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Dual-band near-perfect metamaterial absorber based on cylinder MoS2 -dielectric arrays for sensors
Optics Communications 451 (2019) 226–230
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Dual-band near-perfect metamaterial absorber based on cylinder MoS2 -dielectric arrays for sensors Caiyu Qiu a,b , Jianghong Wu a , Rongrong Zhu c,d , Lian Shen c,d , Bin Zheng c,d ,∗ a
College of microelectronics, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, 310027, China Wenzhou Institute of Biomaterials and Engineering, CAS, Wenzhou 325011, China c State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China d The Electromagnetics Academy at Zhejiang University, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China b
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Keywords: MoS2 Metamaterial absorber Dual-band Polarization-insensitive Sensor
ABSTRACT As a two-dimensional (2D) material, the crystalline monolayer molybdenum disulfide (MoS2 ) has drawn extensive attention due to its interesting optical, mechanical and thermal properties compatible with many applications. Here, a dual-band perfect metamaterial absorber (PMA) composed of a simple periodically patterned cylinder/square MoS2 -dielectric silica (SiO2 ) arrays supported by a metal ground plane is proposed and studied by using finite-difference time-domain (FDTD) simulations. Numerical results reveal that the absorption spectrum of the MoS2 -based structure displays two perfect absorption peaks in the visible–NIR region. The interactions between electromagnetic waves and this PMA structure are analyzed through the field distributions and spectral responses in detail. It is also presented that the peak wavelengths can be tuned by manipulating related structural parameters. Compared with previous dual-band PMA, our absorber has only one shape that can greatly simplify the manufacturing process and the absorber is insensitive to the polarization of incident light. Furthermore, this PMA can work as a refractive index sensor with high performance due to its stable near-unity absorption.
1. Introduction Metamaterials are a class of artificial material constructed with periodic ‘‘meta-atoms’’, which can be engineered to manipulate electromagnetic waves and produce unconventional optical properties. Since the pioneering work of Smith et al. [1], massive theoretical and experimental demonstrations of functioning electromagnetic metamaterials have been reported [2,3]. Among these applications, perfect metamaterial absorbers (PMAs) can harvest the power of incident light with near 100% efficiency over wide range of wavelengths [4–6], which have attracted significant research interests after the first investigation by Landy et al. in 2008 [7]. Many PMAs have been proposed, showing practical usage in tasks as diverse as sensing [8], imaging [9], cloaking [10], photodetector [11], photothermal conversion [12], and so on. The discovery of graphene has spawned a flourishing research on 2D layered materials and mixed-dimensional heterostructure based on them [13], which can also be applied for PMAs [14–18]. In particular, the monolayer MoS2 is of direct-gap semiconductor which emits light strongly and facilitates the excitation of electrons. Thus it has been considered as the more preferable atomically thin materials for photodetection [19], photocatalysis [20,21] as well as photovoltaic ∗
devices [22]. With the thickness of ∼0.6 nm, monolayer MoS2 can absorb about 10% of the incident light at normal incidence in the visible and near-infrared range [23]. This value is well above the absorption of metallic and dielectric materials with the same thickness but is not conducive to the application of monolayer MoS2 . Monolayer MoS2 has two prominent absorption peaks at around 605 nm and 660 nm due to its strongly confined excitons and spin–orbit coupling. The peak wavelengths of MoS2 absorption can be tuned in a wide range by manipulating structural parameters and the incident angle in designed MoS2 -based absorbers. Till now, many studies have focused on the enhancement of the optical absorption efficiency in monolayer MoS2 , including the broadband absorption [24–28] and the narrowband absorption [29–33]. Among these studies, several absorption structures have utilized MoS2 as a component to design broadband PMAs [24,28], but narrowband MoS2 based PMAs are rarely reported and usually have a complicated structure [30]. Nevertheless, narrowband PMAs are also important for applications in frequency-selective photodetectors and sensors. In this work, monolayer MoS2 is covered onto the cylinder/square SiO2 and then periodically aligned on a gold substrate to form a compact dual-band absorber in visible–NIR region. In contrast to other PMA
Correspondence to: Zhejiang University, Zheda Road 38#, Hangzhou, 310027, China. E-mail address: [email protected] (B. Zheng).
https://doi.org/10.1016/j.optcom.2019.06.067 Received 15 April 2019; Received in revised form 21 May 2019; Accepted 26 June 2019 Available online 27 June 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
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Optics Communications 451 (2019) 226–230
Fig. 3. (a) Simulated absorption spectrum of proposed MoS2 -based absorber with cylinder (blue) or square (red) arrays under normal incidence. The parameters are chosen as ℎ = 200 nm, 𝛬 = 580 nm and 𝐹 = 0.8. Two absorption peaks are marked as P1 and P2; (b) Real (black line) and imaginary (blue line) parts of the effective impedance (Z) of the PMA. The dashed lines represent the free space impedance 𝑍0 = 1 (red) and the position of the resonance wavelength (pink), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 1. (a) Schematic of the cylinder/square MoS2 -dielectric arrays; (b) Profile of a unit cell of periodic arrays, x-polarized plane wave incidents normally on the arrays.
