<title>Nonlinear chirped pulses in graded-index optical fibers with longitudinal inhomogeneity</title>

Abstract

Mode structure and nonlinear dynamics of the chirped pulse are studied in the graded-index optical fiber with a longitudinal inhomogeneity of the refractive index. Chirps are classified with respect to the relationship between the depth of the linear frequency modulation and the width of the pulse spectrum. Considered in the paper are the regimes: (1) the modulation depth essentially less than the spectrum width - chirped pulses; (2) the depth of modulation is commensurate with the width ofthe pulse spectrum - strongly chirped pulses. The pulse propagation is modelled with a nonlinear wave equation in which the refractive index depends quadratically on the wave field. This equation is solved asymptotically with two different <i>ansatzes</i> for chirp and strong chirp regimes. The mode structure ofthe pulse is shown to differ for chirped and strongly chirped pulses, and in both cases relationships are stated confining the coefficient of the linear frequency modulation with the phases of high-frequency carrier and envelope. Consequent asymptotic procedure leads to the nonlinear equations governing the dynamics of the envelopes of chirped and strongly chirped pulses. Studied in more details is the envelope of the chirped pulse, in this case some additional assumptions on the longitudinal inhomogeneity of the optical fiber enable to reduce the equation for the envelope to the second Painleve equation. Comparison with <i>sech</i>-soliton of the nonlinear Schroedinger equation is carried out and important features conditioned by the linear frequency modulation are ascertained.