A correlation propagation model for nonlinear fourier transform of second order solitons

Inverse scattering transform or nonlinear Fourier transform (NFT) has been proposed for optic communication to increase channel capacity beyond the well known Shannon limit. Within NFT, solitons, as discrete outputs of the transform, can be a type of resource to carry information. Second-order solitons as the most basic higher order solitons show correlations among their parameters in the nonlinear Fourier domain as they propagate along a fibre. In this work, we report, for the first time, a correlation propagation model for second-order soliton pulses in the nonlinear Fourier domain. The model can predict covariance matrices of soliton pulses at any propagation distance using only the covariance matrices calculated at the input of the fibre with different phases in the nonlinear Fourier domain without the need of propagating the pulses.