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For mode vector modulation, used in conjunction with direct-detection, we present geometrically-optimized signal sets that correspond to the densest sphere packing in the generalized Stokes space. We show that the best trade-off between spectral and energy efficiency occurs for simplex constellations. 

The nonlinear Gaussian-noise (GN) model is a useful analytical tool for the estimation of the impact of distortion due to Kerr nonlinearity on the performance of coherent optical communications systems with no inline dispersion compensation. The original nonlinear GN model was formulated for coherent optical communications systems with identical single-mode fiber spans. Since its inception, the original GN model has been modified for a variety of link configurations. However, its application to coherent optical communications systems with hybrid fiber spans, each composed of multiple fiber segments with different attributes, has attracted scarcely any attention. This invited paper is dedicated to the extended nonlinear GN model for coherent optical communications systems with hybrid fiber spans. We review the few publications on the topic and provide a unified formalism for the analytical calculation of the nonlinear noise variance. To illustrate the usefulness of the extended nonlinear GN model, we apply it to coherent optical communications systems with fiber spans composed of a quasi-single-mode fiber segment and a single-mode fiber segment in tandem. In this configuration, a quasi-single-mode fiber with large effective area is placed at the beginning of each span, to reduce most of the nonlinear distortion, followed by a single-mode fiber segment with smaller effective-area, to limit the multipath interference introduced by the quasi-single-mode fiber to acceptable levels. We show that the optimal fiber splitting ratio per span can be calculated with sufficient accuracy using the extended nonlinear GN model for hybrid fiber spans presented here.