Dielectric resonances of binary random networks
Dielectric resonances of binary random networks
复制标题
二元随机网络的介电共振
DOI：
10.1088/0305-4470/31/16/002
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
J. Luck
中科院分区：
文献类型：
--
作者：
T. Jonckheere;J. Luck
我们研究了二元随机阻抗网络的交流电导率，重点是它对比率的依赖性，其中和是两个相的复电导，以各自的概率p和1-p发生。我们提出了一种算法来确定有限网络电导的有理h依赖性，就其极点和相关残基而言。位于负真实的h轴上的极点被称为谐振，因为它们在具有高品质因数Q的金属-电介质复合物的RL-C模型的AC电导中表现为窄谐振。这种方法是以前的工作致力于孤立的有限集群的介电共振的延伸。该算法的数值实现，在正方形晶格的例子上，允许对二元模型的谐振介电响应的详细调查，包括谐振密度和相关谱函数的p依赖性，谐振谱端点附近这些量的Lifshitz行为，相邻谐振之间的间距分布，以及RL-C模型中可见共振部分的Q依赖性。共振时的局部电场分布是多重分形的。这一结果与观察到的巨大的表面增强拉曼散射，例如，在非连续金属膜的角度来看。
We investigate the AC conductivity of binary random impedance networks, with emphasis on its dependence on the ratio , with and being the complex conductances of both phases, occurring with respective probabilities p and 1-p. We propose an algorithm to determine the rational h-dependence of the conductance of a finite network, in terms of its poles and of the associated residues. The poles, which lie on the negative real h-axis, are called resonances, since they show up as narrow resonances in the AC conductance of the RL-C model of a metal-dielectric composite with a high quality factor Q. This approach is an extension of a previous work devoted to the dielectric resonances of isolated finite clusters. A numerical implementation of the algorithm, on the example of the square lattice, allows a detailed investigation of the resonant dielectric response of the binary model, including the p-dependence of the density of resonances and the associated spectral function, the Lifshitz behaviour of these quantities near the endpoints of the spectrum of resonances, the distribution of spacings between neighbouring resonances, and the Q-dependence of the fraction of visible resonances in the RL-C model. The distribution of the local electric fields at resonance is found to be multifractal. This result is put into perspective with the giant surface-enhanced Raman scattering observed, for example, in semicontinuous metal films.