An accurate wave equation beyond the slowly varying envelope approximation for femtosecond soliton propagation in an optical fiber is derived by the iterative method. The derived equation contains higher nonlinear terms than the generalized nonlinear Schrödinger equation obtained previously. For a silica-based weakly guiding single mode fiber, it is found that those more higher-order nonlinear terms, whose coefficients are proportional to the second-order dispersion parameter, are much smaller than the shock term. The 2.5-fs fundamental solitons is numerically simulated by using the generalized nonlinear Schrödinger equation and the full Maxwell's equations. Comparing these two results, we have found that the generalized nonlinear Schrödinger equation well describes the propagation of the pulse even containing a single optical cycle.
- Femtosecond soliton slowly varying envelope approximation
- Nonlinear Schrödinger equation