Dual-Band Plasmonic Perfect Absorber Based on the Hybrid Halide Perovskite in the Communication Regime

: Due to the weak absorption of (CH 3 NH 3 )PbI 3 in the communication regime, which restricts its optoelectronic applications, we design a adjustable dual-band perfect absorber based on the (CH 3 NH 3 )PbI 3 to signiﬁcantly enhance its absorption capability. Since the localized plasmon (LP) mode and surface plasmon (SP) mode are excited in the structure, which can both greatly enhance light absorption of the (CH 3 NH 3 )PbI 3 layer, dual-band perfect absorption peaks are formed in the communication regime, and the absorption of (CH 3 NH 3 )PbI 3 layer is increased to 43.1% and 64.2% at the dual-band absorption peaks by using ﬁnite-difference time-domain (FDTD) methods, respectively. By varying some key structural parameters, the dual-band absorption peaks of (CH 3 NH 3 )PbI 3 can be separately shifted in a wide wavelength region. Moreover, the designed absorber can keep good performance under wide angles of incidence and manifested polarization correlation. Furthermore, not just for (CH 3 NH 3 )PbI 3 , the physical mechanism in this absorber can also be utilized to strengthen the absorption of other halide perovskites.

Recent years, halide perovskites have been made great progress in the solar field. By using (CH 3 NH 3 )PbI 3 nanoparticles as light harvesters in the solar cells, M. Gratzel et al. enhanced the PCE to 9.7% [24] in 2012. One year later, A. Hey et al. [25] increased the PCE to 12.3% by adjusting the processing temperature of (CH 3 NH 3 )PbI 3−x Cl x solar cells

Structure Design
As seen from Figure 1, the designed absorber is composed of periodic silver (Ag) strips on the SiO 2 layer, which is coated with (CH 3 NH 3 )PbI 3 layer supported by the Ag substrate, and the (CH 3 NH 3 )PbI 3 layer is sandwiched by two anisotropic lossless hexagonal boron nitride (h-BN) films. Compared with only utilizing a SiO 2 layer, the h-BN films and (CH 3 NH 3 )PbI 3 layer together constitute the heterojunction to maintain higher carrier mobility in structure. The thickness of SiO 2 layer is D 1 = 230 nm, the thickness of Ag substrate is D 2 = 800 nm, and the thickness (z direction) of each h-BN film is 10 nm. Since the thickness of the Ag substrate is too thick to let the incident light penetrate through it, the transmission in the whole structure is near zero, that is T = 0. In this condition, the absorption of this structure can be expressed by A = 1 − R (R is the reflection from the whole structure). Simultaneously, the widths (in the x direction) and thicknesses of the Ag strips are expressed by w and h, respectively. Meanwhile P is the period of the Ag strips in the x direction. Then, the filling factor of the Ag strips is described by F = w/p. In calculation, w = 550 nm, P = 800 nm, h = 15 nm, and the (CH 3 NH 3 )PbI 3 layer is employed with thickness of 100 nm in this structure. The permittivity of Ag is calculated by the Drude formula [31], and the optical parameters of h-BN films in our simulation are obtained from the paper [32]. Moreover, the absorption of (CH 3 NH 3 )PbI 3 is described by the equation [33]: where N is the refractive index of (CH 3 NH 3 )PbI 3 , λ is the wavelength of incident light, c is velocity of light in vacuum, V is the volume of (CH 3 NH 3 )PbI 3 , and E l is the local electric field. Then, dual-band perfect absorption peaks are formed in the communication regime through the use of finite-difference time-domain (FDTD) methods, and the absorption of (CH 3 NH 3 )PbI 3 is increased to 43.1% and 64.2% at the dual-band absorption peaks, respectively. Meanwhile, by varying some key structural parameters, the dual-band absorption peaks of (CH 3 NH 3 )PbI 3 can be separately shifted in a wide wavelength region. Moreover, the designed absorber can keep good performance under wide angles of incidence and manifested polarization correlation.
