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Full-Vectorial Matched Interface and Boundary (MIB) Method for the Modal Analysis of Dielectric Waveguides

机译:全矢量匹配界面和边界(MIB)方法用于介质波导的模态分析

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摘要

This paper introduces the matched interface and boundary (MIB) method for the eigenmode analysis of two dimensional step-index waveguides. The MIB method distinguishes itself from other existing interface methods by avoiding the use of the Taylor series expansion and by introducing the concept of the iterative use of low-order jump conditions. The difficulty associated with other interface approaches in extending to ultrahigh order is thus bypassed in the MIB method. In solving rectangular waveguide with a single straight interface, the MIB interface treatment can be carried out systematically so that the resulting scalar approach is of arbitrarily high order, in principle. Orders up to 12 are confirmed numerically for both transverse magnetic and transverse electric modes. In dealing with rectangular waveguide with a dielectric corner, a novel full-vectorial MIB method is proposed, in which an advanced corner handling technique is applied to accommodate the singular behavior of field near the corner. Benchmark problems are employed to validate the proposed full-vectorial approach. Higher order convergence is achieved numerically.
机译:本文介绍了用于二维阶跃折射率波导本征模分析的匹配界面和边界(MIB)方法。 MIB方法通过避免使用泰勒级数展开,并引入了迭代使用低阶跳跃条件的概念,使其与其他现有接口方法区别开来。因此在MIB方法中绕过了与其他接口方法相关联的扩展到超高阶的困难。在求解具有单个直线界面的矩形波导时,可以系统地进行MIB界面处理,因此,所得标量方法原则上可任意高阶处理。对于横向磁模式和横向电模式,数字上最多可确认12个订单。在处理带有介质角的矩形波导时,提出了一种新颖的全矢量MIB方法,该方法采用了一种先进的角处理技术来适应角附近场的奇异行为。基准问题被用来验证所提出的全矢量方法。在数值上实现了更高阶的收敛。

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