Kaspar P, Kappeler R, Erni D, Jäckel H
Electronics Laboratory, ETH Zurich, CH-8092 Zürich, Switzerland.
Opt Express. 2011 Nov 21;19(24):24344-53. doi: 10.1364/OE.19.024344.
The concept of the so-called light line is a useful tool to distinguish between guided and non-guided modes in dielectric slab waveguides. Also for more complicated structures with 2D mode confinement, the light lines can often be used to divide a dispersion diagram into a region of a non-guided continuum of modes, a region of discrete guided modes and a forbidden region, where no propagating modes can exist. However, whether or not the light line is a concept of practical relevance depends on the geometry of the structure. This fact is sometimes ignored. For instance, in the literature on photonic crystal waveguides, it is often argued that substrate-type photonic crystal waveguides with a weak vertical confinement are inherently lossy, since the entire bandgap including the line defect modes is typically located above the light line of the substrate. The purpose of this article is to illustrate that this argument is inaccurate and to provide guidelines on how an improved light line concept can be constructed.
所谓光线的概念是区分介质平板波导中导模和非导模的有用工具。对于具有二维模式限制的更复杂结构，光线通常也可用于将色散图划分为非导模连续区域、离散导模区域和禁带区域，在禁带区域不存在传播模式。然而，光线是否具有实际相关性取决于结构的几何形状。这一事实有时会被忽视。例如，在光子晶体波导的文献中，经常有人认为垂直限制较弱的衬底型光子晶体波导本质上是有损耗的，因为包括线缺陷模式在内的整个带隙通常位于衬底的光线之上。本文的目的是说明这一论点是不准确的，并提供关于如何构建改进的光线概念的指导原则。