Coatings 2021, 11, x FOR PEER REVIEW 3 of 10 (CH3NH3)PbI3 can be separately shifted in a wide wavelength region. Moreover, the designed absorber can keep good performance under wide angles of incidence and manifested polarization correlation. And we used the first-principles to calculate the dielectric function ( = − ) of (CH3NH3)PbI3 in software VASP [34,35]. The electron exchange-correlation function is adopted by the generalized gradient approximation (GGA) in the Perdew Burke-Ernzerhof (PBE) method [36]. In the calculation, the first Brillouin zone is performed with the Monkhorst-Pack k-points grid of 15 × 15 × 15, and the basis set energy cutoff of planewave is set as 500 eV. The convergence criterion of energy and force are assumed as 1 × 10 −8 eV and 1 × 10 −8 eV/Å, respectively. Meanwhile, the usual Kramers-Kronig transformation is used to obtain the real part 1 ε of the dielectric function, while the imaginary part 2 ε is solved from the summation over empty states. The calculation results of the dielectric function are shown in Figure 2, which are almost consistent with the previously reported results [37]. Clearly, the value of imaginary part ( 2 ε ) in the visible band is high, which demonstrates the (CH3NH3)PbI3 is a good material in photovoltaic field. However, its further application in the optical communication is limited by the low value of 2 ε in the communication band. Therefore, it is of great significance to study and improve the absorption of (CH3NH3)PbI3 in the communication regime.  And we used the first-principles to calculate the dielectric function (ε = ε 1 − iε 2 ) of (CH 3 NH 3 )PbI 3 in software VASP [34,35]. The electron exchange-correlation function is adopted by the generalized gradient approximation (GGA) in the Perdew Burke-Ernzerhof (PBE) method [36]. In the calculation, the first Brillouin zone is performed with the Monkhorst-Pack k-points grid of 15 × 15 × 15, and the basis set energy cutoff of plane-wave is set as 500 eV. The convergence criterion of energy and force are assumed as 1 × 10 −8 eV and 1 × 10 −8 eV/Å, respectively. Meanwhile, the usual Kramers-Kronig transformation is used to obtain the real part ε 1 of the dielectric function, while the imaginary part ε 2 is solved from the summation over empty states. The calculation results of the dielectric function are shown in Figure 2, which are almost consistent with the previously reported results [37]. Clearly, the value of imaginary part (ε 2 ) in the visible band is high, which demonstrates the (CH 3 NH 3 )PbI 3 is a good material in photovoltaic field. However, its further application in the optical communication is limited by the low value of ε 2 in the communication band. Therefore, it is of great significance to study and improve the absorption of (CH 3 NH 3 )PbI 3 in the communication regime.
(CH3NH3)PbI3 can be separately shifted in a wide wavelength region. Moreover, the designed absorber can keep good performance under wide angles of incidence and manifested polarization correlation. And we used the first-principles to calculate the dielectric function ( = − ) of (CH3NH3)PbI3 in software VASP [34,35]. The electron exchange-correlation function is adopted by the generalized gradient approximation (GGA) in the Perdew Burke-Ernzerhof (PBE) method [36]. In the calculation, the first Brillouin zone is performed with the Monkhorst-Pack k-points grid of 15 × 15 × 15, and the basis set energy cutoff of planewave is set as 500 eV. The convergence criterion of energy and force are assumed as 1 × 10 −8 eV and 1 × 10 −8 eV/Å, respectively. Meanwhile, the usual Kramers-Kronig transformation is used to obtain the real part 1 ε of the dielectric function, while the imaginary part 2 ε is solved from the summation over empty states. The calculation results of the dielectric function are shown in Figure 2, which are almost consistent with the previously reported results [37]. Clearly, the value of imaginary part ( 2 ε ) in the visible band is high, which demonstrates the (CH3NH3)PbI3 is a good material in photovoltaic field. However, its further application in the optical communication is limited by the low value of 2 ε in the communication band. Therefore, it is of great significance to study and improve the absorption of (CH3NH3)PbI3 in the communication regime.

