Multiple poles resonances coupling with high sensitivity sensing for multiple bulging black phosphorus-based metasurface

Herein, a multiple bulging black phosphorus (BP)-based metasurface is proposed for studying its reflection responses and sensing performances through the finite-difference time-domain simulation method. It is shown that, the reflection dips are caused by the coupling between dipole resonance modes and poly-poles resonance modes. Moreover, the dipoles resonance modes and poly-poles resonance modes can mutually enhance and inhibit each other, and tunable reflection spectra can be realized by symmetrically and asymmetrically adjusting the bulging of the proposed BP-based metasurface. In addition, the reflection spectra as a function of the polarization of incident light are discussed. We can find that a dipole resonance mode on the vertical side at the direction of ZZ for BP is gradually fully excited, resulting in an additional obvious reflection dip as the polarization angle θ increases from 0° to 90°. Especially, the sensing performance with the maximum of sensitivity S = 1.5 μm/RIU can be realized in the proposed BP-based metasurface. The results may provide a way to design micro-nano plasmonic devices.


Introduction
Two-dimensional (2D) materials have advantages of atom-scale thickness, strong light-matter interactions as well as high charge carrier mobility [1][2][3]. Therefore, 2D materials are widely used in various fields including sensors [4], phase shifter [5], transistors [6,7], and absorbers [8,9]. Additionally, in the majority of 2D materials, surface plasmons (SPs) have also been found [10][11][12]. SPs can be distinguishable based on the lattice structure for the 2D material. The first type is the isotropy [13][14][15][16], such as graphene. The other is the anisotropy, such as black phosphorus (BP) [17,18]. Pure planar anisotropy and exceptional photonic-electronic features are both present in the BP [19,20]. In particular, SPs also can be propagated on the surface of the BP [21]. Additionally, the thin BP layer exhibits a significant quantum confinement effect [22] and a high surface-to-volume ratio [23]. In addition, the bandgap of BP for a single-layer is of 2.0 eV, and a multi-layer is of 0.3 eV [24]. Thus, the BP can be applied for a lot of optical devices. For example, optical storages [25], sensors [26][27][28], selectors [29], absorbers [18,[30][31][32]. Xia et al realized polarizationindependent plasmonic absorption in stacked anisotropic 2D material nanostructures [18]. Liu et al investigated biosensor with considerable sensing sensitivity in the BP and graphene metamaterials [25]. He et al discussed non-reciprocal and polarization independent optical absorption in multi-layer BP metamaterials [32]. Zhou et al found sensing application based on lifetime and nonlinearity of modulated SP in the BP metamaterials [28]. Previous studies on anisotropic BP have mainly focused on applications related to strong anisotropy. However, it is still very important to understand the multi-mode coupling mechanism for the BP structure to achieve the high-sensitivity sensing.
In this paper, we propose a multiple bulging BP-based metasurface and study the optical responses and coupling between resonant modes by finite-difference time-domain (FDTD) simulation method. Firstly, The reflection formed by each discrete structure and its physical mechanism are analyzed. Secondly, the dependence of the polarization direction of incident light on reflection spectra is investigated. Thirdly, we investigate the modulating effect of structural parameters on the reflection spectra. At last, the sensing performance of the proposed BP-based metasurface is studied. Figure 1(a) shows the schematic diagram of the multiple bulging BP-based metasurface. The top view of the metasurface is depicted in figure 1(b). The thickness of the bottom Au layer is 0.05 µm, and the SiO 2 substrate with the thickness of 2.0 µm is placed on top of the Au layer. Period p x = 0.2 µm and p y = 0.2 µm. w = 0.1 µm is the length for the side of the square BP in the middle part. w 1 is the width of bulging BP in horizontal and vertical directions. l, l 1 , l 2 , h 1 , and h 2 are adjustable parameters as shown in figure 1(b) in this work. θ is the angle between the polarization direction of the incident light and the x-axis. For the FDTD simulations, the effective area is divided into uniform Yee cells with the step of 1 nm. And we choose perfectly matched layers (periodic boundary conditions) for the z-direction (x and y-directions). The dielectric constants for Au and SiO 2 can be found in the [33,34]. Here, a semi-classical Drude-model is introduced to describe the conductivity of BP [35,36]

