移动边界各向异性材料中Maxwell方程的微扰理论
Perturbation theory for Maxwell's equations in anisotropic materials with shifting boundaries
摘要：
微扰理论是一种基于泰勒展开定理的估计方法，适用于研究微小变化的电磁场解。通过考虑作为平滑系统的限制的尖锐的边界，以前的研究已经解决了这个问题时，应用标准微扰理论的麦克斯韦方程组的小位移在各向同性介电界面。然而，当处理各向异性材料时，进行近似并导致不令人满意的误差。在这里，我们发展了一个修改后的微扰理论，在各向异性介电界面的小位移。通过对介电常数各分量采用优化的平滑函数，得到了一种计算各向异性介电常数场在边界移动时固有频率移动的方法，无需近似。该方法在计算强各向异性介质本征频率偏移时具有较好的精度，可广泛应用于各向异性介质界面的微小偏移。
英文摘要：
Perturbation theory is a kind of estimation method based on theorem of Taylor expansion, and is useful to investigate electromagnetic solutions of small changes. By considering a sharp boundary as a limit of smoothed systems, previous study has solved the problem when applying standard perturbation theory to Maxwell's equations for small shifts in isotropic dielectric interfaces. However, when dealing with anisotropic materials, an approximation is conducted and leads to an unsatisfactory error. Here we develop a modified perturbation theory for small shifts in anisotropically dielectric interfaces. By using optimized smoothing function for each component of permittivity, we obtain a method to calculate the intrinsic frequency shifts of anisotropic permittivity field when boundaries shift, without approximation. Our method shows accurate results when calculating eigenfrequency's shifts in strong-anisotropy materials, and can be widely used for small shifts in anisotropically dielectric interfaces.
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