Band Structure of Metal/Dielectric Photonic Crystals (pp. 57-80)
Authors: (Yi-Xin Zong and Jian-Bai Xia, SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, P. R. China)
Abstract: Owing to the photonic band gap effect, light propagation can be controlled
in photonic crystals (PCs). In this way, the propagation of light
can be controlled, which enables fabrication of novel photonic devices
and improves properties of existing ones. The PCs containing metallic
mediumhave attracted special interests due to the frequency-dependent of
dielectric constant. Based on the numerical results of photonic band structures,
many properties and applications can be predicted. Therefore, it is
of both intrinsic and practical interest to develop a numerical framework
capable of describing and distinguishing the photonic band structures of
metal/dielectric (M/D) PCs.
The traditional plane wave expansion method is a straightforward
method for numerical calculations of dielectric PCs band structures.
However, for theM/D PCs, the resulting secular equation is nonlinear and
hard to solve as the frequency-dependent dielectric constants are involved.
In this chapter, an improved plane wave expansion method is proposed for
the calculation of photonic bands of M/D PCs with the Drude dielectric
function model without solving a nonlinear secular equation. The proposed
method is applicable to all dimensional M/D PCs. For the purpose
of illustration, this method was applied to the band structure calculations
of one-dimensional (1D) and three kinds of two-dimensional (2D) M/D
PC structures. In addition the photon density of state (DOS) is calculated
along with the band structure.
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