Synthesis of the refractive index profile of the optical fiber with the account of Kerr nonlinearity

In the present paper, we investigate the possibilities of reducing the distortions of propagated in optical fibers high-power femtosecond pulses due to the choice of its refractive index profile, taking into account the profile changes due to the cubic nonlinearity of the material of lightguide. Approximate analytical expressions are presented for calculating the dispersion characteristics of an optical fiber with an arbitrary profile of the refractive index. This analytical exspressios take into account the profile changes due to the Kerr nonlinearity. A technique for synthesizing a profile optimized for transmission of optical pulses with given parameters is proposed. An example of a synthesized profile is presented. The results of simulation the propagation of optical pulses in the step-index optical fiber and in the fiber with a synthesized profile are presented.