Abstract
The paper suggests a new perfect absorber design based on the coherent perfect absorption (CPA) phenomenon of two-dimensional MoS2 monolayer in the visible region. Our proposed structure consists of a single MoS2 layer that is sandwiched between a SiO2 layer and a silver film with the nanocube dielectric array. According to the finite difference time domain simulations, CPA occurs at 722.2 nm in the certain structural configuration. Our computational results confirm the tunability of CPA resonant wavelength as a function of geometric and optical parameters of the nanocube dielectric array. Therefore, our CPA design may offer a solution to the light absorption enhancement of MoS2 monolayer in the visible region for optoelectronics applications.
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1. Introduction
In the last decade, a growing interest has been devoted to molybdenum disulfide (MoS2) monolayer, a two-dimensional (2D) material belonging to the family of transition metal dichalcogenides, which is due to its numerous applications in photonics and optoelectronics such as photoluminescence (PL) [1–3], phototransistors [4–6], optical absorbers [7–9], nonlinear optics [10–13], etc.
Previous studies indicate that the intrinsic thickness of 2D MoS2 (∼0.65 nm) limits the light–matter interaction in optoelectronics. In other words, a monolayer of MoS2 absorbs only about 10% of the light within visible and near-infrared regions at the normal incident angle [14, 15]. Therefore, it would be of great scientific interest to explore some strategies to intensify light absorption within 2D MoS2 monolayer. The literature on the absorption enhancement of 2D MoS2 monolayer shows a variety of approaches. One of the first examples of absorption enhancement was presented by Gan et al [16]. They showed the spontaneous emission rate of MoS2 monolayer coupled to a planar photonic crystal nanocavity can be higher than 70. Researches by Najmaei et al [17] and Butun et al [18] have demonstrated the enhancement of PL emission rate in the hybrid MoS2-plasmonic arrays due to near field interaction between excitonic MoS2 monolayer and plasmonic resonator. A research by Janisch et al [14] revealed the 70% absorption of MoS2 monolayer at the wavelength of 450 nm using a 45 nm thick Al2O3/Al substrate. In the recent paper by Lu et al [19], a novel multilayer photonic configuration was suggested that could increase light absorption to 96% at visible wavelengths due to Tamm plasmons excitation. Simulation results by Luo et al [20] confirmed 57% and 80.5% absorption of MoS2 monolayer at the wavelength of 560 and 672 nm, respectively, in a plasmonic perfect absorber scaffold. Furthermore, it has been theoretically and numerically demonstrated that an array of MoS2 nanodisks with a gold reflector and dielectric spacers has nearly perfect absorption in the infrared region [21]. Additionally, a dual band perfect metamaterial absorber composed of periodically patterned cylinder MoS2-dielectric silica arrays was proposed by Qiu et al [22].
Although these aforementioned studies have improved the absorption of 2D MoS2 even to the nearly perfect state, most schemes have reported suffering from lack of controllability and the approach of coherent perfect absorption (CPA) is rarely addressed in the literature. CPA in which two counter-propagating beams with specific phase and amplitude criteria are incident on the structure was first reported in Stone's group theoretically [23] and experimentally [24] with a silicon wafer. In this method, constructive interference of two incident beams causes scattering suppression and perfect absorption at the resonant wavelength [25]. Depending on the interference effects on absorption, CPA provides a potential method to manipulate light with light without nonlinearity. Later, several researchers have employed the concept of CPA to effectively manipulate the absorption of graphene [26–32] and black phosphorus [33, 34] in the THz region.
To the authors' best knowledge, very few publications in recent years have discussed the interferometric control of light absorption in 2D MoS2 monolayer within optical frequencies. Based on the CPA approach, the purpose of this paper is to introduce a new type of MoS2-based CPA structure which is capable of perfectly absorbing light at the visible wavelength.
In this study, a new polarization-independent CPA device consisting of MoS2 monolayer confined between dielectric/metal-dielectric array interfaces is suggested in the visible region. The physical basis of CPA is declared by scattering matrix theorem. Finite difference time domain (FDTD) numerical method is utilized to explore the optical properties of the proposed design. The absorption resonance of the structure is attained at 722.2 nm with polarization independent property due to the central symmetry of the structure. The absorption is comfortably modulated as the initial phase of two counter-propagating incident beams is varied. The FDTD results affirm the sensitivity of the absorption peak to the geometric dimensions as well as refractive index of the dielectric array. Therefore, we expect that our proposed architecture may be an appropriate candidate not only for detecting or modulating technologies, but also for sensing applications.
