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arXiv physics/0703130physics.optics
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谐振型超材料的Q基设计方程及实验验证

Q-based design equations for resonant metamaterials and experimental validation

Steven A. Cummer, Bogdan-Ioan Popa, Thomas H. Hand

摘要:

谐振超材料的实际设计参数,如损耗角正切,导出的谐振有效介质的磁导率或介电常数的品质因数$Q$。通过基于回路的谐振粒子的电磁模拟,还表明有效介质响应的$Q$基本上等于单个谐振粒子的$Q$。因此,通过测量单个制造的超材料颗粒的$Q$,可以简单且准确地计算超材料的有效磁导率或介电常数,而不需要复杂的模拟、制造或测量。实验验证表明,从单个制造的自谐振回路的测量$Q$分析估计的复磁导率与从超材料板的$S$参数测量提取的复磁导率一致,好于20%。这种$Q$等效性将满足给定损耗约束的超材料的设计简化为满足特定$Q$约束的谐振粒子的设计的更简单问题。该分析还产生用于估计由于欧姆损耗而导致的平面环形磁性超材料的损耗角正切的简单解析表达式。结果表明,$\tan δ\approx 0.001$是一个很强的下限磁损耗角正切的频率不太远,从1 GHz。超材料的欧姆损耗与超材料颗粒的电尺寸成反比,这表明在固定频率下减小颗粒尺寸存在损耗损失。

英文摘要:

Practical design parameters of resonant metamaterials, such as loss tangent, are derived in terms of the quality factor $Q$ of the resonant effective medium permeability or permittivity. Through electromagnetic simulations of loop-based resonant particles, it is also shown that the $Q$ of the effective medium response is essentially equal to the $Q$ of an individual resonant particle. Thus, by measuring the $Q$ of a single fabricated metamaterial particle, the effective permeability or permittivity of a metamaterial can be calculated simply and accurately without requiring complex simulations, fabrication, or measurements. Experimental validation shows that the complex permeability analytically estimated from the measured $Q$ of a single fabricated self-resonant loop agrees with the complex permeability extracted from $S$ parameter measurements of a metamaterial slab to better than 20%. This $Q$ equivalence reduces the design of a metamaterial to meet a given loss constraint to the simpler problem of the design of a resonant particle to meet a specific $Q$ constraint. This analysis also yields simple analytical expressions for estimating the loss tangent of a planar loop magnetic metamaterial due to ohmic losses. It is shown that $\tan δ\approx 0.001$ is a strong lower bound for magnetic loss tangents for frequencies not too far from 1 GHz. The ohmic loss of the metamaterial varies inversely with the electrical size of the metamaterial particle, indicating that there is a loss penalty for reducing the particle size at a fixed frequency.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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