Abstract

We have theoretically investigated the electromagnetic properties for one-dimensional (1D) photonic crystals with magnetic and artificial chiral inclusions in the quasi-static limit, that is when the size of the unit cell of the crystal is small with respect to the wavelength of the operating wave. We suggest a homogenization theory to determine the effective tensors of the optical response, to achieve this objective, we apply the Bloch’s plane waves method to describe the electromagnetic modes that can propagate in the periodic structure under consideration. Subsequently, the Maxwell’s “microscopic” equations are homogenized replacing the Bloch waves by plane waves that attenuate the fast oscillations of the electromagnetic fields within the unit cell (macroscopic level), i.e., the average-macroscopic electromagnetic fields are determined by the component corresponding to the null reciprocal lattice vector in the expansion in plane waves. The numerical implementation of our theory of homogenization allow us to study the effective bianisotropic electromagnetic response (effective dielectric permittivity, magnetic permeability and electric-magnetic coupling tensors, this last is described by an effective chiral parameter) for 1D photonic crystals whose constituents in its unit cell are a dielectric layer and another magnetic (both isotropic and anisotropic) or chiral inclusion layer. The results are illustrated and discussed by the effective parameters as a function of the filling fraction of the inclusion and show for each case of homogeneous effective medium different components of anisotropy in the electromagnetic response of permittivity, permeability and chirality with the increase of the filling fraction. Besides, the behaviors of the obtained graphs agree well with Rytov’s formulas of effective medium. The relevant results of this theory will be very useful for the study and better understanding of the nature and design of metamaterials with predetermined anisotropic optical properties.

Graphical abstract

中文翻译：

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具有磁性和手性夹杂物的一维光子晶体的均质化方法

摘要

从理论上讲，我们研究了在准静态极限内具有磁性和人工手性夹杂物的一维（1D）光子晶体的电磁特性，也就是说，相对于晶体的波长，晶体的晶胞尺寸较小操作波。我们提出了一种均质化理论来确定光学响应的​​有效张量，为实现这一目标，我们使用布洛赫的平面波方法来描述可以在所考虑的周期性结构中传播的电磁模式。随后，将Maxwell的“微观”方程式进行均质化，用平面波代替Bloch波，该平面波减弱了晶胞内电磁场的快速振荡（宏观水平），即 平均宏观电磁场由平面波扩展中与零互易晶格矢量对应的分量决定。我们均质化理论的数值实现使我们能够研究一维光子晶体的有效各向异性电磁响应（有效介电常数，磁导率和电磁耦合张量，最后一个由有效手性参数来描述），该一维光子晶体的成分在其单位中单元是介电层和另一个磁性（各向同性和各向异性）或手性包含层。结果通过有效参数作为夹杂物填充分数的函数进行了说明和讨论，并显示了对于均质有效介质的每种情况，随着填充分数的增加，介电常数，磁导率和手性的电磁响应中各向异性的不同组成。此外，所得图的行为与有效介质的Rytov公式非常吻合。该理论的相关结果对于研究和更好地理解具有预定各向异性光学特性的超材料的性质和设计非常有用。

图形概要