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提出一种分析非平行波导的简明方法———耦合系数推广法,把非平行波导几何图形的变化直接转化成波导耦合系数中波导间距的变化,即对耦合系数进行了巧妙的推广,把波导间距的变化以指数的形式潜入到耦合微分方程中,建立了非平行三波导系统的耦合方程。这些耦合方程包含了非平行波导传输的全部信息,即非平行波导输出光的振幅和相位,非平行传输波导的长度及其夹角,非平行波导输入端口的间距,能量转换与波导参量的关系等。对这些微分方程作巧妙的数学变换,得到非平行三波导耦合系统输出光的完整分析解,分析和讨论了对称和不对称输入初始条件下三个非平行波导的耦合情况。由此可以优化非平行波导的设计参量。
A simple method to analyze non-parallel waveguides, the coupling coefficient propagation method, is proposed, which directly transforms the change of the non-parallel waveguides geometry into the variation of the waveguide spacing in the waveguide coupling coefficient, that is, the coupling coefficient is ingeniously popularized. The change of spacing sank into the coupled differential equation in the form of exponential, and the coupling equation of non-parallel three-waveguide system was established. These coupling equations contain all the information about the non-parallel waveguides, that is, the amplitude and phase of the output light of the non-parallel waveguides, the length and the included angle of the non-parallel waveguides, the pitch of the input ports of the non-parallel waveguides, the relationship between energy conversion and the waveguide parameters Wait. Mathematical transformation of these differential equations is used to obtain a complete analytical solution of the output light of a non-parallel three-waveguide system. The coupling of the three non-parallel waveguides under the initial conditions of symmetric and asymmetric input is analyzed and discussed. This makes it possible to optimize the design parameters of non-parallel waveguides.