Self-focusing and self-phase modulation in a parabolic graded-index optical fiber

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Abstract
The spatial profile and the spectral distribution of a pulse propagating in a parabolic graded-index optical fiber are derived. Effects due to the χ(3) nonlinearity (self-focusing and self-phase modulation), diffraction (finite beam-waist effects), and the graded-index waveguiding are incorporated in the theoretical analysis. The fiber graded index generates a periodicity in the beam diameter. Waveguiding, self-focusing, and diffraction determine the minimum magnitude of the beam-waist diameter. The pulse phase, amplitude shape, and spectral distribution are shown to differ from conventional self-phase modulation results.