含石墨烯分界面有耗分层介质的传播矩阵

王飞; 魏兵

doi:10.7498/aps.68.20190823

摘要

给出一种适用于含导电界面的有耗分层介质的传播矩阵方法. 利用相位匹配原理给出斜入射时有耗介质波矢量的实部和虚部, 二者方向不同使得在介质中传播非均匀平面波. 根据边界条件, 推导了跨越石墨烯界面的传播矩阵, 以及“无限薄”石墨烯层的反透射系数解析式. 最终将传播矩阵方法推广应用于含石墨烯界面的有耗分层介质情形, 可用于快速解析分析分层介质与导电界面复合结构的反透射和电波传播特性.

关键词:

In this paper, a propagation matrix method for lossy layered medium with conductive interfaces is presented. Firstly, on the basis of phase matching principle, an approach to calculating the real and imaginary part of wave vector in a lossy layered medium is given for the case of oblique incident plane electromagnetic wave. Since the direction of real and imaginary part of wave vector are different, the plane wave propagating in lossy dielectric layers is inhomogeneous, which extends the traditional propagation matrix method and makes it suitable for the complex lossy medium. Then, the propagation matrix across graphene interface is deduced by using the electromagnetic field boundary conditions, and the analytical expression of the reflection and transmission coefficient for “infinite thin” graphene layer are given. Finally, the propagation matrix of lossy layered medium with conductive interface is obtained by embedding graphene interface into the layered medium, which can be used for fast analyzing the reflection, transmission and propagation of plane wave in composite structure of layered medium and conductive interface. The validity of the proposed method is demonstrated by calculating the single-layered shielding effectiveness of grapheme. The effects of graphene coating on the reflection, transmission and absorption of plane wave in half-space medium and one-dimensional photonic crystal are also investigated. The results show that the graphene layer can enhance surface reflection and optical absorption.

Keywords:

作者及机构信息

王飞^1,2,
魏兵^1,2

1.
西安电子科技大学物理与光电工程学院, 西安　710071

2.
西安电子科技大学信息感知技术协同创新中心, 西安　710071

通信作者: 王飞, wfei79@163.com

基金项目: 国家自然科学基金(批准号: 61401344, 61571348)和高等学校学科创新引智计划(批准号: B17035)资助的课题

Authors and contacts

Wang Fei^1,2,
Wei Bing^1,2

1.
School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China

2.
Collaborative Innovation Center of Information Sensing and Understanding at Xidian University, Xi’an 710071, China

Corresponding author: Wang Fei, wfei79@163.com

Funds: Project supported by the National Natural Scientific Foundation of China (Grant Nos. 61401344, 61571348) and the Overseas Expertise Introduction Project for Discipline Innovation, China (Grant No. B17035)

文章全文 : translate this paragraph

参考文献

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsove A A 2004 Science 306 666 Google Scholar
[2]	Geim A K 2009 Science 324 1530 Google Scholar
[3]	Sensale-Rodriguez B, Yan R, Kelly M, Fang T, Tahy K, Hwang W S, Jena D, Liu L, Xing H G 2012 Nature Commun. 3 780 Google Scholar
[4]	Alaee R, Farhat M, Rockstuhl C, Lederer F 2012 Opt. Express 20 28017 Google Scholar
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施引文献

图 1 分层介质

Fig. 1. Stratified medium.

下载: 全尺寸图片幻灯片

图 2 石墨烯电导率和SE　(a) 电导率实虚部; (b) SE

Fig. 2. Graphene conductivity and shielding effectiveness: (a) Real and imaginary parts of conductivity; (b) SE.

下载: 全尺寸图片幻灯片

图 3 石墨烯单层的反射和透射系数模值　(a) TE模; (b) TM模

Fig. 3. Modulus of reflective and transmittance coefficients of a graphene sheet:(a) TE mode; (b) TM mode.

下载: 全尺寸图片幻灯片

图 4 含石墨烯涂层CdTe半空间的反透射系数模值(TE模)　(a) 反射系数; (b) 透射系数

Fig. 4. Modulus of reflective and transmittance coefficients of CdTe half-space containing graphene coating (TE mode): (a) Reflective coefficient; (b) transmittance coefficient.

下载: 全尺寸图片幻灯片

图 5 含石墨烯涂层CdTe半空间的反透射系数模值(TM模)　(a) 反射系数; (b) 透射系数

Fig. 5. Modulus of reflective and transmittance coefficients of CdTe half-space containing graphene coating (TM mode): (a) Reflective coefficient; (b) transmittance coefficient.

下载: 全尺寸图片幻灯片

图 6 CdTe半空间的反透射光场(TE模)　(a) 无石墨烯涂层; (b) 含石墨烯涂层

Fig. 6. Optical field of reflection and transmission coefficients of CdTe half-space (TE mode): (a) Without graphene coating; (b) with graphene coating.

下载: 全尺寸图片幻灯片

图 7 CdTe半空间的反透射光场(TM模)　(a) 无石墨烯涂层; (b) 含石墨烯涂层

Fig. 7. Optical field of reflection and transmission coefficients of CdTe half-space (TM mode): (a) Without graphene coating; (b) with graphene coating.

下载: 全尺寸图片幻灯片

图 8 Si/SiO₂周期结构型1DPC

Fig. 8. Si/SiO₂ 1DPC with periodic structure.