3. Results and analysis We first start from the case where the electrical vector of plane wave parallels to the 𝑥-axis, that is, illumination of TE-polarized normal incidence light. Fig. 3(a) shows the calculated absorption spectrum of the entire MoS2 -based PMA, where ℎ = 200 nm, 𝛬 = 580 nm and 𝐹 = 0.8, respectively. There are two prominent absorption peaks appear, which are marked as P1 and P2 for the simplicity of following discussion and analysis. It is noted that both maxima of P1 and P2 achieve near perfect absorption. Specifically, P1 reads 96.0%/98%, and P2 reads 99.9%/99.2% for cylinder/square cases. In addition, the two resonant wavelengths for cylinder and square arrays are 583 nm/593 nm 770 nm/795 nm, respectively. For the two situations of cylinder and square, only the ratio of the dielectric for cylinder is smaller than that of square, while other parameters are the same for the two symmetrical shapes. The smaller ratio of the dielectric for cylinder has the same effect as a lower filling factor F, which will reduce the effective refractive index, leading to a blue shift in the resonant frequency compared to that of the square situation. A more detailed discussion about the effect of F on the absorption behavior will be provided later in Fig. 6(b). Since the simulation results are essentially the same no matter cylinder or square arrays are used, we will illustrate the physical mechanisms of the proposed absorber with cylinder arrays in the following. Since the thickness of the gold substrate is much larger than the penetration depth of electromagnetic waves, the transmittance of the whole structure will be considered as zero in simulation (T=0). Then, the absorption of the proposed MoS2 -based absorber can be described by A=1-R, where R is reflectivity of the proposed structure | |2 2 2 and given by: R (𝜔) = ||𝑆11 || = ||𝑆11,𝑥𝑥 || + |𝑆11,𝑥𝑦 | [6]. The xx and | | xy denote the co-polarization and cross-polarization. Since MoS2 films are high-index semiconductor [28], the MoS2 -SiO2 -Au structure here can be broadly considered as a Fabry–Perot (F–P) cavity resonator, allowing the cavity mode in dielectric layer. According to knowledge of electrodynamics, the reflectivity of object reduces to zero when its impedance achieves matching condition with vacuum under specific geometric parameters [7]. In particular, the absorptivity A could also be written by [6]:
Fig. 2. Real (black line) and imaginary (blue line) parts of the complex electrical permittivity of monolayer MoS2 .
structures, only one shape is needed during the manufacturing process in this design, which is relatively easy for experimental realization. We analyze the obvious impact of the geometrical parameters on the two peaks and show a polarization-independent absorption feature. The application of this PMA for refractive index sensor is also demonstrated. It is expected that the proposed PMA with MoS2 embedded may have great potential for applications in the visible and near-infrared spectral ranges such as wavelength selective photodetectors and plasmonic sensors. 2. Design and model The schematic diagram of the proposed absorber is shown in Fig. 1(a), while Fig. 1(b) presents the unit cell profile in the x-z plane. It consists of periodic cylinder/square MoS2 -dielectric SiO2 arrays supported by a flat golden substrate. As is marked in Fig. 1(b), the diameter of the dielectric cylinder’s circular surface (or, the edge length of the square) is W, the thickness of dielectric layer is h, and the period of arrays is 𝛬. 𝐹 = 𝑊 ∕𝛬 is defined as the filling factor of dielectric cylinders in the x direction. In our simulations, the monolayer MoS2 is considered as a thin film with thickness of 0.615 nm. As shown in Fig. 2, the wavelengthdependent complex electrical permittivity of the monolayer MoS2 employed in our simulations is extracted from experimental measurements by Mukherjee et al. reported recently [28]. The refractive index of air is taken to be 1, and the refractive index curve of SiO2 was adopted from the material base of the software Lumerical FDTD Solutions. The material of the metallic mirror is chosen as gold, whose relative permittivity in the wavelengths of interest can be given by fitting the experimental results [34]. In numerical simulations, the perfectly matched layer (PML) absorbing boundary conditions are set at the bottom and top of computational domain. The periodic boundary conditions are employed in the x, and y directions, respectively. The non-uniform mesh is adopted, and the minimum mesh size inside the MoS2 monolayer equals 0.1 nm and gradually increases outside the MoS2 sheet, for saving storage space and computational time.
A (𝜔) =
2𝑍0 𝑅𝑒 (𝑍) + 𝑖 ⋅ 𝐼𝑚 (𝑍) + 𝑍0
(1)
where Z is the effective impedance of our PMA, 𝑅𝑒 (𝑍) and 𝐼𝑚 (𝑍) are respectively the real part and the imaginary part of Z. The complex transmission and reflection coefficients, or S parameters, are related to impedance Z by the following equation [35,36]:
227
1 , ( ) cos (𝑛𝑘ℎ) − 2𝑖 𝑍 + 12 sin (𝑛𝑘ℎ) ( ) 𝑖 1 = − 𝑍 sin (𝑛𝑘ℎ) , 2 𝑍
𝑆21 = 𝑆12 =
(2)
𝑆11 = 𝑆22
(3)
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Optics Communications 451 (2019) 226–230
Fig. 5. (a) Detailed distribution of absorption versus the thickness of dielectric layer h and wavelength; (b) Extracted three typical absorption spectra for arrays as h ranging from 0.15 to 0.25 μm. Other parameters are the same as in Fig. 3.
Fig. 4. (a) The real part of electric field (Ez ) and (b) magnetic field distribution (|H|) in x-z plane at P1; (c) The real part of electric field (Ez ) and (d) magnetic field distribution (|H|) in x-z plane at P2.
