A dynamically tunable anisotropic narrowband absorber based on monolayer black phosphorous (BP) is proposed in the terahertz (THz) band. The proposed absorber consists of a monolayer BP and a silicon (Si) grating, which is placed on a silica (SiO2) isolation layer and a gold (Au) substrate. The benefit from the critical coupling mechanism with guided resonance is the efficiency of the absorption can reach 99.9% in the armchair (AC) direction and the natural anisotropy of BP makes it only 87.2% in the zigzag (ZZ) direction. Numerical and theoretical studies show that the absorption efficiency of the structure is operatively controlled by critical coupling conditions, including the geometric parameters of the Si grating, the electron doping of BP and the angle of incident light, etc. More importantly, in the absence of plasmon response, this structure greatly enhances the interaction between light and matter in monolayer BP. In particular, there are several advantages in this structure, such as extremely high-efficiency absorption, excellent tunability, outstanding intrinsic anisotropy and easy manufacturing, which will show unusual and promising potential applications in the design of BP-based tunable high-performance devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Two-dimensional (2D) materials, due to their extremely significant optical and electrical properties, have attracted widespread attention as plasmonic device materials in the past decade [1–3]. Graphene is a monolayer atomic material with a hexagonal honeycomb structure. As one of the most popular 2D materials, it was isolated by the Manchester research team in 2004 . In the infrared and THz band, the surface plasmon response is supported by graphene [5–8], which is widely designed in new-type photoelectric devices, including polarizers , biosensors [10,11], photodetectors  and optical modulators .
In recent years, graphene-based absorbers have attracted the attention of researchers. In order to achieve high absorption in the range of infrared to THz, various structures have been proposed [14–18]. Graphene has extremely high carrier mobility in 2D materials. However, it is limited by its zero or close to zero band gap in applications with high on-off ratio and strong light-matter interaction . Recently, as one of the alternative 2D materials, unlike graphene, the atoms in the BP material are arranged into a wrinkled hexagonal honeycomb structure, which makes it have unique in-plane anisotropic optical and electrical properties [20–23]. Simultaneously, compared with graphene, there is an obvious direct band gap in BP, which is attributed to its tunable band gap being determined by its thickness. For bulk BP, its band gap is about 0.3 eV, reduce its thickness, and finally, the band gap of monolayer form is about 2 eV [24–26]. In this way, the gap between graphene and transition metal dichalcogenides is bridged by BP materials . In addition, through electrostatic gating or the surface charge transfer method utilizes electron/hole doping, which can more efficiently adjust the band gap of BP, and furthermore, it can provide more selectivity for the design and manufacture of tunable optoelectronic devices [28,29]. Consequently, in the THz band, BP has attracted much attention as a candidate for the absorbers. Nong et al. numerically studied the absorber formed by the strong coupling between graphene and BP, which can only achieve 20% light absorption . Liu et al. theoretically proved that the light absorption efficiency achieved by periodic graphene strips can reach 40% . Cai et al. theoretically studied an anisotropic infrared plasmonic broadband absorber based on graphene-BP multilayer film . Xia et al. numerically realized polarization-independent plasmonic absorption in the nanostructures of stacked anisotropic BP material . By summarizing the above-mentioned research work, we found that the plasmon in BP is excited, which greatly enhances the light-matter interaction, thereby realizing the absorption effect. However, the application of BP-based optoelectronic devices is greatly hindered by weak light absorption and lower sensitivity. Xiao et al. introduced multi-layer BP to achieve stronger absorption, which directly leads to the complexity of the structure and is extremely unfavorable to the processing and manufacturing of the device .
Here, a tunable narrowband anisotropic structure is proposed, which consists of a monolayer BP and a silicon (Si) grating, which is placed on a silica (SiO2) isolation layer and a gold (Au) substrate. Because of the simple geometry of the structure, it is easy to realize actual fabrication. The absorption of monolayer BP is remarkably enhanced, which is due to the principle of critical coupling with guided resonance. The total absorption occurs in the AC direction, but the absorption in the ZZ direction can only reach 87.2%, which is due to the intrinsic anisotropy of the BP material. In addition, the response to the spectrum can be easily adjusted by changing the geometrical parameters of the structure, which shows that the critical coupling can be conveniently controlled. At the same time, the sensitivity of the structure to the environmental refractive index is also studied, which is conducive to the design and application of BP-based sensors. More importantly, the system can be in a state of under coupling, critical coupling or over coupling, which can be achieved by adjusting the level of electronic doping of the BP material. Finally, it is found that the structure exhibits unique and excellent absorption characteristics under different incident angles and polarization angles. Thus, this handy structure markedly improves the absorption efficiency of monolayer BP, which provides guidance for the design of high-performance optoelectronic devices in the future.
