We propose the use of self-defocusing nonlinearities to control nonlinear phase shifts in soliton fiber lasers. By analogy to dispersion management, we refer to this scheme as nonlinearity management. First we describe a map that can be regarded as a combination of nonlinearity management and dispersion management. The map is designed to support solitons in two segments of alternating sign of nonlinearity and dispersion. Analytical and numerical calculations demonstrate that this map can be essentially free of spectral-sideband generation. Suppressing the spectral sidebands should make possible pulse energies 100 times greater than those of existing soliton fiber lasers. We also discuss the less than ideal case of direct reduction of average nonlinearity by use of self-defocusing nonlinearity segments without optimizing dispersion. The second scheme has the advantage of easier implementation. Practical implementations with existing materials are discussed.
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