High-Order Analytical Formulation of Soliton Self-Frequency Shift

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 closely agrees 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.