Superdimensional Metamaterial Resonators From Sub-Riemannian Geometry
Superdimensional Metamaterial Resonators From Sub-Riemannian Geometry
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DOI：
10.1137/17m1130964
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发表时间：
2014-09
期刊：
影响因子：
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通讯作者：
A. Greenleaf;H. Kettunen;Y. Kurylev;M. Lassas;G. Uhlmann
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文献类型：
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作者：
A. Greenleaf;H. Kettunen;Y. Kurylev;M. Lassas;G. Uhlmann
我们提出了一个全新的方法设计的超材料阵列，有效的任何波建模的亥姆霍兹方程，包括标量光学和声学。这些器件的设计和分析是基于具有简谐势和简并势的Schr\“odinger波动方程解的本征值和本征函数渐近性。这些谐振器表现为超维的，具有比从物理维度预期的更高的本征值的局部密度和更大的波集中，例如，平面谐振器用作3维或更高维的介质，而体材料有效地用作4维或更高维的介质。应用包括具有高密度谐振频率和巨大聚焦的天线，并且可能是宽带的。
We propose a fundamentally new method for the design of metamaterial arrays, valid for any waves modeled by the Helmholtz equation, including scalar optics and acoustics. The design and analysis of these devices is based on eigenvalue and eigenfunction asymptotics of solutions to Schr\"odinger wave equations with harmonic and degenerate potentials. These resonators behave superdimensionally, with a higher local density of eigenvalues and greater concentration of waves than expected from the physical dimension, e.g., planar resonators function as 3- or higher-dimensional media, and bulk material as effectively of dimension 4 or higher. Applications include antennas with a high density of resonant frequencies and giant focussing, and are potentially broadband.