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
Fund Project: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)
Received Date:28 May 2019
Accepted Date:29 September 2019
Available Online:27 November 2019
Published Online:01 December 2019
Abstract: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:graphene/ lossy stratified media/ propagation matrix
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 Figure5. Modulus of reflective and transmittance coefficients of CdTe half-space containing graphene coating (TM mode): (a) Reflective coefficient; (b) transmittance coefficient.
图6和图7是该CdTe半空间界面TE和TM入射波的反透射光场分布, 图(a)和(b)分别是界面不含和含有石墨烯涂层时的情形, 从图6和图7可见, 石墨烯涂层不改变反透射角, 但增强了表面反射, 起到了一定屏蔽作用. 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 Figure6. Optical field of reflection and transmission coefficients of CdTe half-space (TE mode): (a) Without graphene coating; (b) with graphene coating.
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 Figure7. Optical field of reflection and transmission coefficients of CdTe half-space (TM mode): (a) Without graphene coating; (b) with graphene coating.
图11和图12分别是TE和TM波情形下, 该光子晶体的吸收率随频率和入射角变化的伪色彩图, 其中子图(a), (b)和(c)分别是无石墨烯涂层、涂层位于表面和底层时的情形, 整体上看, 位于表面的涂层对光吸收的增强效应更为明显, 而且对TE波的吸收要强于TM波. 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 Figure11. 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.
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 Figure12. 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.