Modeling of the origin of photonic bands in the arrayed dielectric and metallic spheres

1.我们导出了模型哈密顿量，称为光子安德森模型，其中局域光子态与外部平面波态之间的耦合常数。由模型哈密顿量得到的球形介质系统的光学响应与数值计算结果吻合较好。我们推导了平面光子晶体的光子态密度公式，该公式考虑了由于光子能量泄漏到外部区域而引起的光子态的有限寿命。利用该公式，分析了计算得到的电子在光子晶体表面附近运动时的光子发射光谱，并指出这是由于其中的漏光子带激发所致。提出了均匀分布光子散射体系统，其中一组介电柱体随机分布，柱体的相互间距不小于某一最小值。结果表明，该系统具有清晰且鲁棒的频率区，其中光子态密度几乎完全消失。提出了利用这一特殊系统的器件应用。

1.We have derived the model Hamiltonian to be called the photonic Anderson model, in which the coupling constant between a localized photonic state and an outer plane-wave state is obtained. The model Hamiltonian leads to an optical response of a spherical dielectric system which agrees quite well with the numerical calculation.2.We derived the formula of the density of states of photons of photonic crystals with a flat surface, which takes account of the finite lifetime of photonic states arising from the leakage of the photonic energy to the exterior region. By using the formula, the calculated photon emission spectrum from an electron traveling near the surface of photonic crystal is analyzed and is shown to be due to the excitation of leaky photonic bands in it.3.The system called uniformly distributed photonic scatterers is proposed, in which a group of dielectric cylinders are distributed randomly with a sole restriction that the mutual spacing of cylinders is not smaller than a certain minimal value. It is shown that this system has a clear-cut and robust frequency region where the density of states of photons vanishes almost completely. The device application making use of this peculiar system is proposed.