2. Structure and model
A monolayer BP and a Si grating compose the upper structure, which is placed on an Au substrate and isolated by a SiO2 layer, as shown in Fig. 1. Among them, the uncut monolayer BP is used as a lossy material, the Si layer acts as a grating structure, the Au substrate forms a metal mirror to prevent the transmission of incident light and the SiO2 layer acts as a partition. Figure 1(a) expresses the relevant geometric parameters of the configuration, the period is P, the thickness and width of the grating are t and w, respectively, the height of the Si layer is h, and the thickness of the SiO2 layer is d. In this article, the detailed geometric parameter settings of the designed configuration are: P=10.6 µm, w=10.2 µm, t=2.6 µm, h=5.4 µm, d=6 µm. These parameters remain unchanged unless otherwise specified. The dielectric constants of Si and SiO2 are set to 12.11 and 2.19, respectively . The permittivity of the Au substrate can be expressed by the Drude model . The photonic properties of monolayer anisotropic BP are described by the semi-classical Drude model [22,31,37,38]. Here, the electronic doping of the monolayer BP material is set as: ns=4.3×1013 cm−2, which remains unchanged unless otherwise specified. In addition, the polarization direction of the incident light remains unchanged along the y-axis, and the AC direction of the in-plane anisotropy BP is along the x-axis and y-axis in Fig. 1(a) and Fig. 1(b), respectively.
In this paper, the 2D finite-difference time-domain (FDTD) method is used to analyze the proposed absorption structure in the numerical simulation process. The periodic condition is set as boundary condition in the x direction. At the same time, a plane wave is incident along the z-axis, and the perfectly matched layer (PML) is used to perfectly absorb the light of the outside boundary in the propagation direction. It is worth noting that the incident light source is placed in air with environmental refractive index of n=1. The configured absorption spectrum can be defined as A=1-T-R, where T and R represent transmission and reflection, respectively. However, since the Au substrate severely hinders the transmission of incident light and the value of T is almost zero, the absorption expression can be more simply expressed by A=1-R.
In the research structure, the physical mechanism of critical coupling is utilized to couple the guided resonance to the lossy BP, so that the total absorption of the narrow band can be realized. The periodic structure of the Si grating can successfully realize the phase-matched coupling between the guided mode and the free-space radiation. In this way, the electromagnetic field energy can be remarkably localized in the guided resonance of the structure. Therefore, the plane incident light can be actively coupled with the guided resonance, resulting in a significant total absorption at the resonance frequency. In addition, the width and height of the Si grating are both smaller than the wavelength of the incident light, so there is only a zero-order guided resonance mode, which makes one peak appear in the absorption spectrum. The coupling mode theory (CMT) can help us to further understand the physical mechanism behind the total absorption in the critical coupling state [35,39–42]. The absorption system can be expressed by the following equation:
Here, a represents the normalized amplitude of the guided resonance, S+ and S- depict the amplitude of the normalized input and output waves, respectively, δ and γ show the intrinsic loss rate and external leakage rate of the system, and ω0 is the resonance frequency. The reflection coefficient of the coupled system model can be displayed as [40,43,44]:
The δ and γ values of the absorption system can be obtained by the excellent methods described in the Ref. . For the structure without BP, the center frequency of the spectrum gives the resonance frequency ω0, and the external leakage rate γ is obtained by the half-width at half-maximum (HWHM). Introducing BP and repeating the calculation, δ+γ is obtained through the HWHM, therefore, the inherent loss rate δ is calculated by δ=(δ+γ)-γ. Combining Eq. (4), a simple analysis shows that at the resonance frequency (ω=ω0), when the intrinsic loss rate of the system is equal to the external leakage rate (δ=γ), the critical coupling condition is satisfied to achieve the total absorption.
