We derive an analytical formulation of the Raman-induced frequency shift experienced by a fundamental soliton. By including propagation losses, self-steepening, and dispersion slope, the resulting formulation is a high-order (HO) extension of the well-known Gordon’s formula for soliton self-frequency shift (SSFS). The HO-SSFS formula agrees closely with numerical results of the generalized nonlinear Schrödinger equation, but without the computational complexity and required computation time. The HO-SSFS formula is a useful tool for the design and validation of wavelength conversion systems and supercontinuum generation systems.

中文翻译：

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孤子自频移的高阶解析公式

我们推导了一个基本孤子所经历的拉曼引起的频移的解析公式。通过包括传播损耗，自加陡度和色散斜率，所得公式是众所周知的孤子自频移（SSFS）的高登公式的高阶（HO）扩展。HO-SSFS公式与广义非线性Schrödinger方程的数值结果非常吻合，但没有计算复杂性和所需的计算时间。HO-SSFS公式是用于波长转换系统和超连续谱生成系统的设计和验证的有用工具。