Shaping lightwaves in time and frequency for optical fiber communication

In optical communications, sphere shaping is used to limit the energy of lightwaves to within a certain value over a period. This minimizes the energy required to contain information, allowing the rate of information transmission to approach the theoretical limit if the transmission medium is linear. However, when shaped lightwaves are transmitted through optical fiber, Kerr nonlinearity manifests itself as nonlinear interference in a peculiar way, potentially lowering communications capacity. In this article, we show that the impact of sphere shaping on Kerr nonlinearity varies with chromatic dispersion, shaping block length and symbol rate, and that this impact can be predicted using a novel statistical measure of light energy. As a practical consequence, by optimally controlling the parameters of sphere-shaped lightwaves, it is experimentally demonstrated that the information rate can be increased by up to 25% in low-dispersion channels on a 2824 km dispersion-managed wavelength-division multiplexed optical fiber link.