多波导定向耦合器耦合特性

利用拉普拉斯变换,将多波导定向耦合器的耦合模方程组变换为三对角线性方程组,并采用追赶法求出了该方程组的通解;进一步,给定初始条件,进行拉普拉斯变换反演,即可严格地求出该耦合模方程组的解。采用该方法研究了5波导定向耦合器光从一个波导入射和等光强从5个波导入射时的耦合特性,求出了耦合模方程组解的解析表达式,给出了每个波导中光功率变化规律曲线。利用该方法,可很方便地求出任意有限数目波导组成的定向耦合器在任意入射条件下耦合模方程组的解,因此对于多波导定向耦合器结构的合理设计,具有非常重要的意义。

Study on Coupling in a Multi-Waveguides Directional Coupler

The coupling equation set,which describes coupling characteristics of a multi-waveguides directional coupler,is transformed into a tridiagonal linear equation set by Laplace transform.And then general solution of this equation group is obtained by use of the chase method.Furthermore,given incidence condition,solution of the coupling equation group can be obtained exactly by inversion of the Laplace transform.Coupling characteristics of a five-waveguides directional coupler are studied in this method under two conditions of that light beam incidence upon one waveguide and five waveguides.And then analytic expressions of solution of the coupling equation group are obtained and variation curves of optical power in each waveguide are given.This method,which can be used to solve coupled-mode equations set of a multi-waveguides directional coupler with both any quantity of waveguides and any incidence condition,is significant for structure design of a multi-waveguides directional coupler.