3. Results and discussions
In the case of normal incidence, we further prove the performance of the absorber. In the absence of BP, the system has extremely weak absorption of the incident light, which is due to the loss of the Au substrate, as shown by the green solid line with beads in Fig. 2(a) and Fig. 2(b). Once BP is introduced, the frequency point of the absorption peak has a slight blue-shift, which is due to the change of effective refractive index caused by BP. The numerical simulation and theoretical analysis of the absorption spectra in the AC and ZZ directions are shown in Fig. 2(a) and Fig. 2(b), respectively. Obviously, in the direction of AC and ZZ, the absorption efficiency of the structure shows more prominent directionality, which is caused by the unique anisotropy of the monolayer BP material. When the AC direction is along the x-axis, it shows a strong absorption efficiency at f0=9.698 THz, and the absorption peak reaches 99.9%, which is shown by the blue sphere in Fig. 2(a). It is confirmed that in the THz spectrum, critical coupling is achieved through guided resonance. The full width at half maximum (FWHM) of the absorption spectrum is Δf=0.0138 THz, indicating that the absorption bandwidth is extremely narrow. Therefore, this structure can be better applied to a narrowband total absorber. The quality factor (Q) can be described as Q = f0/Δf, which can reach approximately 702.75. In particular, combined with the theoretical absorption spectrum analyzed by CMT, as shown by the solid red line in Fig. 2(a), this confirms that it maintains extremely high consistency with the numerical simulation results. It can be known from CMT that the intrinsic loss and external leakage rate of the configuration is δ=γ=2.23×1010 Hz. The intrinsic loss and external leakage rate quality factors of the system are described as Qδ=ω0/2δ and Qγ=ω0/2γ, respectively. The theoretical quality factor is represented by the equation QCMT=Qδ·Qγ/(Qδ+Qγ), and the calculated value of QCMT is 682.77. The extremely close calculated Q and theoretical QCMT proved that the total absorption is due to the critical coupling with a guided resonance mechanism. Simultaneously, the inset in Fig. 2(a) plots the phase (φ) spectrum. Careful observation shows that a sudden π-phase jump will occur in the resonance spectrum of the system when the critical coupling is satisfied . For the case where the AC direction is along the y-axis, as shown by the blue sphere in Fig. 2(b), the maximum absorption peak can only reach 87.2%, at the resonance frequency f0=9.717 THz. Undoubtedly, due to the in-plane anisotropy of the monolayer BP, the absorption spectrum shows strong directional characteristics. At this time, the resonant frequency of the system is increased from 9.698 THz to 9.717 THz, and the corresponding resonance point is shifted by 0.019 THz. The FWHM of the structure absorption spectrum is Δf=0.0239 THz, and the corresponding fitting parameters in the CMT are δ=6.41×1010 Hz and γ=2.23×1010 Hz, respectively. Markedly, the inset in Fig. 2(b) draws the reflection phase spectrum, the phase change range is less than a π-phase, and δ>γ, which proves that the system has transformed from critical coupling to under coupling . The critical coupling state of the system is broken, so the absorber cannot achieve the total absorption of incident light. It is worth noting that in the results of CMT and FDTD simulation, there is a slight deviation in the position far from the resonance frequency point, because of the CMT assumption that there is almost no loss far away from the resonance frequency point . In order to further explore the mechanism behind the greatly enhanced absorption efficiency, Fig. 2(c) and Fig. 2(d) show the simulated electric field |E| distribution of monolayer BP in two different directions. It can be found from Fig. 2(c) that once the system is in the excited resonance state, the electric field is almost entirely confined in the lossless Si grating. In this way, the energy of the incident light can be perfectly absorbed, thereby significantly enhancing the absorption efficiency of the structure.
In this guided resonance absorption system, the external leakage rate γ is dynamically controlled by the width w of the Si grating. In this way, the critical coupling state of the structure can be changed by adjusting the width w of the Si grating, thereby achieving control of the incident light absorption efficiency. Figure 3(a) depicts the spectrum of the absorption efficiency of the resonant system to the light source under different Si grating width w. Here, we regulate w in the range of 10.0 µm to 10.4 µm and other parameters remain consistent with those mentioned above. The absorption spectra from right to left in Fig. 3(a) correspond to different w, which are 10.0 µm, 10.1 µm, 10.2 µm, 10.3 µm and 10.4 µm, respectively. Obviously, as w gradually increases, a red-shift phenomenon occurs in the absorption resonance peak. At the same time, we can also find that the change in the width w of the Si grating extremely significantly affects the absorption efficiency of the structure to the incident light source. By carefully observing Fig. 3(a), it shows that once the width w of the Si grating is far away from w=10.2 µm, the resonance peak of the system will drop sharply. In addition, the absorption spectra by FDTD simulation and CMT analysis are drawn with spherical and solid lines in Fig. 3(a), respectively. The calculated results and theoretical results maintain extremely high consistency. In particular, increasing the value of w will cause the external leakage rate γ decreasing, while the intrinsic loss rate δ of the resonance system remains unchanged. For different values of w, the changes in δ and γ are depicted in Fig. 3(b). According to CMT analysis, the fitted parameters δ=2.23×1010 Hz remain constant, and the fitted values of γ are γ=5.0×1010 Hz, 3.45×1010 Hz, 2.23×1010 Hz, 1.28×1010 Hz, and 0.57×1010 Hz for w=10.0 µm, 10.1 µm, 10.2 µm, 10.3 µm, and 10.4 µm. In this way, we can further prove that the resonant system has experienced a process from under coupling (δ>γ), critical coupling (δ=γ) to over coupling (δ<γ) during the slow reduction of the Si grating width [35,39].
