical communication spectral efficiency and so the total per channel capacity. Indeed, thanks to the recent advances in digital signal processing (DSP) and high speed electronics, the DSP-based coherent detection in optical networks expedited the use of polarization division multiplexing (PDM) as a cost-effective way of doubling system capacity. Furthermore, coherent detection presents many others advantages with respect to direct detection such as the use of multilevel optical modulation formats like N-PSK and N-QAM and compensating linear propagation effects in the electrical domain as chromatic dispersion, polarization mode dispersion (PMD) and optical filtering. On the other hand, transmission reach of WDM systems is a major concern for the deployment of such a solution and is usually mainly limited by cross-nonlinear effects. In WDM transmission systems, the cross-nonlinearities make neighboring channels interact depending on their power and state of polarization (SOP). The last is of particular concern in PDM systems since they are more sensitive to a new kind of distortion that has been generally referred to as cross-polarization modulation (XPolM) as a way to distinguish it from the well known cross-phase modulation (XPM). At the beginning of our research activity in 2009, despite the growing interest and the number of publications on XPolM, many of its features were still unknown. For example, in Sept. 2009 Winter et al. provided a model that successfully measured the degree of polarization degradation in presence of XPolM, but it was still not clear when the bit error rate (BER) is dominated by XPolM and how XPolM relates to the other relevant nonlinear effects, such as XPM and self-phase modulation (SPM). With the investigations presented in this thesis we want to fill the gap, by providing a systematic simulation study of system performance where each nonlinear effect acts individually. Furthermore, thanks to the possibility in Optilux software to take into account separately the nonlinear terms of the propagation equation, we add some new piece of knowledge about XPolM. We quantify the XPolM-induced penalty as a function of transmission parameters such as the channel power, spacing and state of polarization (SOP). We also clarify the role of the Viterbi and Viterbi-based carrier phase estimator in mitigation of XPM and XPolM. We focused our investigation mainly on PDM-quadrature phase shift keying (QPSK) modulation format. The thesis is organized as follows. In the first chapter the principal impairments for long haul transmissions are briefly recalled. They are divided into linear and nonlinear effects, according to whether they are independent of the signal power or not. The first group is composed of fiber attenuation, chromatic dispersion and polarization mode dispersion. The second group is composed of nonlinear polarization-independent effects: such as SPM and XPM. Other linear effects such as polarization dependent loss and nonlinear effects as intra channel cross phase modulation, four wave mixing, nonlinear phase noise and non elastic scattering effects (stimulated Raman and Brillouin scattering) are not included in our discussion, while the XPolM is discussed at length in Ch. 3. The second chapter discusses the joint use of PDM and the coherent detection, as a solution to increase the transmission capacity. We also discuss a new technique, namely mode division multiplexing (MDM), to further increase the transmission capacity thanks to the joint use with PDM and coherent detection.

In Ch.3, after the definition of the XPolM term in the propagation equation, we show the polarization rotation and the PDM-QPSK constellation distortion induced by XPolM as a function of the rotation axis orientation. We perform such analysis both mathematically and by simulation. In Ch. 4 we show when the bit error rate (BER) of a PDM-QPSK channel is dominated by XPolM, through a massive use of simulation in a wide range of system setups. We analyze different pulse shapes, transmission links and transmission fibers in both hybrid (PDM-QPSK -- OOK) and homogeneous systems (PDM-QPSK). Furthermore we clarify the role of channel power, spacing, state of polarization (SOP) and Viterbi and Viterbi-based carrier phase estimator on the XPM- and XPolM-induced penalty. In the last part of the chapter we quantify the nonlinear penalty in a PDM-BPSK transmission system, showing the average performance and its fluctuation induced by the transmission sequences and SOPs. In Ch. 5 we compare different optical methods to improve the resilience of coherent 112-Gb/s PDM-QPSK WDM transmissions against cross-channel nonlinearities. Such methods consist of increasing the line group velocity dispersion (GVD), or the line PMD, or inserting in-line XPM suppressors, which are passive devices that introduce different delays on adjacent channels at specific points of the line. In Ch. 6 we summarize the experimental results obtained during the research activity at Alcatel-Lucent Bell-Labs France on MDM. In such an activity we employ a mode converter based on a liquid-crystal on silicon (LCOS) spatial modulator and a prototype few mode fiber (FMF). Last but not least, in the Appendix we discuss three different rules to correctly simulate the cross-nonlinearities, showing also some artifacts that can arise with a non-correct setting of some numerical parameters, such as the nonlinear step of Split-Step Fourier method, the sequence length and the sequence type.