A fourth-order Runge–Kutta in the interaction picture method for simulating supercontinuum generation in photonic crystal fibers

Abstract

The supercontinuum produced by photonic crystal fibers has a very wide spectral width and good flatness, and it makes the applications of supercontinuum greatly expanded in many areas. However, due to the two-dimensional special structure of photonic crystal fibers and the complex nonlinear effects in supercontinuum generation, a specific kind of supercontinuum is not often easily to be obtained, so it makes the simulation of supercontinuum generation become very important. The widely used split-step Fourier method for solving nonlinear Schrodinger equations to simulate supercontinuum generation can not achieve a very high precision, because the high order nonlinear effect is often ignored and the nature of the algorithm also has an impact on the accuracy. So a high precision single step algorithm called Runge-Kutta method which is widely used for engineering is mentioned in this paper. Taking the higher-order nonlinear effects in supercontinuum generation into consideration, a more accurate and efficient calculation method of supercontinuum simulation is given by solving the generalized nonlinear Schrodinger equation. Simulation on the supercontinuum generation in photonic crystal fiber has been made. While the incident laser pulse with the 120fs pulse width and the 800nm center wavelength transmits in a period of photonic crystal fiber, the supercontinuum that covers the wavelength from 500nm to 1100nm is generated. The flatness of the spectrum will get some improvement with the increase of the incident pulse’s peak power.