2. Simulation
2.1. Structure and model
Figure 1 represents the schematic illustration of the MoS2-based CPA structure under coherent illumination of two counter-propagating beams I1 and I2. In this structure, MoS2 monolayer is sandwiched between a 35 nm thick SiO2 substrate and a 40 nm silver film. A dielectric nanocube array (refractive index n = 1.45) is embedded into the silver film. The facet length of a single nanocube and the period of nanocube array in x and y directions are Lx, Ly, Px and Py , respectively. The height of a single nanocube is 40 nm. It is well-known that the optimized adjustment of the geometric parameters of any unsymmetrical structure may accomplish the CPA condition. In our design, CPA is attained using Lx = Ly = 100 nm and Px = Py = 600 nm.
Figure 1. (Left) 3D schematic (right) top view representation of MoS2-based CPA structure.
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Standard image High-resolution imageThree-dimensional (3D) numerical simulations in the visible region are performed using FDTD method (Lumerical Solutions, Inc.). In the FDTD simulations, the permittivity of silver film is defined by Drude model [35] and the refractive index of SiO2 substrate is taken to be 1.45. Furthermore, the complex permittivity of MoS2 monolayer was invoked from experimental data by Shen et al [36]. In our calculations, periodic boundary condition is applied along x and y directions. However, perfectly matched layer boundary condition is utilized along z direction. Non-uniform mesh setting is employed to compute the optical spectra of the MoS2-based CPA structure with the minimum mesh size of 0.2 nm inside MoS2 monolayer. Mesh size is increased gradually along z direction outside MoS2 monolayer to shorten the computation time and storage space.
From the theoretical point of view as provided in the literature [25, 29, 33], it is assumed that the relationship between two counter-propagating input beams I1 and I2 can be expressed by I2 = αI1ei (ϕ+kz), in which α is the relative ratio of I2 compared with I1 and ϕ is the phase difference between I1 and I2. The scattering output fields at the upper and lower sides of the structure are S1 and S2, respectively. According to the scattering matrix theory, the relation between input and output beams is as follows:
in which r11(t12) and r22(t21) are the reflection (transmission) coefficients at the upper and lower sides of the structure, respectively. If only I1 is incident on the structure, when r11 = r22 = −0.5 and t12 = t21 = 0.5 are satisfied, the maximum incoherent absorption is achieved i.e. Aincoh = 0.5. Considering the effect of both input beams, I1 and I2, the absorption of the CPA structure (Acoh) is deduced from equation (2).
Supposing z = 0, the coherent absorption is described by:
Equation (3) implies that Acoh oscillates periodically between the maximum value of one and minimum value of zero as ϕ varies from 2Nπ to 2(N + 1)π, N is an integer, with α = 1. As can be seen in equation (3), the coherent absorption can be adjusted by initial phase difference.
2.2. Results and discussion
The optical characteristics of MoS2-based CPA structure were simulated by FDTD method within visible region, as shown in figure 2(a). It shows the reflection (R), transmission (T), and absorption (A = 1− R− T) spectra of the system under incoherent illumination (I2 is off). When linearly x-polarized light is illuminated from top of the structure at the normal incident angle, the absorption spectrum displays a peak at resonant wavelength, λres = 722.2 nm. The reflection, transmission and absorption at resonant wavelength are R = 36%, T = 23% and A = 41%, respectively. As discussed previously in the literature, the absorption limit of incoherent illumination is A = 0.5 [27, 37]. Therefore, the absorption peak of the proposed MoS2-based CPA structure is consistent with the absorption limit.
Figure 2. (a) Incoherent (b) coherent optical response of MoS2-based CPA structure.
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Standard image High-resolution imageIn order to overcome the 50% absorption limit, CPA approach is used. To investigate the CPA response of the proposed structure, two counter-propagating beams I1 and I2 (I2 = 1.18I1) are illuminated at the normal incident angle. The initial phase difference of the two beams is 
. Both of the beams have polarization along x-axis. Figure 2(b) outlines the absorption (Acoh) and scattering (S1 and S2) spectra of the structure. It can be found that S1 and S2 diminish at λres = 722.2 nm where perfect absorption (Acoh = 99.9%) is achieved.
