Lattice sums for gratings and arrays
Lattice sums for gratings and arrays
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光栅和阵列的晶格和
DOI：
10.1063/1.1310361
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
K. Grubits
中科院分区：
文献类型：
--
作者：
R. McPhedran;N. Nicorovici;L. Botten;K. Grubits
本文研究了Helmholtz方程的准周期绿色函数在一般二维阵列上的格点和。阵列和与单个准周期线上的阵列和有关，它们的差可用指数收敛级数表示。结果表明，我们的表达式可以用来产生有关的光子带隙态的情况下，与复杂的准周期（布洛赫）矢量的总和。我们的表达式的精度和计算速度的说明。
Lattice sums arising in quasiperiodic Green’s functions for the Helmholtz equation, over general two-dimensional arrays are investigated. The array sums are related to those over a single quasiperiodic line of sources, and their difference is be expressed in terms of exponentially convergent series. It is shown that our expressions can be used to generate the sums pertaining to the case of photonic gap states, associated with complex quasiperiodicity (Bloch) vectors. The accuracy and computational speed of our expressions are illustrated.