where 𝑆11 , 𝑆21 , 𝑆12 , 𝑆22 , n, k and h are S parameters, the effective refractive index, the wave vector and thickness of the cylinder, respectively. Thus, we can get the expression of the impedance Z as: √ √( √ 1 + 𝑆 )2 − 𝑆 2 √ 11 21 𝑍 = ±√ ( . (4) )2 2 1 − 𝑆11 − 𝑆21 It can be seen from Fig. 3(b), the impedance Z of the whole structure reaches extreme value around the resonant wavelength, and obviously approaches to the value of the free space at the two peak wavelengths. Since monolayer MoS2 does not have strong resonant behavior in the visible range, the near-perfect absorption mainly takes advantage of the resonance in the designed resonant structure. In principle, the matching of the wave impedance between air and the metamaterial can be interpreted by the superposition of inverse optical fields resulted from the electric and magnetic surface current. Consequently, electric and magnetic field distribution patterns are necessary to investigate to explain the mechanism of high absorption. At the metal–dielectric interface (SiO2 -Au in our case), collective oscillations of electrons which is known as surface plasmons (SPs) can couple with incident light [37]. The electric field distribution of Fig. 4(a) shows an apparent feature of SPs at the interfaces of MoS2 grating layer and metal-grating layer. The strong coupling between SPs and incident light confines electromagnetic field at the interface, leading to salient near-field enhancement at resonant wavelengths. Meanwhile, there are surface plasmon polaritons (SPPs) propagating along the metal–dielectric interface. Under normal incidence, in order to excite SPPs, the matching condition of wave vector between the Au-SiO2 interface should be: 𝑅𝑒(𝛽) = 𝑚(2𝜋∕ℎ), where m is an integer, Re stands ( )1∕2 for the real part of a wave vector, 𝛽 = 𝑘0 𝜀𝐴𝑢 𝜀𝑆𝑖𝑂2 ∕(𝜀𝐴𝑢 + 𝜀𝑆𝑖𝑂2 ) is the wave vector of SPP, 𝑘0 is the wave vector of vacuum, 𝜀𝐴𝑢 and 𝜀𝑆𝑖𝑂2 are the permittivity of Au and SiO2 , respectively. However, it is worth noting that, this equation is only an approximate expression due to the neglecting imaginary part of wave vector. Thus, there will be differences between the resonant wavelength obtained by theoretical expression and numerical simulation. The cavity modes correspond to the wavelengths of the wave which are reinforced by constructive interference after many reflections from the cavity’s reflecting surfaces. When the phase increases by integer multiples of 2𝜋, which corresponds to an increase in the thickness of spacer, the constructive interference conditions are still satisfied, thereby leading to a series of cavity modes of higher order [38]. On resonance, a particular standing wave pattern forms in the cavity, where more nodes locate axially along or perpendicular to the axis of
Fig. 6. Detailed distribution of absorption versus (a) the period 𝛬 and wavelength; (b) filling factor F and wavelength; (c) polarization angle and wavelength, with polarization angle ranging from 0 to 90◦ ; and (d) the angle of incidence and wavelength. Other parameters are the same as in Fig. 3.
the cavity, corresponding to more higher order modes. As shown in Fig. 4(b), there is large magnetic field enhancement in the dielectric spacer which can be attributed to the second order cavity mode. Therefore, the higher order cavity mode, the plasmon-related dipolar resonance (SPs, SPPs), as well as the coupling effect between two adjacent cells, and their hybridization effects together contribute to the observed absorption at P1. On the other hand, as clearly shown in Fig. 4(c) and (d), the strong enhancement through the cavity mode leads to an even larger absorption at the longer resonant wavelength P2. As a periodic structure, its effective absorption behavior is highly dependent on the parameters such as thickness, filling factor and period. Consequently, the optical properties tuned by manipulating related structural parameters are analyzed. As is mentioned above, the large absorption is closely related to the cavity resonance mode, which obtains absorbance maximum when the thickness h is about a quarter wave distance in dielectric layer to produce the constructive interference between incident and reflected light [39]. Therefore, we investigate the effects of the thickness of dielectric layer h on the PMA’s optical feature, as illustrated in Fig. 5(a). It is encouraging that for h ranging from 0.17 to 0.30 μm, both two absorption peaks achieve unity absorbance. And the absorption peaks are red-shifted with the increase of h due to the increase of the optical length in the cavity. The more obvious redshift of P2 with h also verifies that P2 is mainly caused by cavity mode. According to the discussion above, the order of cavity mode is closely related to h. Consequently, the absorption at P1 is relatively low with small h because high-order cavity mode is basically absent when h is small. Similarly, we can see that when h increases to about 0.25 μm, an extra absorption peak appears as a result of the appearance of higher-order cavity modes (Fig. 5(b)). The influence of the period length 𝛬 and the filling factor F to the absorption behavior are also analyzed. As illustrated in Fig. 6(a) and 228
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5. Conclusions In summary, a simple and compact dual-band PMA based on MoS2 /dielectric metamaterial structure coupled with a metal substrate has been proposed. Two absorption bands with the maximal absorbance up to 99.9% are achieved in the visible range. Optical cavity resonances of the high-index dielectric resonators and the plasmon-related dipolar resonance at the metal–dielectric interface are the main mechanisms of the observed absorption behaviors. Moreover, the obtained PMA is polarization-insensitive and with high scalability in the frequency range by tuning the structural parameters. Meanwhile, this PMA shows good sensing properties as refractive index sensor, which can find wide applications in detecting variation in environment such as humidity, chemicals, pressure and so on.
Fig. 7. (a) Absorption spectra as a function of refractive index of the analyte. (b) Spectral position of the two absorption peaks P1 and P2 as a function of refractive index of the analyte. Other parameters are the same as in Fig. 3.
(b), the position of P1 is almost equal to the period 𝛬 and weakly affected by F. This is because SPP is fundamentally the harmonic oscillations of surface charges at the interface, the layout of which is determined by the arrangement form of periodic arrays [40]. Nevertheless, the cavity mode induced P2 experiences a redshift with 𝛬 and F (which will increase with W ), given by the increase in effective refractive index of the cavity. On the other hand, larger W will promote the intensity of field enhancement at Au-SiO2 interface and reinforce concentration between neighboring cylinders through coupling effect. Hence, with the increase of F, the intensity of P1 increases. An advantage of this cylinder structure is its rotational symmetry, which makes the absorption efficiency of the PMA insensitive to the polarization angle at normal incidence. The polarization angle is defined as the angle between the positive 𝑥-axis and electric vector of plane wave, while the plane wave still incidents normally. As shown in Fig. 6(c), the absorption performance is apparently identical for the polarization angle varying from 0◦ to 90◦ . Furthermore, the incident angle dependences of the absorption of the absorber are shown in Fig. 6(d). Simulation results show that the spectral position of the absorption peak P1 blueshifts while P2 redshifts as the incident angle increases. To maintain the nearly perfect absorbance, the angle of incidence can only be as wide as around 20◦ . The absorption response to the incident angle for both TE and TM polarizations are the same due to the rotational symmetry. In addition, the absorption peak P2 exhibits frequency splitting with a smaller peak at lower frequency when the incident angle is larger than 2◦ . Since P2 mainly comes from the cavity mode confines in the dielectric layer, the spatial symmetry of the diffraction wave distribution in the cavity will be destroyed when the incident angle deviates from normal incidence. As a result, the ±mth diffraction orders will not superpose anymore, thereby causing this splitting of resonance peak P2 [41].
