摘要
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．
Thenumerical solution of Gel'fand-Levitan-Marchenkoequation for the presence of guidedmodes is studied in this paper.It is found that the solution by using iterative method undergoesdivergence beyond a certain distance because the characteristic function of reflection coefficient whichpossesses poles on the positive imaginary axes in complex k-plane contains exponentially growingterms.In order to overcome this difficuIty we resort to the relaxation technique.The reconstructiondistance is,therefore,efficiently extended by introducing an underrelaxation factor.The reconstructedpotential in inverse scattering can directly be applied to the profile design of dielectric planarwaveguide via the scaling transformation for Schrodinger equation.
出处
《光子学报》
EI
CAS
CSCD
1996年第5期439-445,共7页
Acta Photonica Sinica
关键词
介质
波导
逆散射
迭代方法
Dielectric waveguide
Inverse scattering
Iterative method
