Adaptive step size Gill method for the modeling of ultrashort pulse propagation in optical fiber

An adaptive step size Gill method is proposed to numerically solve the normal and generalized nonlinear Schrödinger equations. In this method, the Gill algorithm in the interaction picture and the conservation quantity error (CQE) method are used for integration scheme and adaptive step size control, respectively. Numerical simulations of the propagation of second-order soliton and soliton collision show that the proposed method can reduce the round-off error in the process of computation. The adaptive step size Gill method exhibits the expected global fourth-order accuracy for the problems studied. It is an efficiently alternative method for the modeling of ultrashort pulse propagation in optical fiber. In addition, we adopt a more accurate Raman response function (MA-RRF) in the simulation of supercontinuum generation. The results illustrate that the MA-RRF is necessary to provide a more accurate description of the Raman-induced frequency shift effect in supercontinuum generation.