Design of a Numerical Simulator for Optical Signal Propagation in a Multimode Fiber Structure

??The theory behind the implementation of a numerical solver for the generalized multimode nonlinear Schroedinger equation (GMMNLSE) modeling the propagation of a modulated electromagnetic field in a fiber subject to linear and nonlinear effects is presented. ?? ??Firstly, the mode-independent linear effects up to second-order in frequency are reviewed. Secondly, particular attention is devoted to the two polarization mode case where the linear effects arising from fiber perturbations are referred to as polarization mode dispersion (PMD). The understanding of PMD phenomena is basic for the study of linear and nonlinear phenomena in the higher-dimensional multimode case. Within the framework of PMD, a segment of uniformly perturbed fiber is initially considered, both for frequency-independent and frequency-dependent birefringence. Then, the case of random nonuniform perturbations, in both regimes of frequency-independent and frequency-dependent birefringence, is addressed exploiting the model of a fiber as a concatenation of uniform segments. The concept of principal states of polarizations (PSPs), extending the role of the eigenpolarizations in carrying an undistorted signal in a segment with uniform birefringence, is reviewed as a theoretical tool for the description of PMD. The study takes advantage of both Jones space, where the analytic description of signal evolution is natural, and Stokes space, where a graphical analysis is possible. The role of mode coupling in reducing the differential group delay (DGD) is shown through simulations, and relevant statistical considerations about PMD and DGD are offered. ?? ??PMD concepts are extended to the multimode fibers supporting different spatial modes, where linear coupling is accounted for by modeling physical impairments like core ellipticity, bends and axis rotation between different uniformly perturbed segments. ?? ??Finally, the main nonlinear effects appearing in the GMMNLSE and stemming out from the third-order nonlinear susceptibility, namely self-phase modulation (SPM), cross-phase modulation (XPM) and four-wave mixing (FWM), are considered for a single-carrier modulation system, together with the previously discussed linear effects. A numerical solution of the GMMNLSE is provided through the split-step Fourier method (SSFM) and the massive parallel algorithm (MPA).?? ??An outlook on possible directions for research and improvement is offered in the end.?? ??Simulations have been carried out throughout the whole study to qualitatively support the theoretical knowledge, drive the intuition and provide feedback about the impact of the various distorting effects on the transmitted pulse shapes. ?? ??The present work can be helpful both for an accurate study of signal propagation in short-reach direct-detection optical systems where a single signal excites all the modes, and for the development of space division multiplexing (SDM) coherent systems where different independent signals excite different modes of a multimode structure, with the aim of increasing the data rates of the current optical networks.