As illustrated in figure 3(a), the proposed CPA structure is a polarization-insensitive device due to its central symmetric feature. Although the polarization of incident light has been rotated from the x-polarized (0°) to y-polarized (90°) one with the 30° step, the perfect absorption remains the same.
Figure 3. (a) Absorption spectra of MoS2-based CPA structure with various polarization angles ranging from 0° (x-polarized) to 90° (y-polarized), electric field distribution at (b) resonant (c) non-resonant wavelength.
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Standard image High-resolution imageThe electric field distribution within XY plane, e.g. the interface between MoS2 monolayer and silver film, at resonant and non-resonant wavelength is shown in figures 3(b) and (c), respectively. Obviously, the electric field is confined and trapped along nanocube edges at the absorption peak, which enhances the near field and concentrates the light energy. In fact, the electric field is enhanced up to seven times around nanocube borders along x-axis at CPA resonant wavelength. Hot spots are formed at the corners of the nanocube, which contribute to the perfect absorption of MoS2 monolayer at this wavelength.
Figure 4(a) plots the dependence of Acoh on the initial phase difference ϕini at CPA wavelength. Clearly, the coherent absorption acts as a cosine function versus the initial phase difference. The coherent absorption is easily and continuously tuned from 99.9% to less than 5%. That is to say, our CPA structure can be converted repeatedly from a constructive interference with highly absorptive state into a destructive one with highly transparent state. Moreover, as seen in figure 4(b), the coherent absorption depends on the relative amplitude of I1 and I2. First, by increasing α from 0.59 to 1.18, the coherent absorption is increased from 88.5% to 99.9%. Then, further increase of α leads to absorption declining. Thus, the absorption of our CPA structure can achieve all-optical controls by variation of the phase and amplitude of the incident waves.
Figure 4. Optical response of the MoS2-based CPA structure vs. (a) initial phase difference (b) relative amplitude ratio.
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Standard image High-resolution imageAdditionally, the influence of structural parameters on the CPA performance of the proposed structure has been investigated. The coherent absorption spectra of MoS2-based CPA structure with various nanocube sizes under x-polarized illumination are depicted in figure 5. As follows from figure 5(a) increasing Lx = Ly from 80 to 120 nm causes a prominent absorption decline as well as resonant red shift from ∼698 to ∼753 nm. Since our structure consists of a nanohole array in a silver film, we suppose that the physical mechanism of light absorption in our structure is due to the hole plasmon resonance (HPR). Previous works have shown that the HPR wavelength has a red-shift manner as the diameter of the hole is increased [38, 39]. Furthermore, the criteria of perfect absorption are violated in other nanocube sizes except, Lx = Ly = 100 nm, where the intensity of HPR is the strongest and perfect absorption is achieved. Moreover, HPR wavelength depends on the dielectric environment of the hole. As the refractive index is increased, HPR wavelength shifts to longer wavelength [40].
Figure 5. Absorption spectra of MoS2-based CPA structure by varying (a) Lx = Ly (b) refractive index of the dielectric nanocube array.
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It can be found in figure 5(b), as the refractive index of nanocube array is increased from 1.30 to 1.60, the CPA resonant wavelength is red shifted from ∼715 to ∼732 nm. Therefore, different dielectric arrays with refractive index ranging from 1.30 to 1.60 are capable of perfect absorption in our structure.
3. Conclusion
In conclusion, this paper clearly introduced a CPA structure based on the 2D MoS2 monolayer within the visible region. The FDTD simulation results indicate that our proposed structure is a polarization-independent coherent perfect absorber at 722.2 nm. Evidently, the absorption can be tuned between 5% and 99.9% as the initial phase of the counter-propagating beams varied periodically. Moreover, CPA resonant wavelength was sensitive to the embedded nanocube size. Appropriate selection of geometric parameters in the structure satisfied the CPA condition within 696–760 nm spectral regions. Furthermore, depending on the refractive index of dielectric nanocube, CPA resonant wavelength can be tuned in 715–732 nm interval.
Acknowledgments
The authors would like to thank M Jahanbakhshian for his valuable insights and recommendations. X Luo gratefully acknowledges the generous financial support of Natural Science Foundation of Jiangxi Province (Grant No. 20192BAB212003).