Manipulating bandwidth of light absorption at critical coupling: An example of graphene integrated with dielectric photonic structure

Jie Wang, Ang Chen, Yiwen Zhang, Jianping Zeng, Yafeng Zhang, Xiaohan Liu, Lei Shi, and Jian Zi

Phys. Rev. B 100, 075407 – Published 5 August 2019

Abstract

For an optical absorber, its efficiency and bandwidth determine ultimately its light-collection performance. A general way to realize the high-efficiency absorption and manipulate the absorption bandwidth is certainly important and highly desired. In this paper, based on the coupled-mode theory, a general strategy for tailoring the bandwidth of an absorber (to broaden or narrow it) is presented. A graphene-based absorber integrated with a lossless resonator is designed, and it is shown that by increasing the layer number of graphene and adjusting structure parameters, the broadband absorber at critical coupling could be realized. Meanwhile, by adjusting the location of graphene in the structure, an ultra-narrow-band absorber could also be realized. Present work of controlling both efficiency and bandwidth of an absorber would be particularly favorable for applications in light harvesting, light emitting devices, and optical modulators.

Received 20 May 2019
Revised 11 July 2019

DOI:https://doi.org/10.1103/PhysRevB.100.075407

Physics Subject Headings (PhySH)

Light propagation, transmission & absorption Nanophotonics Photonic crystals

Graphene

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Jie Wang^1,2, Ang Chen^1,2, Yiwen Zhang^1,2, Jianping Zeng^1,2, Yafeng Zhang³, Xiaohan Liu^1,2,*, Lei Shi^1,2,*, and Jian Zi^1,2,*

¹Department of Physics, Key Laboratory of Micro- and Nano-Photonic Structures (MOE), State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
²Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433, China
³State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China

^*Corresponding authors: liuxh@fudan.edu.cn; lshi@fudan.edu.cn; jzi@fudan.edu.cn

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Issue

Vol. 100, Iss. 7 — 15 August 2019

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Images

Figure 1
(a) Schematic of an optical resonator system coupled with $m$ free-space ports. The arrows indicate the incoming and outgoing waves. (b)–(d) Three key parameters describing absorption performance of a resonance absorber, (b) resonance frequency $ω_{0}$ , (c) intensity, and (d) bandwidth of absorption. $ω_{0}$ is determined by the resonance mode the resonantor could support. The absorption intensity and bandwidth are determined by two rates, absorption rate $γ_{a}$ and radiation rate $γ_{r}$ . The ratio $γ_{a} / γ_{r}$ and sum $γ_{a} + γ_{r}$ determine absorption intensity and bandwidth, respectively.
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Figure 2
(a) Schematic of a ${Si}_{3} N_{4}$ PhC slab which is a square lattice at each lattice point located one cylindrical air hole. (b) The reflection spectra as a function of wavelength and filling fraction represented by the diameter of the air hole at normal incidence. (c) shows the distribution of ${| E |}^{2}$ on the $x − z$ cross-sectional plane through the center of air hole where the diameter of the air hole is $d = 200 nm$ . The scale bar is 200 nm. (d) The reflection spectra of the PhC slab with $p = 500, h = 100$ , and $d = 200 nm$ . The CMT results (dashed red curve) agree excellently with the simulation (solid black curve). (e) $γ_{r}$ of the resonance guided mode as a function of air hole diameter for different thicknesses of the slab.
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Figure 3
(a)–(e) Upper black curves correspond to the graphene absorption for different layers at the critical coupling condition, and the lower panels show absorption spectra as a function of wavelength and filling fraction. Critical coupling points are marked by arrows. From (a)–(e), the layer numbers of graphene are increased as 1, 2, 4, 7, and 8, respectively. The red curves show the absorption of bare graphene with different layer numbers. The inset in (a): schematic of graphene located at the center plane of the slab. The inset in (e): detailed maximum absorption of graphene for eight (black curve), nine (red curve), and ten (blue curve) layers. For the PhC slab, $p = 500$ and $h = 100 nm$ .
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Figure 4
(a) Absorption of graphene with different layers versus normalized resonance wavelength. Solid black, green, red, and blue curves represent the absorption of graphene with one, three, six, and eight layers, respectively, whereas dashed blue, black, and red curves in the inset (a) represent eight-, nine-, and ten-layer graphene, respectively. (b) Absorption efficiency of a two-port absorber at resonance wavelength as a function of absorption rate $γ_{a}$ and radiation rate $γ_{r}$ . Hollow dots represent $γ_{a}$ and $γ_{r}$ of the graphene-based absorber integrated with the PhC slab for different layers of graphene. The arrow shows the increasing trend of graphene layers. Parameters of the PhC slab are the same as those shown in Fig. 3.
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Figure 5
(a) and (b) show the narrow-band and ultra-narrow-band absorptions of monolayer graphene at two different locations versus the wavelength for the odd mode, respectively. One is at 20 nm outside the boundary of the slab (a) whereas another is at the center plane of the slab (b). The insets in (a) and (b) are schematic cross-sectional views of the graphene-based absorber integrated with the PhC slab. (c) shows the distribution of ${| E |}^{2}$ at the resonance wavelength 561.66 nm on the $x − z$ cross-sectional plane passing through the center of the air hole for $d = 200 nm$ . The scale bar is 100 nm.
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Figure 6
(a) and (b) show the narrow-band and ultra-narrow-band absorptions of monolayer graphene located at 100 and 200 nm outside the boundary of the slab versus the wavelength for the even mode, respectively. The insets in (a) and (b) are schematic cross-sectional views of the graphene-based absorber integrated with the PhC slab. (c) $γ_{a}$ and filling fraction of the PhC slab at critical coupling as a function of the distance of graphene away from the center plane of the slab.
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