Ultrashort optical pulses with nonlinear chirps in non-Kerr media exhibiting higher-order nonlinearities

We consider a higher-order nonlinear Schrödinger equation that models the evolution of ultrashort optical pulses in nonlinear media exhibiting nonlinearities up to the ninth order. The modulational stability of the continuous-wave background which supports chirped nonlinear waves is analyzed. The condition of baseband modulational instability is established. Employing a phase-imprint transformation with a novel form of chirping, we present solitary wavelike solutions that describe chirped soliton propagation on nonzero continuous wave background. We show that the nonlinear chirp associated with each of these optical pulses is directly proportional to the wave intensity and depends on higher-order nonlinearities. The requirements concerning the optical material parameters for the existence of embedded chirped nonlinear waves are discussed. These chirped solitons exist due to a balance among competing septic-nonic nonlinearities, the self-steepening parameter, and the quintic non-Kerr nonlinearities. Interestingly, we show how to manipulate the free parameter of the second-order rogue wave solution to build second-order rogue wave singlet, doublets, and triplets. Our results can be useful for possible chirped-soliton-based applications of highly nonlinear optical fiber systems.