Results and Discussion
Firstly, under normal incidence condition, we consider the absorption of this absorber and (CH 3 NH 3 )PbI 3 layer by shining from p-polarized and s-polarized light separately, as exhibited in Figure 3. When the structure is shined from s-polarized light, both the absorption of the absorber and (CH 3 NH 3 )PbI 3 are rather weak in this condition. It is because plasmonic resonance is hardly excited when the electric field of s-polarized light is parallel to the Ag strips. On the other hand, when the structure is shined from p-polarized light, both the surface plasmonic resonance and localized plasmonic resonance can be excited in the proposed absorber. Meanwhile, the absorption of (CH 3 NH 3 )PbI 3 has been obviously increased to 43.1% at λ 1 = 1291 nm and 64.2% at λ 2 = 1548 nm, respectively. Thus, the performance of our proposed absorber is remarkably polarization-sensitive, s-polarized light is not conducive to increase absorption in (CH 3 NH 3 )PbI 3. For this reason, the impacts of p-polarized light are our main concern on the next content.
Firstly, under normal incidence condition, we consider the absorption of this absorber and (CH3NH3)PbI3 layer by shining from p-polarized and s-polarized light separately, as exhibited in Figure 3. When the structure is shined from s-polarized light, both the absorption of the absorber and (CH3NH3)PbI3 are rather weak in this condition. It is because plasmonic resonance is hardly excited when the electric field of s-polarized light is parallel to the Ag strips. On the other hand, when the structure is shined from p-polarized light, both the surface plasmonic resonance and localized plasmonic resonance can be excited in the proposed absorber. Meanwhile, the absorption of (CH3NH3)PbI3 has been obviously increased to 43.1% at λ1 = 1291 nm and 64.2% at λ2 = 1548 nm, respectively. Thus, the performance of our proposed absorber is remarkably polarization-sensitive, s-polarized light is not conducive to increase absorption in (CH3NH3)PbI3. For this reason, the impacts of p-polarized light are our main concern on the next content. Next, we will go through how to realize the function of the dual-band perfect absorption for this structure. As seen from Figure 1, the whole structure can be approximately regarded as a periodic metal-insulator-metal (MIM) structure, which can suppress the reflection at the resonant wavelength. As mentioned before, the absorption of this structure can be expressed by A = 1−R, that is, the absorption peak corresponds to the reflection dip when the reverse light fields are superimposed on each other in the absorber. Thus, we can explain the absorption enhancement for the (CH3NH3)PbI3 layer by analyzing the light field distributions. As depicted from Figure  ing to the interaction of optical fields at the interface of Ag strip/air separatrix and Ag strip/hBN interface. Thus, the electric fields surrounding the Ag strips are accumulated and strengthened, as described in Figure 4a,c. And the magnetic field is assembled between each Ag strip and substrate for the resonance mode at λ1, although both of them are also gathered around the Ag strips, as described in Figure 4a,b. Actually, these char- Next, we will go through how to realize the function of the dual-band perfect absorption for this structure. As seen from Figure 1, the whole structure can be approximately regarded as a periodic metal-insulator-metal (MIM) structure, which can suppress the reflection at the resonant wavelength. As mentioned before, the absorption of this structure can be expressed by A = 1 − R, that is, the absorption peak corresponds to the reflection dip when the reverse light fields are superimposed on each other in the absorber. Thus, we can explain the absorption enhancement for the (CH 3 NH 3 )PbI 3 layer by analyzing the light field distributions. As depicted from Figure 4, at the peak wavelength of λ 1 = 1291 nm, the skin depth of Ag is S 1 ≈ λ 2πIm(Ag) ≈ 23.16 nm, as the complex refractive index of Ag is 0.3534 + 8.876i. Simultaneously, at the absorption peak of λ 2 = 1548 nm, the skin depth of Ag is S 2 ≈ λ 2π Im(Ag) ≈ 22.80 nm, as the complex