Smith G H, Botten L C, McPhedran R C, Nicorovici N A
School of Mathematical Sciences, University of Technology, Sydney, New South Wales 2007, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Nov;66(5 Pt 2):056604. doi: 10.1103/PhysRevE.66.056604. Epub 2002 Nov 19.
We develop a formulation for cylinder gratings in conical incidence, using a multipole method. The theory, and its numerical implementation, is applied to two-dimensional photonic crystals consisting of a stack of one-dimensional gratings, each characterized by its plane wave scattering matrix. These matrices are used in combination with Bloch's theorem to determine the band structure of the photonic crystal from the solution of an eigenvalue problem. We show that the theory is well adapted to the difficult task of locating the complete band gaps needed to support air-guided modes in microstructured optical fibers, that is, optical fibers in which the confinement of light in a central air hole is achieved by photonic band-gap effects in a periodic cladding comprising a lattice of air holes in a glass matrix.
我们使用多极方法开发了一种用于圆锥入射圆柱光栅的公式。该理论及其数值实现被应用于由一维光栅堆叠组成的二维光子晶体，每个一维光栅都由其平面波散射矩阵表征。这些矩阵与布洛赫定理结合使用，通过求解特征值问题来确定光子晶体的能带结构。我们表明，该理论非常适合定位支持微结构光纤中空气引导模式所需的完整带隙这一艰巨任务，即通过在包含玻璃基质中气孔晶格的周期性包层中的光子带隙效应来实现光在中心气孔中的限制的光纤。
