Abstract
This work studies the transmission dynamics of self-similar optical beams through an inhomogeneous tapered graded-index waveguide under diffraction and nonlinearity management as well as self-frequency shift arising from stimulated Raman scattering (SRS). A similarity transformation connecting with the constant-coefficient higher-order nonlinear Schrö dinger’s equation (HNLSE) is employed to construct new self-similar solitons for wave field. We demonstrate that the self-frequency shift term alone turns the self-similar pulses to be nonlinear chirped. The results indicate that the nonlinear chirp related to the self-similar localized waves is directly proportional to the intensity of the optical beam. The necessary and sufficient conditions on tapered graded-index nonlinear waveguide parameters for such nonlinearly chirped self-similar localized waves exist in this model are suggested. The dynamical behaviors of those chirped optical similaritons are also investigated in a periodically distributed waveguide as well as a diffraction decreasing waveguide.