EVOLUTION EQUATION OF OPTICAL SOLITONS IN FEMTOSECOND REGIME

A modified nonlinear Schrodinger equation (MNLSE), which is defined as the equation obtained by putting some higher-order terms (the higher-order dispersion and nonlinearity) into a nonlinear Schrodinger equation (NLSE), has been derived from the Maxwell equations in a nonlinear medium with the derivative-expansion procedure in the method of multi-scale singular perturbation. Meanwhile its two equivalent expressions are given. First, the first fourth-order perturbed equations of the Maxwell equations in a source-free nonlinear medium waveguide are obtained. Then, in the special case of the monomode waveguide, the third-order perturbed equation solution is the NLSE, and the fourth-order one is MNLSE. Careful investigation shows that the MNLSE obtained with the reductive perturbation technique (Y. Kodama and A. Hasegawa, IEEE J. Quantum Electron, QE-23(1987), 510) should be corrected.