Three-dimensional dispersive metallic photonic crystals with a bandgap and a high cutoff frequency.

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.

Institutional change and coproduction of public services: The effect of charter schools on parental involvement

Recent discussions of school choice have revived arguments that the decentralization of governing institutions can enhance the quality of public services by increasing the participation of intended beneficiaries in the production of those services. We use data from the Schools and Staffing Survey to examine the extent to which the decentralization of authority to charter schools induces parents to become more involved in their children's schools. We find that parents are indeed more involved in charter schools than in observationally similar public schools, especially in urban elementary and middle schools. Although we find that this difference is partly attributable to measurable institutional and organizational factors, we also find that charter schools tend to be established in areas with above-average proportions of involved parents, and we find suggestive evidence that, within those areas, it is the more involved parents who tend to select into charter schools. Thus, while the institutional characteristics of charter schools do appear to induce parents to become more involved in their children's schools, such characteristics are only part of the explanation for the greater parental involvement in charter schools than in traditional public schools. © The Author 2005. Published by Oxford University Press. All rights reserved.