计算光栅的一个改进的Rouard方法

An Improved Rouard′s Method for Grating Analysis

对计算光栅的Rouard方法作了两点改进。首先将半个周期而不是一个周期作为反射单元 ,其次每层薄膜端面的反射系数不是用耦合波理论求得的近似值 ,而是用真实的反射系数值。这样它就成为一个完全的Rouard方法 ,精度也相应提高了。改进的Rouard方法不仅简单而且与耦合波理论无关 ,因此不必先求光栅的耦合系数。还给出了用改进的Rouard方法计算均匀与非均匀光栅的实例 ,并将所得结果与未经改进的方法及耦合波理论的结果进行了比较。

Two improvements have been made to Rouard′s method for the analysis of fiber and waveguide gratings. The element of reflection is chosen to be a section of half period instead of a period, and the real reflectivity of each interface is used instead of an approximate value obtained by coupled mode theory. The improved Rouard′s method becomes a complete Rouard′s method with higher accuracy. It is simple and independent on coupled mode theory for no calculation of the coupling coefficient required. Numerical examples of uniform and nonuniform gratings are given.