  Polarization-division multiplexed (PDM) transmission based on the nonlinear
Fourier transform (NFT) is proposed for optical fiber communication. The NFT
algorithms are generalized from the scalar nonlinear Schr\"odinger equation for
one polarization to the Manakov system for two polarizations. The transmission
performance of the PDM nonlinear frequency-division multiplexing (NFDM) and PDM
orthogonal frequency-division multiplexing (OFDM) are determined. It is shown
that the transmission performance in terms of Q-factor is approximately the
same in PDM-NFDM and single polarization NFDM at twice the data rate and that
the polarization-mode dispersion does not seriously degrade system performance.
Compared with PDM-OFDM, PDM-NFDM achieves a Q-factor gain of 6.4 dB. The theory
can be generalized to multi-mode fibers in the strong coupling regime, paving
the way for the application of the NFT to address the nonlinear effects in
space-division multiplexing.
