负折射率材料：一些数学观点
Negative index materials: some mathematical perspectives
摘要：
负折射率材料是人工结构，其折射率在某些频率范围内具有负值。这些材料由Veselago在1964年提出并进行了理论研究，并由Shelby，Smith和Schultz在2001年进行了实验证实。新的制造技术现在允许负折射率材料的建设规模是有趣的应用，这使他们成为一个非常活跃的研究课题。本文报道了有关负折射率材料性质的各种数学结果及其应用。本文讨论的主题包括使用互补介质的超透镜，使用互补介质的隐身，通过异常局域共振隐身物体，以及由色散超材料组成的介质中的适定性和有限速度传播。有些结果已经改进，并有比原来的更简单的证明。
英文摘要：
Negative index materials are artificial structures whose refractive index has a negative value over some frequency range. These materials were postulated and investigated theoretically by Veselago in 1964 and were confirmed experimentally by Shelby, Smith, and Schultz in 2001. New fabrication techniques now allow for the construction of negative index materials at scales that are interesting for applications, which has made them a very active topic of investigation. In this paper, we report various mathematical results on the properties of negative index materials and their applications. The topics discussed herein include superlensing using complementary media, cloaking using complementary media, cloaking an object via anomalous localized resonance, and the well-posedness and the finite speed propagation in media consisting of dispersive metamaterials. Some of the results have been refined and have simpler proofs than the original ones.
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。