Acknowledgments This work was sponsored by the National Natural Science Foundation of China under Grants No. 61601408, the ZJNSF, China under Grant No. LY19F010015, the Fundamental Research Funds for the Central Universities, Project funded by China Postdoctoral Science Foundation under Grant No. 2018M632463, Wenzhou Science and Technology, China Plan under Grant No. G20170020. References [1] D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, S. Schultz, Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett. 84 (2000) 4184–4187. [2] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Extraordinary optical transmission through sub-wavelength hole arrays, Nature 391 (1998) 667. [3] P.M. Valanju, R.M. Walser, A.P. Valanju, Wave refraction in negative-index media: Always positive and very inhomogeneous, Phys. Rev. Lett. 88 (2002) 187401. [4] Y. Cui, K.H. Fung, J. Xu, H. Ma, Y. Jin, S. He, N.X. Fang, Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab, Nano Lett. 12 (2012) 1443–1447. [5] T. Chen, S.-J. Li, X.-Y. Cao, J. Gao, Z.-X. Guo, Ultra-wideband and polarizationinsensitive fractal perfect metamaterial absorber based on a three-dimensional fractal tree microstructure with multi-modes, Appl. Phys. A 125 (2019) 232. [6] S.-J. Li, P.-X. Wu, H.-X. Xu, Y.-L. Zhou, X.-Y. Cao, J.-F. Han, C. Zhang, H.H. Yang, Z. Zhang, Ultra-wideband and polarization-insensitive perfect absorber using multilayer metamaterials, lumped resistors, and strong coupling effects, Nanoscale Res. Lett. 13 (2018) 386. [7] N.I. Landy, S. Sajuyigbe, J.J. Mock, D.R. Smith, W.J. Padilla, Perfect metamaterial absorber, Phys. Rev. Lett. 100 (2008). [8] R. Yahiaoui, S. Tan, L. Cong, R. Singh, F. Yan, W. Zhang, Multispectral terahertz sensing with highly flexible ultrathin metamaterial absorber, J. Appl. Phys. 118 (2015) 083103. [9] K. Lee, H.J. Choi, J. Son, H.-S. Park, J. Ahn, B. Min, THZ near-field spectral encoding imaging using a rainbow metasurface, Sci. Rep. 5 (2015) 14403. [10] W. Cai, U.K. Chettiar, A.V. Kildishev, V.M. Shalaev, Optical cloaking with metamaterials, Nat. Photonics 1 (2007) 224. [11] S.C. Song, Q. Chen, L. Jin, F.H. Sun, Great light absorption enhancement in a graphene photodetector integrated with a metamaterial perfect absorber, Nanoscale 5 (2013) 9615–9619. [12] X.T. Kong, L.K. Khorashad, Z.M. Wang, A.O. Govorov, Photothermal circular dichroism induced by plasmon resonances in chiral metamaterial absorbers and bolometers, Nano Lett. 18 (2018) 2001–2008. [13] J. Wu, Y. Lu, S. Feng, Z. Wu, S. Lin, Z. Hao, T. Yao, X. Li, H. Zhu, S. Lin, The interaction between quantum dots and graphene: The applications in graphene-based solar cells and photodetectors, Adv. Funct. Mater. 28 (2018) 180471. [14] J. Wang, Y. Jiang, Z. Hu, Dual-band and polarization-independent infrared absorber based on two-dimensional black phosphorus metamaterials, Opt. Express 25 (2017) 22149–22157. [15] H. Meng, X. Xue, Q. Lin, G. Liu, X. Zhai, L. Wang, Tunable and multi-channel perfect absorber based on graphene at mid-infrared region, Appl. Phys. Express 11 (2018) 052002. [16] H. Meng, L. Wang, G. Liu, X. Xue, Q. Lin, X. Zhai, Tunable graphene-based plasmonic multispectral and narrowband perfect metamaterial absorbers at the mid-infrared region, Appl. Opt. 56 (2017) 6022–6027. [17] P. Fu, F. Liu, G.J. Ren, F. Su, D. Li, J.Q. Yao, A broadband metamaterial absorber based on multi-layer graphene in the terahertz region, Opt. Commun. 417 (2018) 62–66.