The absorption spectra of the resonance system under different geometric parameters are plotted in Fig. 4(a)–(c). Figure 4(a) illustrates that during the continuous increase of the width w of the Si grating, the absorption efficiency of the system gradually increases to the maximum value and then decreases sharply. At the same time, the absorption bandwidth decreases, and the resonance frequency points push toward the red-shift direction. It helps us to find the best absorption performance of the absorber more accurately and efficiently in the device manufacturing process. Not only w, but the thickness t of the Si grating also affects the absorption efficiency of the periodic structure to incident light. Figure 4(b) shows the relationship between the absorption spectrum and t under incident light along the positive z-axis. Clearly, with the gradual increase of t, the absorption peak is pushed to a lower frequency point. Although t changes, the narrower FWHM and the higher absorption efficiency of the spectrum can still be maintained. In this way, the studied absorption system can maintain an extremely high deviation tolerance to the thickness of Si grating in manufacturing process. Next, we further explore the influence of the height h of the Si layer on the absorption characteristics of the structure, as shown in Fig. 4(c). When h is slowly increased, the resonant peak of the absorber gradually undergoes a red-shift. Moreover, the absorber not only maintains a high level of absorption efficiency for the light source, but also has a negligible effect on the FWHM of the spectrum. It is worth noting that the performance requirements of the device have increased dramatically nowadays, and the controllability of some unique absorbers based on geometric parameters is necessary. Furthermore, we also studied the influence of the environmental refractive index n on the absorption performance of the system. The corresponding numerical simulation results are depicted in Fig. 4(d). As the environmental refractive index n slowly increases, the resonance frequency of the absorption peak gradually pushes toward the red-shift direction. This proves that the proposed monolayer BP-based absorber has excellent potential in sensing applications.
As we all know, whether the critical coupling of the structure can be achieved is determined by the match between the intrinsic loss rate of the structure and the external leakage rate of the guided resonance. In the THz frequency band of interest, the main intrinsic loss of the proposed research structure comes from monolayer BP. Because the electronic doping of the monolayer BP has the advantage of dynamic controllability, the surface conductivity of the monolayer BP can be dynamically changed, so as to realize the regulation of the critical coupling condition and the absorption efficiency of the system. Figure 5(a) and Fig. 5(b) depict the absorption map of the configuration when the AC direction of the monolayer BP is along the x-axis and y-axis, respectively. Gradually increase the electronic doping of the monolayer BP, the absorption spectrum bandwidth of the structure becomes wider, and the resonance frequency point moves toward the blue-shift direction, as shown in Fig. 5(a) and Fig. 5(b). In addition, the absorption efficiency of the structure depicted in Fig. 5(a) gradually increases, in the process of increasing ns, on the contrary, the absorption efficiency of the system shown in Fig. 5(b) gradually decreases. Due to the in-plane anisotropy of the monolayer BP, when the AC direction of the monolayer BP is along the x-axis, the critical coupling status of the structure is gradually satisfied. However, when the AC direction of the monolayer BP is along the y-axis, the critical coupling condition of the absorber is broken.
