Mathematical analysis of plasmonic resonance for 2-D photonic crystal |
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Authors: | Guang-Hui Zheng |
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Institution: | College of Mathematics and Econometrics, Hunan University, Changsha 410082, Hunan Province, PR China |
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Abstract: | In this article, we study the plasmonic resonance of infinite photonic crystal mounted by the double negative nanoparticles in two dimensions. The corresponding physical model is described by the Helmholz equation with so called Bloch wave condition in a periodic domain. By using the quasi-periodic layer potential techniques and the spectral theorem of quasi-periodic Neumann–Poincaré operator, the quasi-static expansion of the near field in the presence of nanoparticles is derived. Furthermore, when the magnetic permeability of nanoparticles satisfies the Drude model, we give the conditions under which the plasmonic resonance occurs, and the rate of blow up of near field energy with respect to nanoparticle's bulk electron relaxation rate and filling factor are also obtained. It indicates that one can appropriately control the bulk electron relaxation rate or filling factor of nanoparticle in photonic crystal structure such that the near field energy attains its maximum, and enhancing the efficiency of energy utilization. |
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Keywords: | Plasmonic resonance Photonic crystal Quasi-periodic Neumann–Poincaré operator Quasi-periodic layer potential Drude model Quasi-static regime |
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