二维电磁晶体带隙结构的PWE法分析

Analysis of Band Structure of Two-dimensional Electromagnetic Crystal Using PWE Method

针对常见的电磁晶体带隙分析方法存在耗时、不易理解等问题,推导了二维电磁晶体的平面波展开法(Plane Wave Expansion,PWE)模型,并采用平面波展开法分析了不同形状填充单元二维方格子电磁晶体的带隙结构。将电场(或磁场)、介电常数(或其倒数)展开为双重傅里叶级数,然后将其代入所满足的标量波动方程中,经过运算整理得出二维电磁晶体的本征方程,求解该方程,就可得到电磁晶体的带隙结构。计算结果表明,填充单元尺寸和相对介电常数均对带隙结构存在影响。最后,采用周期延拓,得出了两种电磁晶体的等效结构。通过结构等效,无需再推导相应电磁晶体的结构系数,利用本文的平面波展开法模型即可实现其带隙结构的求解,因而实现了简化分析。仿真数据与文献中的实验数据对比,验证了本方法的有效性。

Aimed at the problems, of analysis on band gap of electromagnetic crystal using usual method, such as time -consuming, hard to be understood, a model of plane wave expansion （PWE） method is introduced in this paper and the plane wave expansion method is adopted to analyze the band gap structure of two - dimensional electromagnetic crystal with different shape of filling cell. By using this method, electrical field or magnetic field and dielectric constant or its reciprocal are expanded in the form of double Fourier series, which are then substituted into the scalar wave equation they must fulfill. Again, a characteristic equation for 2 - D electromagnetic crystal is achieved, and by solving it the band gap structure is obtained. Moreover, two equivalent structures are introduced. The results of calculation show that the size of filling cell and the relative dielectric constant all have influence on band gap structure. Comparison between the numerical solution and literature data indicates that the method in this paper is valid. At last, two equivalent structures are obtained by using periodic prolongation. It is not required to deduce the structure coefficients, and the analysis of band gap structure using the model of plane wave expansion method is realized, so simplification of analysis is achieved.