Abstract
The transient nonlinear Schrodinger equation in which the frequency is a function of time is established to describe the fast-varying field in the process of supercontinuum generation. It is solved with two methods and validated by comparing its simulation results with those of reported experiments. Based on the simulations of this extended equation, it is also demonstrated that the second-order differential of the field to longitude ( z ) can be ignored in the supercontinuum generation, and the additive item caused by the relationship between frequency and time will induce a homogeneous frequency shift.
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