下载: 全尺寸图片幻灯片

图 9 含石墨烯涂层Si/SiO₂周期结构1DPC的反透射系数　(a) 反射系数; (b) 透射系数

Fig. 9. Modulus of reflective and transmittance coefficients of Si/SiO₂ 1DPC containing graphene sheet: (a) Reflective coefficient; (b) transmittance coefficient.

下载: 全尺寸图片幻灯片

图 10 含石墨烯界面Si/SiO₂周期结构1DPC的吸收率

Fig. 10. Absorbance of Si/SiO₂ 1DPC containing graphene sheet.

下载: 全尺寸图片幻灯片

图 11 含石墨烯涂层Si/SiO₂周期结构1DPC的吸收率(TE模)　(a) 无涂层; (b) 表面涂层; (c) 底层涂层

Fig. 11. Contour plots of the absorbance of the Si/SiO₂ 1DPC as a function of the light frequency and the incident angles for the TE mode: (a) Without graphene sheet; (b) graphene sheet on the top; (c) graphene sheet on the bottom.

下载: 全尺寸图片幻灯片

图 12 含石墨烯涂层Si/SiO₂周期结构1DPC的吸收率(TM模)　(a) 无涂层; (b) 表面涂层; (c) 底层涂层

Fig. 12. Contour plots of the absorbance of the Si/SiO₂ 1DPC as a function of the light frequency and the incident angles for the TE mode: (a) Without graphene sheet; (b) graphene sheet on the top; (c) graphene sheet on the bottom.

下载: 全尺寸图片幻灯片

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsove A A 2004 Science 306 666 Google Scholar
[2]	Geim A K 2009 Science 324 1530 Google Scholar
[3]	Sensale-Rodriguez B, Yan R, Kelly M, Fang T, Tahy K, Hwang W S, Jena D, Liu L, Xing H G 2012 Nature Commun. 3 780 Google Scholar
[4]	Alaee R, Farhat M, Rockstuhl C, Lederer F 2012 Opt. Express 20 28017 Google Scholar
[5]	Fallahi A, Perruisseau-Carrier J 2012 Phys. Rev. B 86 195408 Google Scholar
[6]	Sensale-Rodriguez B, Yan R, Rafique S, Zhu M, Li W, Liang X, Gundlach D, Protasenko V, Kelly M M, Jena D, Liu L, Xing H G 2012 Nano Lett. 12 4518 Google Scholar
[7]	Fu M X, Zhang Y 2013 JECT 11 352
[8]	Lee S H, Choi M, Kim T T, Lee S, Liu M, Yin X, Choi H K, Lee S S, Choi C G, Choi S Y, Zhang X, Min B 2012 Nat. Mater. 11 936
[9]	Zuo Z G, Wang P, Ling F R, Liu J S, Yao J Q 2013 Chin. Phys. B 22 097304 Google Scholar
[10]	张玉萍, 张洪艳, 尹贻恒, 刘陵玉, 张晓, 高营, 张会云 2012 物理学报 61 047803 Google Scholar Zhang Y P, Zhang H Y, Yin Y H, Liu L Y, Zhang X, Gao Y, Zhang H Y 2012 Acta Phys. Sin. 61 047803 Google Scholar
[11]	Zhu X L, Yan W, Jepsen P U, Hansen O, Mortensen N A Xiao S S 2013 Appl. Phys. Lett. 102 131101 Google Scholar
[12]	Pomar J L G, Alexey Y N, Luis M M 2013 ACS Nano 7 4988 Google Scholar
[13]	Thongrattanasiri S, Koppens F H L, de Abajo F J G 2012 Phys. Rev. Lett. 108 047401 Google Scholar
[14]	Ferreira A, Peres N M R, Ribeiro R M, Stauber T 2012 Phys. Rev. B 85 115438 Google Scholar
[15]	Tian Y C, Jia W, Ren P W, Fan C Z 2018 Chin. Phys. B 27 124205 Google Scholar
[16]	Jia W, Ren P W, Fan C Z, Tian Y C 2019 Chin. Phys. B 28 026102 Google Scholar
[17]	Liu J T, Liu N H, Li J, Li X J, Huang J H 2012 Appl. Phys. Lett. 101 052104 Google Scholar
[18]	Peres N M R, Bludov Y V 2013 EPL 101 58002 Google Scholar
[19]	谢凌云, 肖文波, 黄国庆, 胡爱荣, 刘江涛 2014 物理学报 63 057803 Google Scholar Xie L Y, Xiao W B, Huang G Q, Hu A R, Liu J T 2014 Acta Phys. Sin. 63 057803 Google Scholar
[20]	Zhang H J, Zheng G G, Chen Y Y 2018 Chin. Phys. Lett. 35 038102 Google Scholar
[21]	Lovat G 2012 IEEE Trans. Electromagn. Compat. 54 101 Google Scholar
[22]	葛德彪, 魏兵 2011 电磁波理论 (北京: 科学出版社) 第32, 56−65页 Ge D B, Wei B 2011 Electromagnetic Wave Theory (Beijing: Science Press) pp32, 56−65 (in Chinese)
[23]	George W H 2008 J. Appl. Phys. 103 064302 Google Scholar
[24]	孙旺, 李粮生, 张景, 殷红成 2018 雷达学报 7 67 Google Scholar Sun W, Li L S, Zhang J, Yin H C 2018 J. Radars 7 67 Google Scholar

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含石墨烯分界面有耗分层介质的传播矩阵