Analysis of nonlinear electromagnetic metamaterials
Analysis of nonlinear electromagnetic metamaterials
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DOI：
10.1088/1367-2630/12/9/093010
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发表时间：
2010-09-06
影响因子：
3.3
通讯作者：
Smith, David R.
中科院分区：
文献类型：
--
作者：
Poutrina, Ekaterina;Huang, Da;Smith, David R.
我们分析了通过将非线性元件或材料集成到超材料元件的电容区域中而形成的非线性超材料的特性。一个简单的均匀化过程导致的复合超材料介质的非线性极化率的一般表达式。该表达式是方便的，因为它们使散射元件的非均匀系统能够使用非线性光学的标准符号被描述为连续介质。我们通过以类似于Wang等人（2008 Opt.Express 16 16058）的方式对由开口环谐振器（SRR）阵列与嵌入电容间隙中的封装变容二极管组成的制造的超材料样品进行测量来说明我们的理论框架的有效性和准确性。由于SRR表现出对电磁场的主要磁响应，因此变容二极管加载的SRR复合材料可以被描述为在其有效磁化率中具有非线性项的磁性材料。将复合材料视为非线性有效介质，我们可以定量评估介质的性能，以增强和促进非线性过程，包括二次谐波产生，三波和四波混频，自聚焦和其他众所周知的非线性现象。我们通过预测变容二极管加载SRR介质的有效磁导率中的强度依赖性谐振频率偏移并与实验测量值进行比较来说明我们的方法的准确性。
We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable an inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated metamaterial sample composed of an array of split ring resonators (SRRs) with packaged varactors embedded in the capacitive gaps, in a manner similar to that of Wang et al (2008 Opt. Express 16 16058). Because the SRRs exhibit a predominantly magnetic response to electromagnetic fields, the varactor-loaded SRR composite can be described as a magnetic material with nonlinear terms in its effective magnetic susceptibility. Treating the composite as a nonlinear effective medium, we can quantitatively assess the performance of the medium to enhance and facilitate nonlinear processes, including second harmonic generation, three- and four-wave mixing, self-focusing and other well-known nonlinear phenomena. We illustrate the accuracy of our approach by predicting the intensity-dependent resonance frequency shift in the effective permeability of the varactor-loaded SRR medium and comparing with experimental measurements.