4. Sensing properties Furthermore, based on the robust narrowband perfect absorption property, the designed PMA can be incorporated into sensors to detect refractive index. The sensing performance are studied and shown in Fig. 7. Usually, the sensing capability of refractive index sensors is described by the spectral sensitivity 𝑆 [42,43]: S=
𝛥𝜆 . 𝛥n
(5)
where 𝛥𝜆 is spectral shift as a result of a refractive index change 𝛥𝑛 of the analyte. As presented in Fig. 7(a), the absorption peaks P1 and P2 of the structure is red-shifted with the refractive index of the background analyte. The n-dependent position of P1 and P2 are summarized in Fig. 7(b). The slope of the curves in the figure shows that the sensitivity 𝑆 reaches 500 nm/RIU and 200 nm/RIU for P1 and P2, respectively, where RIU is per refractive index unit. Since P2 originates from the cavity mode, the electromagnetic field energy will be localized in dielectric layer (Fig. 4(d)), resulting in its lower sensitivity. 229
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Dual-band near-perfect metamaterial absorber based on cylinder MoS2 -dielectric arrays for sensors Caiyu Qiu a,b , Jianghong Wu a , Rongrong Zhu c,d , Lian Shen c,d , Bin Zheng c,d ,∗ a
College of microelectronics, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, 310027, China Wenzhou Institute of Biomaterials and Engineering, CAS, Wenzhou 325011, China c State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China d The Electromagnetics Academy at Zhejiang University, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China b
ARTICLE
INFO
Keywords: MoS2 Metamaterial absorber Dual-band Polarization-insensitive Sensor
ABSTRACT As a two-dimensional (2D) material, the crystalline monolayer molybdenum disulfide (MoS2 ) has drawn extensive attention due to its interesting optical, mechanical and thermal properties compatible with many applications. Here, a dual-band perfect metamaterial absorber (PMA) composed of a simple periodically patterned cylinder/square MoS2 -dielectric silica (SiO2 ) arrays supported by a metal ground plane is proposed and studied by using finite-difference time-domain (FDTD) simulations. Numerical results reveal that the absorption spectrum of the MoS2 -based structure displays two perfect absorption peaks in the visible–NIR region. The interactions between electromagnetic waves and this PMA structure are analyzed through the field distributions and spectral responses in detail. It is also presented that the peak wavelengths can be tuned by manipulating related structural parameters. Compared with previous dual-band PMA, our absorber has only one shape that can greatly simplify the manufacturing process and the absorber is insensitive to the polarization of incident light. Furthermore, this PMA can work as a refractive index sensor with high performance due to its stable near-unity absorption.
1. Introduction Metamaterials are a class of artificial material constructed with periodic ‘‘meta-atoms’’, which can be engineered to manipulate electromagnetic waves and produce unconventional optical properties. Since the pioneering work of Smith et al. [1], massive theoretical and experimental demonstrations of functioning electromagnetic metamaterials have been reported [2,3]. Among these applications, perfect metamaterial absorbers (PMAs) can harvest the power of incident light with near 100% efficiency over wide range of wavelengths [4–6], which have attracted significant research interests after the first investigation by Landy et al. in 2008 [7]. Many PMAs have been proposed, showing practical usage in tasks as diverse as sensing [8], imaging [9], cloaking [10], photodetector [11], photothermal conversion [12], and so on. The discovery of graphene has spawned a flourishing research on 2D layered materials and mixed-dimensional heterostructure based on them [13], which can also be applied for PMAs [14–18]. In particular, the monolayer MoS2 is of direct-gap semiconductor which emits light strongly and facilitates the excitation of electrons. Thus it has been considered as the more preferable atomically thin materials for photodetection [19], photocatalysis [20,21] as well as photovoltaic ∗
devices [22]. With the thickness of ∼0.6 nm, monolayer MoS2 can absorb about 10% of the incident light at normal incidence in the visible and near-infrared range [23]. This value is well above the absorption of metallic and dielectric materials with the same thickness but is not conducive to the application of monolayer MoS2 . Monolayer MoS2 has two prominent absorption peaks at around 605 nm and 660 nm due to its strongly confined excitons and spin–orbit coupling. The peak wavelengths of MoS2 absorption can be tuned in a wide range by manipulating structural parameters and the incident angle in designed MoS2 -based absorbers. Till now, many studies have focused on the enhancement of the optical absorption efficiency in monolayer MoS2 , including the broadband absorption [24–28] and the narrowband absorption [29–33]. Among these studies, several absorption structures have utilized MoS2 as a component to design broadband PMAs [24,28], but narrowband MoS2 based PMAs are rarely reported and usually have a complicated structure [30]. Nevertheless, narrowband PMAs are also important for applications in frequency-selective photodetectors and sensors. In this work, monolayer MoS2 is covered onto the cylinder/square SiO2 and then periodically aligned on a gold substrate to form a compact dual-band absorber in visible–NIR region. In contrast to other PMA
Correspondence to: Zhejiang University, Zheda Road 38#, Hangzhou, 310027, China. E-mail address: [email protected] (B. Zheng).
https://doi.org/10.1016/j.optcom.2019.06.067 Received 15 April 2019; Received in revised form 21 May 2019; Accepted 26 June 2019 Available online 27 June 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
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Optics Communications 451 (2019) 226–230
Fig. 3. (a) Simulated absorption spectrum of proposed MoS2 -based absorber with cylinder (blue) or square (red) arrays under normal incidence. The parameters are chosen as ℎ = 200 nm, 𝛬 = 580 nm and 𝐹 = 0.8. Two absorption peaks are marked as P1 and P2; (b) Real (black line) and imaginary (blue line) parts of the effective impedance (Z) of the PMA. The dashed lines represent the free space impedance 𝑍0 = 1 (red) and the position of the resonance wavelength (pink), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 1. (a) Schematic of the cylinder/square MoS2 -dielectric arrays; (b) Profile of a unit cell of periodic arrays, x-polarized plane wave incidents normally on the arrays.
