Rumpf Raymond C, Pazos Javier
EM Lab, W. M. Keck Center for 3D Innovation, University of Texas at El Paso, 500 West University Avenue, El Paso, Texas 79968, USA.
Opt Express. 2012 Jul 2;20(14):15263-74. doi: 10.1364/OE.20.015263.
It is often desired to functionally grade and/or spatially vary a periodic structure like a photonic crystal or metamaterial, yet no general method for doing this has been offered in the literature. A straightforward procedure is described here that allows many properties of the lattice to be spatially varied at the same time while producing a final lattice that is still smooth and continuous. Properties include unit cell orientation, lattice spacing, fill fraction, and more. This adds many degrees of freedom to a design such as spatially varying the orientation to exploit directional phenomena. The method is not a coordinate transformation technique so it can more easily produce complicated and arbitrary spatial variance. To demonstrate, the algorithm is used to synthesize a spatially variant self-collimating photonic crystal to flow a Gaussian beam around a 90° bend. The performance of the structure was confirmed through simulation and it showed virtually no scattering around the bend that would have arisen if the lattice had defects or discontinuities.
人们常常希望对诸如光子晶体或超材料之类的周期性结构进行功能分级和/或空间变化，但文献中尚未提供这样做的通用方法。这里描述了一种直接的程序，它允许晶格的许多属性同时在空间上变化，同时产生仍然光滑和连续的最终晶格。这些属性包括晶胞取向、晶格间距、填充率等等。这为设计增加了许多自由度，例如通过空间改变取向来利用方向现象。该方法不是坐标变换技术，因此它可以更容易地产生复杂和任意的空间变化。为了进行演示，该算法被用于合成一种空间变化的自准直光子晶体，以使高斯光束围绕90°弯曲流动。通过模拟证实了该结构的性能，并且它在弯曲处几乎没有散射，而如果晶格有缺陷或不连续则会出现散射。
