| Summary: | 碩士 === 國立臺灣大學 === 物理研究所 === 99 === Magnetic resonances are essential for achieving negative permeability and play important roles in realizing negative refraction phenomena. Surface plasmonic resonances confined in metallic nanostructures (i.e. metamaterials) are known to exhibit magnetic resonances that can be tailored by the structural geometries. In the past, researchers utilized standing wave model to explain the resonant frequencies of simply-connected metamaterials. Based on this model, the resonant frequencies of a metamaterial are inversely proportional to its structural length. In this work, we find that for a multiply-connected metamaterial, its resonant frequencies can largely deviate from the standing wave model. Remarkably, when the longest or the total length of the metamaterial is fixed, we find that the resonant frequency shows linear dependence on the circumference of the enclosed loop, an unusual phenomenon clearly violates the standing wave model. We also find that self-interactions can affect the frequency vs. length relationships in metamaterials. Importantly, when there is a balance between these effects, we discover a metamaterial whose resonant frequency is independent of its shape, length, or even the constituent materials.
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