Krokhin A A, Reyes E
Department of Physics, University of North Texas, P.O. Box 311427, Denton, Texas 76203, USA.
Phys Rev Lett. 2004 Jul 9;93(2):023904. doi: 10.1103/PhysRevLett.93.023904.
We calculate the low-frequency index of refraction of a medium which is homogeneous along axis z and possesses a periodic dependence of the permittivity epsilon(r) and permeability micro(r) in the x-y plane (2D magnetodielectric photonic crystal). Exact analytical formulas for the effective index of refraction for two eigenmodes with vector E or H polarized along axis z are obtained. We show that, unlike nonmagnetic photonic crystals where the E mode is ordinary and the H mode is extraordinary, now both modes exhibit extraordinary behavior. Because of this distinction, the magnetodielectric photonic crystals exhibit optical properties that do not exist for natural crystals. We also discuss the limiting case of perfectly conducting cylinders and clarify the so-called problem of noncommuting limits, omega-->0 and epsilon--> infinity.
我们计算了一种介质的低频折射率，该介质沿z轴均匀，并且在x - y平面（二维磁电介质光子晶体）中其电容率ε(r)和磁导率μ(r)具有周期性依赖关系。得到了沿z轴方向矢量E或H偏振的两个本征模的有效折射率的精确解析公式。我们表明，与非磁性光子晶体不同，在非磁性光子晶体中E模是寻常的而H模是非寻常的，现在两种模式都表现出非寻常行为。由于这种区别，磁电介质光子晶体展现出天然晶体所不存在的光学性质。我们还讨论了理想导电圆柱体的极限情况，并阐明了所谓的非对易极限问题，即ω→0和ε→∞。
