Theoretical Study On Supercontinuum Spectrum Of Highly Nonlinear Photonic Crystal Fibers

The technology of supercontinuum spectrum can be used in many other areas. Solving nonlinear Schrodinger equation is an effective way to learn the mechanism of supercontinuum spectrum's generation. There are so many numerical methods used to solve nonlinear Schrodinger equation, Split-Step Fourier method is the most popular way among them. Nonetheless, Split-Step Fourier method's step-by-step process isolates the effects of dispersion and nonlinearity of the optical medium, this way will increase calculation error. To conquer the problem above, this paper used a method called rapid numerical difference recurrence algorithm which has been proposed lately. The most significant advantage of this method is that it has taken into account the dispersion effects and the nonlinearity effects simultaneously along each fiber segment. A new modified algorithm has been proposed just in order to solve the general form of NLSE with the higher-order nonlinear items that are very important for the simulation of supercontinuum. After that, we did some comparison between traditional analytical result and the modified method of this paper, the contrast results show that the modified rapid numerical difference recurrence algorithm is a correct numerical method, and the comparison between Split-Step Fourier method, Runge-Kutta method, and the modified method still shows that the new way has more computing efficiency.This paper made a brief introduction of the characteristics of and analysis methods of photonic crystal fibers, and makes some simple discussion about the light propagation mechanism of two groups of photonic crystal fibers:photonic band-gap photonic crystal fibers and total internal reflection photonic crystal fibers. High nonlinear is a necessary condition for supercontinuum's generation, so we chose highly nonlinear photonic crystal fibers as the carrier of supercontinuum in this paper. Therefore, this paper built a high nonlinear photonic crystal fiber model to compute the dispersion and nonlinearity parameters. Finally, we use these fiber parameters extracted from the model and the modified method to solve NLSE, and make some further discussion to the generation mechanism of supercontinuum.