Results and discussions
Here, the reflection spectra for three configurations are discussed as shown in figure 2. From figure 2(a), we can see that the two reflection peaks appear for the single square BP in the middle part when θ = 0 • (θ = 0 • , which means that the polarization direction of the incident light is the same as the x-axis and also the same as the AC direction of the BP layer). From the inset figure of figure 2(a), the normalized electric field diagram reveals that the two reflection dips are caused by the dipole resonance and quadrupole resonance, respectively. Since the dipole resonance formed by the side mode has less bound charge than that for the quadrupole resonance formed by the angle mode, the dipole resonance is weaker than the quadrupole resonance. Thus, its reflection dip caused by the dipole resonance is higher than that for the quadrupole resonance dip as shown in figure 2(a). When the horizontal bulging appears with l = 1.5 µm, l 1 = l 2 = 0.25 µm, h 1 = h 2 = 0 µm and θ = 0 • , the reflection spectrum and the normalized electric field diagram are plotted in figure 2(b). We can observe that the dipole resonance reflection dip formed by the edge mode disappears, the quadrupole resonance reflection dip caused by the angle mode become weakens. At the same time, an obvious reflection dip appears, which is caused by the dipole resonance at the position of the horizontal bulging. The suppressed quadrupole resonance reflection dip is a results of the large amount of electric charge is transferred from the four corners to the horizontal bulging. The results shows that the horizontal bulging can effectively tune the reflection spectra of the BP-based metasurface. Then, the reflection spectra and the normalized electric field diagram for appearing of the vertical bulging when l 1 = l 2 = 0 µm, h 1 = h 2 = 0.25 µm, and θ = 0 • , are discussed in figure 2(c). We can see that the reflection dip appears caused by the vertical dipole resonance, and the dip formed by the quadrupole resonance is clearly excited. Interestingly, a new dip occurs as a result of the hexapole resonance. The two inconspicuous reflection dips are due to the appearance of longitudinal bulge, which makes part of the charge transfer from the four corners and two sides to the position of the vertical bulging. Just imagine what happens to the reflectance spectrum if there are bulges in both the horizontal and vertical directions at the same time. In figure 3(a), the reflection responses are discussed when the two bulges appear with l 1 = l 2 = 0.25 µm, h 1 = h 2 = 0.25 µm, and θ = 0 • . We can see that there are three dips named as    Figures 3(b) and (c) investigate the electric field distribution for the three dips. We can see that the quadrupole resonance is suppressed by two bulges, comparing with figures 2(a) and (c). This suppression feature is due to the fact that the bulge makes the structure have more sharp areas, so that the charge is easier to gather in these areas, thus the previous quadrupole mode is suppressed. At the same time, both vertical quadrupole resonance and horizontal dipole resonance form the Dip1 and Dip3 at the wavelength of 6.12 µm and 10.66 µm. It is well known that the polarization angle has an important modulation effect on the excitation of SPs. Here, the reflection versus the polarization angle θ is investigated in figure 3(f); we can clearly see a new dip appears caused by the fully excited SPs at the direction of ZZ for BP as shown in figure 3(e).
Then the reflection spectra as a function of the length for the horizontal bulging is investigated as depicted in figure 4. Here, we study the influence from two aspects, namely, the symmetrical bulging and asymmetric bulging for the reflection spectra. Figure 4(a) shows the effect of symmetrical bulging length on the reflection spectra when h 1 = h 2 = 0.25 µm, and θ = 0 • , we can see that the Dip3 shows nonlinear red-shift when both l 1 and l 2 increase from 0 to 0.8 µm, which is caused by the forming mechanism gradually changes from the quadrupole resonance to the dipole resonance. However, the Dip1 caused by vertical  bulging dipole resonances keeps the same shape. Interestingly, Dip2 is caused by the hexapole resonance when l 1 = l 2 = 0 µm, but the Dip2 gradually disappears and then becomes apparent with increasing l 1 and l 2 . This phenomenon is caused by the gradual disappearance of the hexapole resonance mode changing into the quadrupole resonance mode. The reflection spectra versus the asymmetric bulging length when l 2 = 0.25 µm, h 1 = h 2 = 0.25 µm, and θ = 0 • as shown in figure 4(b). We can find that the Dip1 keeps the same spectra, and Dip2 shows weakened firstly and then strengthened as l 1 increases from 0 to 0.8 µm. Importantly, the split for Dip3 gradually merge and re-split with a clear red-shift, which is caused by the symmetry breaking. These results suggest that increasing the length of bulging not only increases the resonant wavelength, but also can achieve the suppression and conversion for some of the polar resonant modes.
