Local density of states in three-dimensional photonic crystals: Calculation and enhancement effects
Local density of states in three-dimensional photonic crystals: Calculation and enhancement effects
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DOI：
10.1103/physrevb.67.155114
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发表时间：
2003-04
影响因子：
3.7
通讯作者：
Rongzhou Wang;Xue-Hua Wang;B. Gu;Guo-zhen Yang
中科院分区：
文献类型：
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作者：
Rongzhou Wang;Xue-Hua Wang;B. Gu;Guo-zhen Yang
光子晶体（PC）中的电场特征向量模\E-n(k,r)\被证实对于k星中的k个点集合是不同的，即\E-n(alpha[k],r)\不等于\E-n(k,r)\，其中{alpha}表示晶格点群的操作。因此，在计算局域态密度（LDOS）时，应包括整个布里渊区的所有k点；否则，结果通常是不正确的。根据群论，严格证明了变换关系\E-n(alpha[k],r)\ = \E-n(k,{alpha\t}(-1)r)\（这里t表示晶体的平移算子，包括滑移算子）。这种变换可以大大节省本征模方程对角化过程所花费的计算时间。基于该变换，给出了计算LDOS的正确表达式。 LDOS 的这个表达式满足晶格的对称性。给出了与之前基于 \E-n(alpha[k],r)\ = \E-n(k,r)\ 的结果的详细比较。与真空情况相比，揭示了具有 fcc 结构和金刚石结构的 PC 中 LDOS 的增强效果。发现LDOS在金刚石结构中的增强效果远大于fcc结构中的增强效果。
The modulus of electric field eigenvector in photonic crystals (PCs), \E-n(k,r)\, is confirmed to be variant for a set of k points in a k star, namely, \E-n(alpha[k],r)\ not equal \E-n(k,r)\, where {alpha} represents the operations of the lattice point group. Therefore, in the calculation of the local density of states (LDOS), all k points in the entire Brillioun zone should be included; otherwise, the results are generally incorrect. According to group theory, the transformation relation \E-n(alpha[k],r)\ = \E-n(k,{alpha\t}(-1)r)\ (here t represents the translation operator of the crystal, including the glide operation) is rigorously proven. This transformation can greatly save computing time spent in the diagonalization procedure of the eigenmode equation. Based upon this transform, a correct expression of calculating the LDOS is presented. This expression of the LDOS satisfies symmetry of the lattice. The detailed comparisons with the previous results based upon \E-n(alpha[k],r)\ = \E-n(k,r)\ are given. The enhancement effects of the LDOS in the PCs with a fcc structure and a diamond structure, compared to the vacuum case, are revealed. It is found that the enhancement effect of the LDOS in the diamond structure is much larger than that in the fcc structure.