Theoretical formalism for collective electromagnetic response of discrete metamaterial systems
Theoretical formalism for collective electromagnetic response of discrete metamaterial systems
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DOI：
10.1103/physrevb.86.085116
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发表时间：
2012-08-13
影响因子：
3.7
通讯作者：
Ruostekoski, Janne
中科院分区：
文献类型：
--
作者：
Jenkins, Stewart D.;Ruostekoski, Janne
我们发展了一个描述近谐振电磁场在由磁介质谐振器组成的介质中传播的一般形式。由于超材料阵列中纳米谐振器的尺寸和空间间隔往往小于波长，我们将其描述为离散的散射体，支持由单个动态变量表示的单一模式的电流振荡。我们通过Power-Zienau-Woolley变换得到了长度规中耦合电磁场和振荡电流的拉格朗日和哈密顿形式。然后，每个谐振器对电磁场的响应由极化和磁化密度来描述，在多极展开中，极化和磁化密度最低，产生电偶极子和磁偶极子激发。在旋转波近似下，我们导出了每个谐振器电流振荡的相干散射场和简正模振幅的闭合方程组，在旋转波近似下，辐射衰减率远小于共振频率，并且没有这样的假设。这组方程包括由电磁场调节的一组离散谐振器之间的辐射耦合，完全包含了所有阶次的递归散射过程。通过考虑一个二维分裂环谐振器超材料阵列的例子，我们证明了该系统对近谐振场的协同响应，表现出集中的本征模、共振频率和辐射线宽，这些集中的本征模式、共振频率和辐射线宽是由紧密间隔的谐振器之间的强辐射相互作用产生的。
We develop a general formalism to describe the propagation of a near-resonant electromagnetic field in a medium composed of magnetodielectric resonators. As the size and the spatial separation of nanofabricated resonators in a metamaterial array are frequently less than the wavelength, we describe them as discrete scatterers, supporting a single mode of current oscillation represented by a single dynamic variable. We derive a Lagrangian and Hamiltonian formalism for the coupled electromagnetic fields and oscillating currents in the length gauge, obtained by the Power-Zienau-Woolley transformation. The response of each resonator to electromagnetic field is then described by polarization and magnetization densities that, to the lowest order in a multipole expansion, generate electric and magnetic dipole excitations. We derive a closed set of equations for the coherently scattered field and normal mode amplitudes of current oscillations of each resonator both within the rotating wave approximation, in which case the radiative decay rate is much smaller than the resonance frequency, and without such an assumption. The set of equations includes the radiative couplings between a discrete set of resonators mediated by the electromagnetic field, fully incorporating recurrent scattering processes to all orders. By considering an example of a two-dimensional split ring resonator metamaterial array, we show that the system responds cooperatively to near-resonant field, exhibiting collective eigenmodes, resonance frequencies, and radiative linewidths that result from strong radiative interactions between closely spaced resonators.