论文部分内容阅读
本文研究存在导（行）模时Ｇｅｌ＇ｆａｎｄ－Ｌｅｖｉｔａｎ－Ｍａｒｃｈｅｎｋｏ方程的数值解法．由于反射系数在复数ｋ平面正虚数轴上有极点，其特征函数中出现指数增长项，应用数值迭代求解到一定距离后便产生发散．为了克服这一困难，我们在迭代中采用了松弛方法，通过引入欠松弛因子延伸了势函数重建的有效距离。应用Ｓｃｈｒｏｄｉｎｇｅｒ方程下的比例变换关系，逆散射所重建势函数可以直接用于介质波导折射率剖面设计．
In this paper, we study the numerical solution of the Gel’fand-Levitan-Marchenko equation in the presence of a derivative. As the reflection coefficient has a pole on the positive imaginary axis of the complex k-plane, the exponential growth term appears in the eigenfunction of the complex k-plane. After numerical iteration, the divergence is solved by a certain distance. In order to overcome this difficulty, we adopt a relaxation method in the iteration, extending the effective distance of potential function reconstruction by introducing under-relaxation factor. Applying the scaling transformation under the Schrodinger equation, the inverse scattering reconstruction potential function can be directly applied to the refractive index profile of dielectric waveguides.