refractive index of sliver is 0.5378 + 10.81i. Consequently, the thicknesses of Ag strips are much less than both S 1 and S 2 leading to the interaction of optical fields at the interface of Ag strip/air separatrix and Ag strip/hBN interface. Thus, the electric fields surrounding the Ag strips are accumulated and strengthened, as described in Figure 4a,c. And the magnetic field is assembled between each Ag strip and substrate for the resonance mode at λ 1 , although both of them are also gathered around the Ag strips, as described in Figure 4a,b. Actually, these characteristics refer to the excitation of localized plasmon (LP) mode. On the other hand, parallel electromagnetic field stripes extending the z-axis are taken shape for the resonance mode at λ 2 , as seen in Figure 4d. This means that the resonance mode at λ 2 as a surface plasmon (SP) mode accumulates the light energy surrounding the (CH 3 NH 3 )PbI 3 layer and enhances the near field. Thus, both LP mode and SP mode can greatly enhance light absorption of the (CH 3 NH 3 )PbI 3 layer. However, as seen in Figure 4e,f, at the wavelength of λ 3 = 1400 nm, which is away from resonance wavelength, light energies and optical fields are not concentrated and enhance the absorption of (CH 3 NH 3 )PbI 3 layer. allel electromagnetic field stripes extending the z-axis are taken shape for the resonance mode at λ2, as seen in Figure 4d. This means that the resonance mode at λ2 as a surface plasmon (SP) mode accumulates the light energy surrounding the (CH3NH3)PbI3 layer and enhances the near field. Thus, both LP mode and SP mode can greatly enhance light absorption of the (CH3NH3)PbI3 layer. However, as seen in Figure 4e,f, at the wavelength of λ3 = 1400 nm, which is away from resonance wavelength, light energies and optical fields are not concentrated and enhance the absorption of (CH3NH3)PbI3 layer. Subsequently, we study the effect of different widths of Ag strips on the absorption peaks of (CH3NH3)PbI3 layer, as shown in Figure 5a. Since every Ag strip exhibits as a Fabry-Perot (F-P) cavity for the LP mode, the wavelengths of absorption peaks are significantly correlated with the width of Ag strip. Therefore, when the width of Ag strip is increased, the absorption peak at λ1 will be remarkably red-shifted owe to the gradually increasing effective wavelength of LP mode, which further leads to the enhancement and concentration of optical fields inside (CH3NH3)PbI3 layer and between adjacent Ag strips. Thus, the absorption will firstly increase with w. Unfortunately, if the width of Ag strip continues to be increased, too much Ag strips will cover the (CH3NH3)PbI3 layer. The ab- Subsequently, we study the effect of different widths of Ag strips on the absorption peaks of (CH 3 NH 3 )PbI 3 layer, as shown in Figure 5a. Since every Ag strip exhibits as a Fabry-Perot (F-P) cavity for the LP mode, the wavelengths of absorption peaks are significantly correlated with the width of Ag strip. Therefore, when the width of Ag strip is increased, the absorption peak at λ 1 will be remarkably red-shifted owe to the gradually increasing effective wavelength of LP mode, which further leads to the enhancement and concentration of optical fields inside (CH 3 NH 3 )PbI 3 layer and between adjacent Ag strips. Thus, the absorption will firstly increase with w. Unfortunately, if the width of Ag strip continues to be increased, too much Ag strips will cover the (CH 3 NH 3 )PbI 3 layer. The absorption efficiency will stop increasing and turn into reduce. Meanwhile, since the wavelength of SP mode is not sensitive to w, when we change the width of Ag strip, the absorption peak at λ 2 has only a slight shift, which depends heavily on the period P of Ag strips. As seen from Figure 5c, both the absorption peaks at λ 1 and λ 2 will be obviously red-shifted with the increase of P, due to the resonance wavelengths of LP and SP modes become longer and longer. By the same token, the absorption will firstly increase and then decline in whole process of increasing P. sorption efficiency will stop increasing and turn into reduce. Meanwhile, since the wavelength of SP mode is not sensitive to