The study of photonic crystals, artificial materials whose dielectric properties can be tailored according to the stacking of their constituents, remains an attractive research field, and it is the basis of photonic devices based on the generation, processing, and storage of photons. In this paper, we employ a transfer-matrix treatment to study the propagation of light waves in periodic, quasiperiodic (Fibonacci, Octonacci, and Dodecanacci), and random dielectric multilayers with graphene embedded. The structures considered here are composed of two building blocks, silicon dioxide (building block $A = {\rm{Si}}{{\rm{O}}_2}$) and titanium dioxide (building block $B = {\rm{Ti}}{{\rm{O}}_2}$). We calculate their transmission spectra as a function of incident angle $\theta$ and reduced frequency $\Omega$. Our main goal is to investigate the enhancement of the transmission due to the presence of graphene. In particular, we show that bandgap regions become passband regions when graphene is embedded in the optical multilayers. More specifically, for a range of the incident angle $\theta$ and reduced frequency $\Omega$, the PCs with graphene embedded display an unexpected property: the electromagnetic radiation is transmitted mainly through the multilayers and not reflected or absorbed as expected for large structures.

中文翻译：

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嵌入的石墨烯在周期性，准周期性和随机光子晶体中诱导的透射增强

光子晶体是一种人工材料，其介电性能可以根据其组成的堆叠进行调整，因此仍然是一个有吸引力的研究领域，它是基于光子的产生，处理和存储的光子器件的基础。在本文中，我们采用转移矩阵处理来研究光波在周期性，准周期（Fibonacci，Octonacci和Dodecanacci）以及嵌有石墨烯的无规介电多层中的传播。这里考虑的结构由两个构造块组成，二氧化硅（构造块$ A = {\ rm {Si}} {{\ rm {O}} _ 2} $）和二氧化钛（构造块$ B = {\ rm {Ti}} {{\ rm {O}} _ 2} $）。我们计算它们的透射光谱作为入射角$ \ theta $的函数并降低了频率$ \ Omega $。我们的主要目标是研究由于石墨烯的存在而导致的透射增强。特别地，我们显示出当石墨烯嵌入光学多层膜中时，带隙区域变为通带区域。更具体地说，对于入射角$ \ theta和降低的频率$ \ Omega $而言，嵌入石墨烯的PC显示出意外的特性：电磁辐射主要通过多层传输，并且不会像预期的那样被反射或吸收结构。