  Pure solitons are for the first time distilled from the resonant continuous
wave (CW) background in a fiber laser by utilizing nonlinear Fourier transform
(NFT). It is identified that the soliton and the resonant CW background have
different eigenvalue distributions in the nonlinear frequency domain. Similar
to water distillation, we propose the approach of soliton distillation, by
making NFT on a steady pulse generated from a fiber laser, then filtering out
the eigenvalues of the resonant CW background in the nonlinear frequency
domain, and finally recovering the soliton by inverse NFT (INFT). Simulation
results verify that the soliton can be distinguished from the resonant CW
background in the nonlinear frequency domain and pure solitons can be obtained
by INFT.