3. Results and analysis We first start from the case where the electrical vector of plane wave parallels to the 𝑥-axis, that is, illumination of TE-polarized normal incidence light. Fig. 3(a) shows the calculated absorption spectrum of the entire MoS2 -based PMA, where ℎ = 200 nm, 𝛬 = 580 nm and 𝐹 = 0.8, respectively. There are two prominent absorption peaks appear, which are marked as P1 and P2 for the simplicity of following discussion and analysis. It is noted that both maxima of P1 and P2 achieve near perfect absorption. Specifically, P1 reads 96.0%/98%, and P2 reads 99.9%/99.2% for cylinder/square cases. In addition, the two resonant wavelengths for cylinder and square arrays are 583 nm/593 nm 770 nm/795 nm, respectively. For the two situations of cylinder and square, only the ratio of the dielectric for cylinder is smaller than that of square, while other parameters are the same for the two symmetrical shapes. The smaller ratio of the dielectric for cylinder has the same effect as a lower filling factor F, which will reduce the effective refractive index, leading to a blue shift in the resonant frequency compared to that of the square situation. A more detailed discussion about the effect of F on the absorption behavior will be provided later in Fig. 6(b). Since the simulation results are essentially the same no matter cylinder or square arrays are used, we will illustrate the physical mechanisms of the proposed absorber with cylinder arrays in the following. Since the thickness of the gold substrate is much larger than the penetration depth of electromagnetic waves, the transmittance of the whole structure will be considered as zero in simulation (T=0). Then, the absorption of the proposed MoS2 -based absorber can be described by A=1-R, where R is reflectivity of the proposed structure | |2 2 2 and given by: R (𝜔) = ||𝑆11 || = ||𝑆11,𝑥𝑥 || + |𝑆11,𝑥𝑦 | [6]. The xx and | | xy denote the co-polarization and cross-polarization. Since MoS2 films are high-index semiconductor [28], the MoS2 -SiO2 -Au structure here can be broadly considered as a Fabry–Perot (F–P) cavity resonator, allowing the cavity mode in dielectric layer. According to knowledge of electrodynamics, the reflectivity of object reduces to zero when its impedance achieves matching condition with vacuum under specific geometric parameters [7]. In particular, the absorptivity A could also be written by [6]:
Fig. 2. Real (black line) and imaginary (blue line) parts of the complex electrical permittivity of monolayer MoS2 .
structures, only one shape is needed during the manufacturing process in this design, which is relatively easy for experimental realization. We analyze the obvious impact of the geometrical parameters on the two peaks and show a polarization-independent absorption feature. The application of this PMA for refractive index sensor is also demonstrated. It is expected that the proposed PMA with MoS2 embedded may have great potential for applications in the visible and near-infrared spectral ranges such as wavelength selective photodetectors and plasmonic sensors. 2. Design and model The schematic diagram of the proposed absorber is shown in Fig. 1(a), while Fig. 1(b) presents the unit cell profile in the x-z plane. It consists of periodic cylinder/square MoS2 -dielectric SiO2 arrays supported by a flat golden substrate. As is marked in Fig. 1(b), the diameter of the dielectric cylinder’s circular surface (or, the edge length of the square) is W, the thickness of dielectric layer is h, and the period of arrays is 𝛬. 𝐹 = 𝑊 ∕𝛬 is defined as the filling factor of dielectric cylinders in the x direction. In our simulations, the monolayer MoS2 is considered as a thin film with thickness of 0.615 nm. As shown in Fig. 2, the wavelengthdependent complex electrical permittivity of the monolayer MoS2 employed in our simulations is extracted from experimental measurements by Mukherjee et al. reported recently [28]. The refractive index of air is taken to be 1, and the refractive index curve of SiO2 was adopted from the material base of the software Lumerical FDTD Solutions. The material of the metallic mirror is chosen as gold, whose relative permittivity in the wavelengths of interest can be given by fitting the experimental results [34]. In numerical simulations, the perfectly matched layer (PML) absorbing boundary conditions are set at the bottom and top of computational domain. The periodic boundary conditions are employed in the x, and y directions, respectively. The non-uniform mesh is adopted, and the minimum mesh size inside the MoS2 monolayer equals 0.1 nm and gradually increases outside the MoS2 sheet, for saving storage space and computational time.
A (𝜔) =
2𝑍0 𝑅𝑒 (𝑍) + 𝑖 ⋅ 𝐼𝑚 (𝑍) + 𝑍0
(1)
where Z is the effective impedance of our PMA, 𝑅𝑒 (𝑍) and 𝐼𝑚 (𝑍) are respectively the real part and the imaginary part of Z. The complex transmission and reflection coefficients, or S parameters, are related to impedance Z by the following equation [35,36]:
227
1 , ( ) cos (𝑛𝑘ℎ) − 2𝑖 𝑍 + 12 sin (𝑛𝑘ℎ) ( ) 𝑖 1 = − 𝑍 sin (𝑛𝑘ℎ) , 2 𝑍
𝑆21 = 𝑆12 =
(2)
𝑆11 = 𝑆22
(3)
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Optics Communications 451 (2019) 226–230
Fig. 5. (a) Detailed distribution of absorption versus the thickness of dielectric layer h and wavelength; (b) Extracted three typical absorption spectra for arrays as h ranging from 0.15 to 0.25 μm. Other parameters are the same as in Fig. 3.
Fig. 4. (a) The real part of electric field (Ez ) and (b) magnetic field distribution (|H|) in x-z plane at P1; (c) The real part of electric field (Ez ) and (d) magnetic field distribution (|H|) in x-z plane at P2.
