Giant Farady effect in tow- and three-dimensional photonic crystals

本项目的目的是(A)建立孤立介质球中磁场对光子场的影响，(B)完善涵盖(A)的哈密顿公式，以及(C)从数值上获得由球组成的光子晶体中的法拉第旋转的可靠数据。(A)100%完成，(B)50%完成。结果表明，当电磁泄漏引起的光子态的阻尼常数较大时，所得到的哈密顿量不足以完全覆盖光子态。由于这个悬而未决的问题，该项目没有走到目标(C)结束的地步。相反，我们专注于光子晶体Smith-Purcell光谱的实验和理论之间尚未解决的差异。我们发现，当电子束的速度相对较高时，有限性起着至关重要的作用。我们最终得到了与实验非常吻合的线形。

The purposes of the present project are (a) formulating the magnetic-field effects on photonic fields in an isolated dielectric sphere, (b) completing the Hamiltonian formalism that covers (a), and (c) obtaining numerically the reliable data for the Farady rotation in photonic crystals made of spheres. (a) is done 100% and (b) is accomplished 50%. It is found that the Hamiltonian obtained is not sufficient to cover fully the photonic states when their damping constant, caused by electromagnetic leakage, is relatively large. Because of this unsolved problem, the project did not go so far as the end of aim (c). Instead, we concentrate on the existing discrepancy unsolved between experiment and theory on the Smith-Purcell spectra from photonic crystals. We found that the finiteness plays an essential role when the velocity of electron beam is relativistically high. We finally obtained the line shape which agrees very well with the experiment.