w, when we change the width of Ag strip, the absorption peak at λ2 has only a slight shift, which depends heavily on the period P of Ag strips. As seen from Figure 5c, both the absorption peaks at λ1 and λ2 will be obviously redshifted with the increase of P, due to the resonance wavelengths of LP and SP modes become longer and longer. By the same token, the absorption will firstly increase and then decline in whole process of increasing P. In the following, what influences on the absorption of (CH3NH3)PbI3 layer caused by changing the thickness of Ag strips are considered, as shown in Figure 5b. When h = 15 nm, which is much thinner than the depth of penetration, the optical fields inside the air/Ag strip interface and h-BN/Ag strip interface are efficiently interacted with each other to improve the absorption of (CH3NH3)PbI3 layer, as mentioned above. When h is increased from 15 nm to 20 nm, the optical loss in the Ag strips is increased, and the coupling intensity between the top and bottom of Ag strips is weakened. As a result, both the absorption peaks of (CH3NH3)PbI3 layer at λ1 and λ2 are attenuated and blue-shifted slightly due to the reduction of resonance wavelength. However, much too thin Ag strips are not conducive to improve the absorption of (CH3NH3)PbI3 layer, owing to the reduction of optical fields around the (CH3NH3)PbI3 layer, and the strong light diffraction around the Ag strips. Consequently, when h is reduced from 15 nm to 10 nm, the absorption of (CH3NH3)PbI3 layer is obviously reduced. Furthermore, not just for (CH3NH3)PbI3, the physical mechanism in this absorber can also be utilized to strengthen the absorption of other halide perovskites, such as (CH3NH3)PbBr3, and (CH3NH3)PbCl3. As shown in Figure 5d, when the (CH3NH3)PbI3 layer in this absorber is changed by (CH3NH3)PbBr3 and (CH3NH3)PbCl3 respectively, both the absorption peaks of (CH3NH3)PbBr3 and (CH3NH3)PbCl3 layer also appear in the communication regime. Although the absorption peaks of (CH3NH3)PbBr3 and (CH3NH3)PbCl3 are not high enough in this case, we believe In the following, what influences on the absorption of (CH 3 NH 3 )PbI 3 layer caused by changing the thickness of Ag strips are considered, as shown in Figure 5b. When h = 15 nm, which is much thinner than the depth of penetration, the optical fields inside the air/Ag strip interface and h-BN/Ag strip interface are efficiently interacted with each other to improve the absorption of (CH 3 NH 3 )PbI 3 layer, as mentioned above. When h is increased from 15 nm to 20 nm, the optical loss in the Ag strips is increased, and the coupling intensity between the top and bottom of Ag strips is weakened. As a result, both the absorption peaks of (CH 3 NH 3 )PbI 3 layer at λ 1 and λ 2 are attenuated and blue-shifted slightly due to the reduction of resonance wavelength. However, much too thin Ag strips are not conducive to improve the absorption of (CH 3 NH 3 )PbI 3 layer, owing to the reduction of optical fields around the (CH 3 NH 3 )PbI 3 layer, and the strong light diffraction around the Ag strips. Consequently, when h is reduced from 15 nm to 10 nm, the absorption of (CH 3 NH 3 )PbI 3 layer is obviously reduced. Furthermore, not just for (CH 3 NH 3 )PbI 3 , the physical mechanism in this absorber can also be utilized to strengthen the absorption of other halide perovskites, such as (CH 3 NH 3 )PbBr 3 , and (CH 3 NH 3 )PbCl 3 . As shown in Figure 5d, when the (CH 3 NH 3 )PbI 3 layer in this absorber is changed by (CH 3 NH 3 )PbBr 3 and (CH 3 NH 3 )PbCl 3 respectively, both the absorption peaks of (CH 3 NH 3 )PbBr 3 and (CH 3 NH 3 )PbCl 3 layer also appear in the communication regime. Although the absorption peaks of (CH 3 NH 3 )PbBr 3 and (CH 3 NH 3 )PbCl 3 are not high enough in this case, we believe they can be optimized by manipulating the other structure parameters. Therefore, this method can be considered as a general approach to enhance absorption of most halide perovskites. Meanwhile, we also consider the effects of changing the thicknesses of h-BN layers, as shown in Figure 6. When the thicknesses of h-BN layers are increased from 6 nm to 10 nm, the intensities and