where 𝑆11 , 𝑆21 , 𝑆12 , 𝑆22 , n, k and h are S parameters, the effective refractive index, the wave vector and thickness of the cylinder, respectively. Thus, we can get the expression of the impedance Z as: √ √( √ 1 + 𝑆 )2 − 𝑆 2 √ 11 21 𝑍 = ±√ ( . (4) )2 2 1 − 𝑆11 − 𝑆21 It can be seen from Fig. 3(b), the impedance Z of the whole structure reaches extreme value around the resonant wavelength, and obviously approaches to the value of the free space at the two peak wavelengths. Since monolayer MoS2 does not have strong resonant behavior in the visible range, the near-perfect absorption mainly takes advantage of the resonance in the designed resonant structure. In principle, the matching of the wave impedance between air and the metamaterial can be interpreted by the superposition of inverse optical fields resulted from the electric and magnetic surface current. Consequently, electric and magnetic field distribution patterns are necessary to investigate to explain the mechanism of high absorption. At the metal–dielectric interface (SiO2 -Au in our case), collective oscillations of electrons which is known as surface plasmons (SPs) can couple with incident light [37]. The electric field distribution of Fig. 4(a) shows an apparent feature of SPs at the interfaces of MoS2 grating layer and metal-grating layer. The strong coupling between SPs and incident light confines electromagnetic field at the interface, leading to salient near-field enhancement at resonant wavelengths. Meanwhile, there are surface plasmon polaritons (SPPs) propagating along the metal–dielectric interface. Under normal incidence, in order to excite SPPs, the matching condition of wave vector between the Au-SiO2 interface should be: 𝑅𝑒(𝛽) = 𝑚(2𝜋∕ℎ), where m is an integer, Re stands ( )1∕2 for the real part of a wave vector, 𝛽 = 𝑘0 𝜀𝐴𝑢 𝜀𝑆𝑖𝑂2 ∕(𝜀𝐴𝑢 + 𝜀𝑆𝑖𝑂2 ) is the wave vector of SPP, 𝑘0 is the wave vector of vacuum, 𝜀𝐴𝑢 and 𝜀𝑆𝑖𝑂2 are the permittivity of Au and SiO2 , respectively. However, it is worth noting that, this equation is only an approximate expression due to the neglecting imaginary part of wave vector. Thus, there will be differences between the resonant wavelength obtained by theoretical expression and numerical simulation. The cavity modes correspond to the wavelengths of the wave which are reinforced by constructive interference after many reflections from the cavity’s reflecting surfaces. When the phase increases by integer multiples of 2𝜋, which corresponds to an increase in the thickness of spacer, the constructive interference conditions are still satisfied, thereby leading to a series of cavity modes of higher order [38]. On resonance, a particular standing wave pattern forms in the cavity, where more nodes locate axially along or perpendicular to the axis of
Fig. 6. Detailed distribution of absorption versus (a) the period 𝛬 and wavelength; (b) filling factor F and wavelength; (c) polarization angle and wavelength, with polarization angle ranging from 0 to 90◦ ; and (d) the angle of incidence and wavelength. Other parameters are the same as in Fig. 3.
the cavity, corresponding to more higher order modes. As shown in Fig. 4(b), there is large magnetic field enhancement in the dielectric spacer which can be attributed to the second order cavity mode. Therefore, the higher order cavity mode, the plasmon-related dipolar resonance (SPs, SPPs), as well as the coupling effect between two adjacent cells, and their hybridization effects together contribute to the observed absorption at P1. On the other hand, as clearly shown in Fig. 4(c) and (d), the strong enhancement through the cavity mode leads to an even larger absorption at the longer resonant wavelength P2. As a periodic structure, its effective absorption behavior is highly dependent on the parameters such as thickness, filling factor and period. Consequently, the optical properties tuned by manipulating related structural parameters are analyzed. As is mentioned above, the large absorption is closely related to the cavity resonance mode, which obtains absorbance maximum when the thickness h is about a quarter wave distance in dielectric layer to produce the constructive interference between incident and reflected light [39]. Therefore, we investigate the effects of the thickness of dielectric layer h on the PMA’s optical feature, as illustrated in Fig. 5(a). It is encouraging that for h ranging from 0.17 to 0.30 μm, both two absorption peaks achieve unity absorbance. And the absorption peaks are red-shifted with the increase of h due to the increase of the optical length in the cavity. The more obvious redshift of P2 with h also verifies that P2 is mainly caused by cavity mode. According to the discussion above, the order of cavity mode is closely related to h. Consequently, the absorption at P1 is relatively low with small h because high-order cavity mode is basically absent when h is small. Similarly, we can see that when h increases to about 0.25 μm, an extra absorption peak appears as a result of the appearance of higher-order cavity modes (Fig. 5(b)). The influence of the period length 𝛬 and the filling factor F to the absorption behavior are also analyzed. As illustrated in Fig. 6(a) and 228
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5. Conclusions In summary, a simple and compact dual-band PMA based on MoS2 /dielectric metamaterial structure coupled with a metal substrate has been proposed. Two absorption bands with the maximal absorbance up to 99.9% are achieved in the visible range. Optical cavity resonances of the high-index dielectric resonators and the plasmon-related dipolar resonance at the metal–dielectric interface are the main mechanisms of the observed absorption behaviors. Moreover, the obtained PMA is polarization-insensitive and with high scalability in the frequency range by tuning the structural parameters. Meanwhile, this PMA shows good sensing properties as refractive index sensor, which can find wide applications in detecting variation in environment such as humidity, chemicals, pressure and so on.
Fig. 7. (a) Absorption spectra as a function of refractive index of the analyte. (b) Spectral position of the two absorption peaks P1 and P2 as a function of refractive index of the analyte. Other parameters are the same as in Fig. 3.
(b), the position of P1 is almost equal to the period 𝛬 and weakly affected by F. This is because SPP is fundamentally the harmonic oscillations of surface charges at the interface, the layout of which is determined by the arrangement form of periodic arrays [40]. Nevertheless, the cavity mode induced P2 experiences a redshift with 𝛬 and F (which will increase with W ), given by the increase in effective refractive index of the cavity. On the other hand, larger W will promote the intensity of field enhancement at Au-SiO2 interface and reinforce concentration between neighboring cylinders through coupling effect. Hence, with the increase of F, the intensity of P1 increases. An advantage of this cylinder structure is its rotational symmetry, which makes the absorption efficiency of the PMA insensitive to the polarization angle at normal incidence. The polarization angle is defined as the angle between the positive 𝑥-axis and electric vector of plane wave, while the plane wave still incidents normally. As shown in Fig. 6(c), the absorption performance is apparently identical for the polarization angle varying from 0◦ to 90◦ . Furthermore, the incident angle dependences of the absorption of the absorber are shown in Fig. 6(d). Simulation results show that the spectral position of the absorption peak P1 blueshifts while P2 redshifts as the incident angle increases. To maintain the nearly perfect absorbance, the angle of incidence can only be as wide as around 20◦ . The absorption response to the incident angle for both TE and TM polarizations are the same due to the rotational symmetry. In addition, the absorption peak P2 exhibits frequency splitting with a smaller peak at lower frequency when the incident angle is larger than 2◦ . Since P2 mainly comes from the cavity mode confines in the dielectric layer, the spatial symmetry of the diffraction wave distribution in the cavity will be destroyed when the incident angle deviates from normal incidence. As a result, the ±mth diffraction orders will not superpose anymore, thereby causing this splitting of resonance peak P2 [41].
