颗粒膜电介质光子晶体低频折射率问题分析

应用颗粒膜电介质晶体在低频极限下的准静态折射率和静态折射率的关系，分析和计算了光子晶体低频折射率，结果表明：由于低频电磁波诱导的涡流（或极化电流），使非磁性光子晶体显现反磁性共振，这个共振依赖于周期性颗粒的半径和趋肤深度之间的关系。即，如果趋肤深度远远小于周期性颗粒的半径，包含物内部电磁场被屏蔽，使每一种包含物的行为像理想反磁性体。对于平行颗粒膜平面的（H偏振）电磁波，光子晶体的反磁性磁导率总体上是随填充数的增加而线性的减少；相反的，当趋肤层大于半径，则反磁性体共振可以忽略。周期性颗粒的磁化引起静态和准静态折射率的结论，解释了非对易限制的问题。

Analysis of low-frequency index of refractive for granular film dielectric photonic crystal

Using relationship of the quasi-static index of refractive and the static one in granular film dielectric,  the index of refractive of photonic crystal were calculated in the low-frequency limit. The index of refractive of photonic crystal were calculated in the low-frequency limit. the calculation indicates that, due to the eddy current (or the polarized current) induced by the low-frequency waves, the non-magnetic photonic crystal appears the diamagnetic resonance, which depends on the relationship between the radius of the cylinder and skin deep . If skin deep is far less than the radius of the cylinder, the inside of  electromagnetic field of the inclusion is concealed. Each inclusion behaves like the ideal diamagnetic. The diamagnetic permeability of (H polarization wave) photon crystal is linearly reduced with the increase of the filling fractions. On the contrary, when skin layer is larger than the radius, the diamagnetic resonance can be neglected. The magnetization of the periodicity particle composite media induces distinct values of the quasistatic and static indices of refraction, which explains a paradox with noncommuting limits.