• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文会议>Metamaterials: Fundamentals and applications IV >Lyapunov exponents for one-dimensional aperiodic photonic bandgap structures
【24h】

Lyapunov exponents for one-dimensional aperiodic photonic bandgap structures

机译：一维非周期性光子带隙结构的李雅普诺夫指数

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Existing in the "gray area" between perfectly periodic and purely randomized photonic bandgap structures are the so-called aperoidic structures whose layers are chosen according to some deterministic rule. We consider here a one-dimensional photonic bandgap structure, a quarter-wave stack, with the layer thickness of one of the bilayers subject to being either thin or thick according to five deterministic sequence rules and binary random selection. To produce these aperiodic structures we examine the following sequences: Fibonacci, Thue-Morse, Period doubling, Rudin-Shapiro, as well as the triadic Cantor sequence. We model these structures numerically with a long chain (approximately 5,000,000) of transfer matrices, and then use the reliable algorithm of Wolf to calculate the (upper) Lyapunov exponent for the long product of matrices. The Lyapunov exponent is the statistically well-behaved variable used to characterize the Anderson localization effect (exponential confinement) when the layers are randomized, so its calculation allows us to more precisely compare the purely randomized structure with its aperiodic counterparts. It is found that the aperiodic photonic systems show much fine structure in their Lyapunov exponents as a function of frequency, and, in a number of cases, the exponents are quite obviously fractal.
机译：存在于完全周期性和纯粹随机化的光子带隙结构之间的“灰色区域”中的是所谓的非周期性结构，其层根据某种确定性规则进行选择。我们在这里考虑一维光子带隙结构，四分之一波堆叠，根据五个确定性序列规则和二元随机选择，双层中一个双层的层厚可能变薄或变厚。为了产生这些非周期性结构，我们检查了以下序列：斐波那契，图埃-莫尔斯，周期倍增，鲁丁-萨皮罗以及三重Cantor序列。我们使用一个长链（大约5,000,000）的传递矩阵对这些结构进行数值建模，然后使用Wolf的可靠算法为矩阵的长积计算（上）Lyapunov指数。 Lyapunov指数是统计上表现良好的变量，用于在层随机化时表征安德森局部化效应（指数约束），因此其计算使我们可以更精确地将纯随机化结构与非周期性结构进行比较。已经发现，非周期性光子系统的李雅普诺夫指数显示出非常精细的结构，随频率变化，并且在许多情况下，指数显然是分形的。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号