Three-dimensional dispersive metallic photonic crystals with a bandgap and a high cutoff frequency.
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The goal of this work is to analyze three-dimensional dispersive metallic photonic crystals (PCs) and to find a structure that can provide a bandgap and a high cutoff frequency. The determination of the band structure of a PC with dispersive materials is an expensive nonlinear eigenvalue problem; in this work we propose a rational-polynomial method to convert such a nonlinear eigenvalue problem into a linear eigenvalue problem. The spectral element method is extended to rapidly calculate the band structure of three-dimensional PCs consisting of realistic dispersive materials modeled by Drude and Drude-Lorentz models. Exponential convergence is observed in the numerical experiments. Numerical results show that, at the low frequency limit, metallic materials are similar to a perfect electric conductor, where the simulation results tend to be the same as perfect electric conductor PCs. Band structures of the scaffold structure and semi-woodpile structure metallic PCs are investigated. It is found that band structures of semi-woodpile PCs have a very high cutoff frequency as well as a bandgap between the lowest two bands and the higher bands.
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Professor of Electrical and Computer Engineering
Qing H. Liu received the Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign in 1989. His research interests have been in computational electromagnetics and acoustics, inverse problems, and their application in geophysics, nanophotonics, and biomedical imaging. He has published more than 300 refereed journal papers in these areas. He was a Research Assistant (September 1986 to December 1988) and then a Postdoctoral Research Associate (January 1989 to Feb