Li Zhi-Yuan, Lin Lan-Lan
Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Apr;67(4 Pt 2):046607. doi: 10.1103/PhysRevE.67.046607. Epub 2003 Apr 15.
Transfer-matrix methods adopting a plane-wave basis have been routinely used to calculate the scattering of electromagnetic waves by general multilayer gratings and photonic crystal slabs. In this paper we show that this technique, when combined with Bloch's theorem, can be extended to solve the photonic band structure for 2D and 3D photonic crystal structures. Three different eigensolution schemes to solve the traditional band diagrams along high-symmetry lines in the first Brillouin zone of the crystal are discussed. Optimal rules for the Fourier expansion over the dielectric function and electromagnetic fields with discontinuities occurring at the boundary of different material domains have been employed to accelerate the convergence of numerical computation. Application of this method to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method.
采用平面波基的转移矩阵方法已被常规用于计算一般多层光栅和光子晶体平板对电磁波的散射。在本文中，我们表明，当该技术与布洛赫定理相结合时，可以扩展用于求解二维和三维光子晶体结构的光子带结构。讨论了三种不同的本征解方案，用于求解晶体第一布里渊区中沿高对称线的传统能带图。已采用在不同材料域边界处出现不连续性的介电函数和电磁场的傅里叶展开的最优规则，以加速数值计算的收敛。将该方法应用于一类重要的三维逐层光子晶体，揭示了这种不同方法相对于传统平面波展开法的卓越收敛性。