Acknowledgments This work was sponsored by the National Natural Science Foundation of China under Grants No. 61601408, the ZJNSF, China under Grant No. LY19F010015, the Fundamental Research Funds for the Central Universities, Project funded by China Postdoctoral Science Foundation under Grant No. 2018M632463, Wenzhou Science and Technology, China Plan under Grant No. G20170020. References [1] D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, S. Schultz, Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett. 84 (2000) 4184–4187. [2] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Extraordinary optical transmission through sub-wavelength hole arrays, Nature 391 (1998) 667. [3] P.M. Valanju, R.M. Walser, A.P. Valanju, Wave refraction in negative-index media: Always positive and very inhomogeneous, Phys. Rev. Lett. 88 (2002) 187401. [4] Y. Cui, K.H. Fung, J. Xu, H. Ma, Y. Jin, S. He, N.X. Fang, Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab, Nano Lett. 12 (2012) 1443–1447. [5] T. Chen, S.-J. Li, X.-Y. Cao, J. Gao, Z.-X. Guo, Ultra-wideband and polarizationinsensitive fractal perfect metamaterial absorber based on a three-dimensional fractal tree microstructure with multi-modes, Appl. Phys. A 125 (2019) 232. [6] S.-J. Li, P.-X. Wu, H.-X. Xu, Y.-L. Zhou, X.-Y. Cao, J.-F. Han, C. Zhang, H.H. Yang, Z. Zhang, Ultra-wideband and polarization-insensitive perfect absorber using multilayer metamaterials, lumped resistors, and strong coupling effects, Nanoscale Res. Lett. 13 (2018) 386. [7] N.I. Landy, S. Sajuyigbe, J.J. Mock, D.R. Smith, W.J. Padilla, Perfect metamaterial absorber, Phys. Rev. Lett. 100 (2008). [8] R. Yahiaoui, S. Tan, L. Cong, R. Singh, F. Yan, W. Zhang, Multispectral terahertz sensing with highly flexible ultrathin metamaterial absorber, J. Appl. Phys. 118 (2015) 083103. [9] K. Lee, H.J. Choi, J. Son, H.-S. Park, J. Ahn, B. Min, THZ near-field spectral encoding imaging using a rainbow metasurface, Sci. Rep. 5 (2015) 14403. [10] W. Cai, U.K. Chettiar, A.V. Kildishev, V.M. Shalaev, Optical cloaking with metamaterials, Nat. Photonics 1 (2007) 224. [11] S.C. Song, Q. Chen, L. Jin, F.H. Sun, Great light absorption enhancement in a graphene photodetector integrated with a metamaterial perfect absorber, Nanoscale 5 (2013) 9615–9619. [12] X.T. Kong, L.K. Khorashad, Z.M. Wang, A.O. Govorov, Photothermal circular dichroism induced by plasmon resonances in chiral metamaterial absorbers and bolometers, Nano Lett. 18 (2018) 2001–2008. [13] J. Wu, Y. Lu, S. Feng, Z. Wu, S. Lin, Z. Hao, T. Yao, X. Li, H. Zhu, S. Lin, The interaction between quantum dots and graphene: The applications in graphene-based solar cells and photodetectors, Adv. Funct. Mater. 28 (2018) 180471. [14] J. Wang, Y. Jiang, Z. Hu, Dual-band and polarization-independent infrared absorber based on two-dimensional black phosphorus metamaterials, Opt. Express 25 (2017) 22149–22157. [15] H. Meng, X. Xue, Q. Lin, G. Liu, X. Zhai, L. Wang, Tunable and multi-channel perfect absorber based on graphene at mid-infrared region, Appl. Phys. Express 11 (2018) 052002. [16] H. Meng, L. Wang, G. Liu, X. Xue, Q. Lin, X. Zhai, Tunable graphene-based plasmonic multispectral and narrowband perfect metamaterial absorbers at the mid-infrared region, Appl. Opt. 56 (2017) 6022–6027. [17] P. Fu, F. Liu, G.J. Ren, F. Su, D. Li, J.Q. Yao, A broadband metamaterial absorber based on multi-layer graphene in the terahertz region, Opt. Commun. 417 (2018) 62–66.
4. Sensing properties Furthermore, based on the robust narrowband perfect absorption property, the designed PMA can be incorporated into sensors to detect refractive index. The sensing performance are studied and shown in Fig. 7. Usually, the sensing capability of refractive index sensors is described by the spectral sensitivity 𝑆 [42,43]: S=
𝛥𝜆 . 𝛥n
(5)
where 𝛥𝜆 is spectral shift as a result of a refractive index change 𝛥𝑛 of the analyte. As presented in Fig. 7(a), the absorption peaks P1 and P2 of the structure is red-shifted with the refractive index of the background analyte. The n-dependent position of P1 and P2 are summarized in Fig. 7(b). The slope of the curves in the figure shows that the sensitivity 𝑆 reaches 500 nm/RIU and 200 nm/RIU for P1 and P2, respectively, where RIU is per refractive index unit. Since P2 originates from the cavity mode, the electromagnetic field energy will be localized in dielectric layer (Fig. 4(d)), resulting in its lower sensitivity. 229
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