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 Schro 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.

中文翻译：

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锥形渐变折射率波导中啁啾自相似孤子的自频移效应

摘要 这项工作研究了自相似光束通过非均匀锥形渐变折射率波导在衍射和非线性管理以及受激拉曼散射 (SRS) 引起的自频移下的传输动力学。采用与常系数高阶非线性薛定谔方程（HNLSE）相联系的相似变换来构造新的波场自相似孤子。我们证明了自频移项单独将自相似脉冲变为非线性啁啾。结果表明，与自相似局域波相关的非线性啁啾与光束强度成正比。对于这种非线性啁啾自相似局域波，该模型提出了锥形渐变折射率非线性波导参数的充分必要条件。这些啁啾光学相似的动力学行为也在周期性分布的波导和衍射衰减波导中进行了研究。