wavelengths of LP and SP modes are also increased, which lead to the increase and red-shift of absorption peaks of (CH 3 NH 3 )PbI 3 layer. However, much too thick h-BN layers will weaken the coupling of plasmonic near fields between each Ag strip and the continuous Ag substrate, which lead to the reduction of optical fields around the (CH 3 NH 3 )PbI 3 layer. Thus, when the thicknesses of h-BN layers are increased from 10 nm to 14 nm, the absorption peaks of (CH 3 NH 3 )PbI 3 layer are decreased. they can be optimized by manipulating the other structure parameters. Therefore, this method can be considered as a general approach to enhance absorption of most halide perovskites. Meanwhile, we also consider the effects of changing the thicknesses of h-BN layers, as shown in Figure 6. When the thicknesses of h-BN layers are increased from 6 nm to 10 nm, the intensities and wavelengths of LP and SP modes are also increased, which lead to the increase and red-shift of absorption peaks of (CH3NH3)PbI3 layer. However, much too thick h-BN layers will weaken the coupling of plasmonic near fields between each Ag strip and the continuous Ag substrate, which lead to the reduction of optical fields around the (CH3NH3)PbI3 layer. Thus, when the thicknesses of h-BN layers are increased from 10 nm to 14 nm, the absorption peaks of (CH3NH3)PbI3 layer are decreased. In the next, it should be emphasized that all of results are obtained under the condition of normal incidence, however, the absorber in the application need keep good performance under wide angles of incidence. Then, we investigate the optical absorption of (CH3NH3)PbI3 as a function of angle and the wavelength of incident light. As shown in Figure 7, the absorption of (CH3NH3)PbI3 at λ1 and λ2 are still more than 22% and 30%, even if the angle of incident light is increased to 50°. Therefore, our designed absorber can keep good performance under wide angles of incidence in practical applications. In the next, it should be emphasized that all of results are obtained under the condition of normal incidence, however, the absorber in the application need keep good performance under wide angles of incidence. Then, we investigate the optical absorption of (CH 3 NH 3 )PbI 3 as a function of angle and the wavelength of incident light. As shown in Figure 7, the absorption of (CH 3 NH 3 )PbI 3 at λ 1 and λ 2 are still more than 22% and 30%, even if the angle of incident light is increased to 50 • . Therefore, our designed absorber can keep good performance under wide angles of incidence in practical applications.

Conclusions
In the summary, this paper designs a adjustable dual-band perfect absorber based on (CH3NH3)PbI3 in the communication regime, and the corresponding features are investigated through the use of FDTD methods. It is shown that the absorption of (CH3NH3)PbI3 layer is enhanced up to 43.1% and 64.2% at the dual-band absorption peaks in the communication regime, respectively. By varying some key structural parameters, the dualband absorption peaks of (CH3NH3)PbI3 can be separately shifted in a wide wavelength region. Moreover, the designed absorber can keep good performance under wide angles

Conclusions
In the summary, this paper designs a adjustable dual-band perfect absorber based on (CH 3 NH 3 )PbI 3 in the communication regime, and the corresponding features are investigated through the use of FDTD methods. It is shown that the absorption of (CH 3 NH 3 )PbI 3 layer is enhanced up to 43.1% and 64.2% at the dual-band absorption peaks in the communication regime, respectively. By varying some key structural parameters, the dual-band absorption peaks of (CH 3 NH 3 )PbI 3 can be separately shifted in a wide wavelength region. Moreover, the designed absorber can keep good performance under wide angles of incidence and manifested polarization correlation. Furthermore, not just for (CH 3 NH 3 )PbI 3 , the physical mechanism in this absorber can also be utilized to strengthen the absorption of other halide perovskites. Thus, the proposed absorber has great application potential for dual-frequency and frequency selective photovoltaic devices in the communication regime.