Asatryan A A, Busch K, McPhedran R C, Botten L C, de Sterke C M, Nicorovici N A
School of Physics, University of Sydney, Sydney, NSW 2006, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Apr;63(4 Pt 2):046612. doi: 10.1103/PhysRevE.63.046612. Epub 2001 Mar 29.
Using the exact theory of multipole expansions, we construct the two-dimensional Green's function for photonic crystals, consisting of a finite number of circular cylinders of infinite length. From this Green's function, we compute the local density of states (LDOS), showing how the photonic crystal affects the radiation properties of an infinite fluorescent line source embedded in it. For frequencies within the photonic band gap of the infinite crystal, the LDOS decreases exponentially inside the crystal; within the bands, we find "hot" and "cold" spots. Our method can be extended to three dimensions as well as to treating disorder and represents an important and efficient tool for the design of photonic crystal devices.
利用多极展开的精确理论，我们构建了由有限数量无限长圆柱组成的二维光子晶体格林函数。基于此格林函数，我们计算了局域态密度（LDOS），展示了光子晶体如何影响嵌入其中的无限长荧光线源的辐射特性。对于无限晶体光子带隙内的频率，晶体内部的LDOS呈指数下降；在能带内，我们发现了“热点”和“冷点”。我们的方法可以扩展到三维以及处理无序情况，是光子晶体器件设计的一种重要且高效的工具。