In order to further explore the physical mechanism behind the absorption characteristics of the proposed absorber to the light source under different electron doping of BP, shown in Fig. 6(a) and Fig. 6(b). It is worth noting that ns can interfere with absorption efficiency of the proposed structure for the electromagnetic energy of the light source. This is mainly due to the fact that ns directly determines the surface conductivity of the monolayer BP. Specifically, in Fig. 6(a), when ns=2.3×1013 cm−2, at f0=9.692 THz, a 90.9% absorption peak can be clearly found. The inset in Fig. 6(a) shows the relevant reflection phase spectrum, indicated by a solid red line. The phase difference Δφ covers almost the entire 2π range without a sudden π-phase jump, which indicates that the system is in an over coupling state at this time. In particular, only the electronic doping of the monolayer BP is changed here, while other geometric parameters remain unchanged. The research system can be considered to have only the intrinsic loss rate δ, while the external leakage rate γ is constant. The fitting parameters used in the CMT analysis are δ=1.19×1010 Hz, γ=2.23×1010 Hz, and δ<γ, which once again proves that the proposed system is in an over coupling state. At ns=4.3×1013 cm−2, the previous Fig. 1(a) has explained that δ=γ, and the system is in a critical coupling state. The absorption spectrum drawn by the blue sphere and the blue solid line in Fig. 6(a), and when ns=6.3×1013 cm−2, the absorption rate of the system drops from the total absorption to 97.6% at f0=9.704 THz. The reflected phase spectrum of the solid blue line in Fig. 6(a) shows that the phase difference Δφ can only be in the range of less than the π-phase. The fitting parameters of CMT analysis are δ=3.36×1010 Hz, γ=2.23×1010 Hz, and δ>γ. Therefore, both FDTD simulation and CMT analysis prove that the system has changed from critical coupling to under coupling. The result of the above discussion is obtained when the AC direction of the monolayer BP is along the x-axis. Due to the unique in-plane anisotropy of single-layer BP, the above research method is also applicable to the case where the AC direction of BP is along the y-axis. As shown in Fig. 6(b), at ns=0.5×1013 cm−2, 1.6×1013 cm−2, and 2.3×1013 cm−2, the corresponding absorption states are in over coupling, critical coupling, and under coupling. This provides a potential and promising platform for BP-based functional devices, such as phase modulators , perfect absorbers , and reflectors .
Finally, we explore the absorption characteristics of the proposed absorber under oblique incidence. Figure 7(a) and Fig. 7(b) depict the relationship of the absorption spectrum between the incident angle and frequency, when the AC direction of the monolayer BP is along the x-axis and y-axis, respectively. The electron doping of BP in Fig. 7(a) and Fig. 7(b) are both set to ns=4.3×1013 cm−2. Figure 7(a) and Fig. 7(b) both show that the resonant frequency advances toward the blue-shift direction, and it changes almost linearly as the incident angle is slowly increased. At the same time, the bandwidth of the absorption spectrum becomes narrower, but the absorption peak of the structure gradually decreases, which still keeps high absorption efficiency. Furthermore, we also discuss the absorption features of the studied structure under various polarization angles. For normal incidence, the direction of electrical polarization parallel to the y-axis is defined as 0°, and parallel to the x-axis is defined as 90°. As shown in Fig. 7(c) and Fig. 7(d), setting ns=4.3×1013 cm−2, the proposed absorber exhibits the remarkable characteristic of polarization dependence, thanks to the in-plane anisotropy of the monolayer BP. When the polarization angle changes slowly and smoothly from 0° to 90°, the absorption efficiency decreases rapidly, the spectral bandwidth gradually narrows, and the frequency of absorption remains unchanged until the incident light cannot be absorbed. The flexible characteristic of this structure is a rare advantage in actual BP-based equipment.
In conclusion, the narrowband total absorber based on in-plane anisotropy BP is studied through FDTD simulation and CMT analysis. The simple geometry of the structure is more conducive to the manufacture of the absorption device. In the absence of the plasmon response in the monolayer BP, the absorption efficiency of incident light can be significantly enhanced, which benefits from the critical coupling mechanism with guided resonance. At the same time, the unique in-plane anisotropy of the monolayer BP, so that the absorption efficiency of the structure shows special characteristics in the AC direction and the ZZ direction. Moreover, the red-blue shift of the resonant frequency is achieved by adjusting the electronic doping of the monolayer BP, and the system state can be converted from critical coupling to under coupling or over coupling. Finally, by changing the angle of incident light, the proposed structure still maintains a high level of absorption. In addition, by adjusting the polarization angle, the characteristics of the absorption spectrum are significantly dependent. Such a simple and flexible characteristic of this structure will show a unique and extremely promising potential application in BP-based high-performance devices.
Natural Science Foundation of Hunan Province (2020JJ5551, 2020JJ5565); National Natural Science Foundation of China (11947062, 61505052, 61775055).
The authors declare no conflicts of interest.
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