Here, the reflection spectra as a function of the length for the vertical bulging in the symmetrical and asymmetric case are studied in figure 5. From figure 5(a), we can clearly find that the Dip3 keep the same spectra when l 1 = l 2 = 0.25 µm, and θ = 0 • as h 1 and h 2 increase from 0 to 0.8 µm. However, Dip1 becomes more and more obvious, and shows slightly blue-shift caused by the enhanced vertical resonant mode, and Dip2 firstly turns obviously and then becomes weakened. Figure 5(b) shows the reflection spectra as a function of h 1 when l 1 = l 2 = 0.25 µm, h 2 = 0.25 µm, and θ = 0 • . We can see that Dip1 and Dip2 become obvious, and Dip3 keeps the same spectra as h 1 increases from 0 to 0.8 µm. Compared with figure 4, the modulation in figure 5 is mainly for the Dip1 and Dip2, while figure 4 is mainly for Dip2 and Dip3 as a result of fixed polarization direction of the incident light. For figure 5, whether changing the vertical bulge symmetrically or changing the vertical bulge asymmetrically has a weak impact on the quadrupole resonant dip formed by the angular mode, because the polarization direction of the incident makes a large number of charges transfer to the transverse bulge. However, as the vertical bulge becomes more and more obvious, the amount of charge on the vertical bulging and four corners changes gradually, so the Dip1 and Dip2 will change significantly.
At last, the sensing property is investigated in figure 6. Figure 6(a) shows the reflection spectra as a function of the refractive index n e of the external environment. The obvious red-shift for Dip1, Dip2, and Dip3 as the refractive index increases from 1.5 to 1.8. Thus, the movement of the reflected spectral lines can be used to achieve accurate detection of changes in the refractive index of the environment. From figure 6(a), we can find that the sensing for Dip3 is more sensitive than that at the Dip1 and Dip2. Figure 6(b) study the resonant wavelength versus the refractive index. We can see that the resonant wavelength varies linearly with the increase of the refractive index. Here, we introduce sensitivity S = ∆λ/∆n e for describing the sensing performance of the proposed metasurface. Through calculation, we find that the sensing sensitivity for Dip3 can reach up to 1.5 µm/RIU, which is higher than previously reported pure BP-based metasurface [19,26]. Thus, the findings have important implications for designing high-sensitivity sensing devices.

Summary
In summary, a multi-bulging BP-based metasurface is proposed for investigating the reflection and sensing properties by using FDTD simulation method. The finding showed that the reflection Dip1, Dip2, Dip3, and Dip4 are caused by vertical quadrupole resonance, middle quadrupole resonance, horizontal dipole resonance, and vertical dipole resonance, respectively. In addition, the middle quadrupole resonance mode can be effectively suppressed as a result of the horizontal bulging. The modulation of the reflection dips can be achieved by changing the length of the bulging by symmetric and asymmetric methods. At the same time, it can realize the enhancement, inhibition, and mutual conversion between the dipole resonance, quadrupole resonance, and hexapole resonance. Then, the reflection versus the polarization angle θ is investigated; we can clearly see a new dip appears, which is caused by the fully excited SPs at the direction of ZZ for the BP. At last, the sensing performance with the maximum of sensitivity S = 1.5 µm/RIU can be realized in the proposed BP-based metasurface. The results would play a significant role for the research and designing of tunable plasmonic sensing devices.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.

Funding
This work was funded in part by the National Natural Science Foundation of China under Grant 62065017, funded by Epidemic Prevention and Control Emergency Scientific Research Projects of Yan'an University (ydfk064).