随机介质结构中的谐振效应
Resonant effects in random dielectric structures
摘要：
近年来，利用均匀化技术发展了大波长二维光子晶体中的人工磁性理论。在本文中，我们在严格的随机框架内追求这种方法：电介质平行纳米棒随机布置，每个纳米棒都具有随机介电常数ε（ω），直到很大的比例因子，其定律由窗口上的密度表示Δ=[a，b]x[0，h]复平面。我们给出了精确的条件下，可以进行均匀化过程的初始概率法（介电常数，半径和位置的杆），从而导致一个确定性的色散规律的有效磁导率可能是负的实部。随后，极限分析h->0，考虑ε的密度定律，其集中在实轴上，揭示了由于微观结构中存在共振而导致的奇异行为。
英文摘要：
Recently, a theory for artificial magnetism in two-dimensional photonic crystals has been developed for large wavelength using homogenization techniques. In this paper we pursue this approach within a rigorous stochastic framework: dielectric parallel nanorods are randomly disposed, each of them having, up to a large scaling factor, a random permittivity ε(ω) whose law is represented by a density on a window Δ=[a,b]x[0,h] of the complex plane. We give precise conditions on the initial probability law (permittivity, radius and position of the rods) under which the homogenization process can be performed leading to a deterministic dispersion law for the effective permeability with possibly negative real part. Subsequently a limit analysis h->0, accounting a density law of ε, which concentrates on the real axis, reveals singular behavior due to the presence of resonances in the microstructure.
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。
