Properties of a metamaterial element: Analytical solutions and numerical simulations for a singly split double ring
Properties of a metamaterial element: Analytical solutions and numerical simulations for a singly split double ring
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DOI：
10.1063/1.1652251
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发表时间：
2004-04-01
影响因子：
3.2
通讯作者：
Solymar, L
中科院分区：
文献类型：
--
作者：
Shamonin, M;Shamonina, E;Solymar, L
推导了一个由体元和分布元组成的等效电路，用于描述具有负磁导率的潜在超材料元的特性。它是单分裂双环（SSDR），分裂环谐振器（J. B. Pendry，IEEE Trans.微波理论技术。47，2075（1999）），当内环中的差距电容无限大时获得。变量是环间电压和在内环和外环中流动的电流。假设激励的形式是一个空间恒定的随时间变化的磁场。通过求解一组在分裂位置施加边界条件的微分方程来找到表示变量角度变化的函数。从解析解中可以看出，SSDR可以在从很低到很高的频率的全频谱中具有谐振频率。它特别指出，每当环的平均直径等于半波长的奇数倍，它总是可以找到一组参数，这将引起共振。作为示例，针对八组参数确定谐振频率。结果也来自通过用一些离散电路代替分布式电路。最后表明，从等效电路模型得到的结果是在很好的协议与那些来自MICRO-STRIPES数值包，解决了麦克斯韦方程在时域。(C)2004年，美国物理学会。
An equivalent circuit, consisting of bulk and distributed elements, is derived for describing the properties of a potential metamaterial element capable of providing negative effective permeability. It is the singly split double ring (SSDR), a special case of the split ring resonator (J. B. Pendry , IEEE Trans. Microwave Theory Tech. 47, 2075 (1999)), obtained when the gap capacitance in the inner ring is infinitely large. The variables are the inter-ring voltage and the currents flowing in the inner and outer rings. The excitation is assumed in the form of a spatially constant temporally varying magnetic field. The functions, showing the angular variation of the variables, are found by solving a set of differential equations with boundary conditions imposed at the position of the split. It is shown from the analytical solution that the SSDR can have resonant frequencies in the full spectrum from very low to very high frequencies. It is pointed out in particular that whenever the mean diameter of the ring is equal to an odd multiple of the half wavelength it is always possible to find a set of parameters which will give rise to resonance. As examples the resonant frequencies are determined for eight sets of parameters. Results are also derived by replacing the distributed circuit with a number of discrete circuits. It is finally shown that the results obtained from the equivalent circuit model are in excellent agreement with those derived from the MICRO-STRIPES numerical package which solves Maxwell's equations in the time domain. (C) 2004 American Institute of Physics.