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的公式，（B）完成覆盖（a）的哈密顿公式，（c）数值计算得到球构成的光子晶体中法拉第旋转的可靠数据。(a)完成100%，并且（B）完成50%。研究发现，当光子态的电磁泄漏阻尼常数较大时，所得到的哈密顿量不足以完全覆盖光子态。由于这个问题没有得到解决，该项目没有达到目标（c）的终点。相反，我们集中在现有的实验和理论之间的史密斯-珀塞尔光谱从光子晶体未解决的差异。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。最后得到了与实验符合得很好的线形。

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.