1. Introduction

Infrared (IR) photodetectors are essential components in various fields, especially for telecommunications, thermal imaging, non-destructive testing, biomedical imaging, military reconnaissance and night vision imaging [1,2]. Since the very discovery of graphene, two-dimensional (2D) materials-based IR photodetection has received enormous attentions due to the unique physical properties, such as atomic-level thickness, high carrier mobility, and easy integration characteristics [3–5]. The light absorption capacity of the detection materials determines the quantum efficiency and affects the performance of the photodetectors. However, 2D materials have limited light absorption for their inherent atomically thin thickness. Therefore, it is necessary to enhance the interaction of light and 2D materials for real and wide applications.

For this purpose, many methods have been proposed, such as integrated waveguides [6,7], diffraction gratings [8], and plasmonic nanostructures [9,10]. For instance, Wang's group demonstrated a graphene/silicon heterostructure waveguide photodetector with a high responsivity of 0.13AW⁻¹ at a 1.5 V bias for 2.75 µm [7]. Yao et al. showed that metallic antenna structures can improve light absorption in graphene detectors [11]. Li et al. fabricated a grating-patterned nanoparticle structure to enhance optical absorption by coupling of the MoS₂ to localized surface plasmons [12]. Previous researches have confirmed that optical absorption can be significantly enhanced by excited localized surface within metal nanostructure [13–15]. However, the efficiency of metallic structures is limited due to the ohmic loss [16,17], and the permittivities lack active tunability at specific wavelengths [18]. Components based on one-dimensional high-contrast gratings have higher efficiencies, but cannot realize accurate phase or polarization profiles in the direction along the grating lines due to lack of necessarily high spatial resolution [19,20]. There are also researches on the method of designing nano-patterns [21–23] or constructing heterojunctions [24]. For the former, an infinite periodic structure is often required; for the latter, the realization of high-quality interfaces remains a challenge.

Recently, the quick development of planar subwavelength optics provides us a new method to concentrate light into a strongly localized active volume, which is also known as metasurface. The metasurface is composed of artificially designed units, and it has arbitrarily adjustable electromagnetic parameters, ultrathin profile, and ultralight characteristics which natural materials do not possess [25]. By altering the shape and the size of each meta-unit and arranging these meta-units in a proper way, the metasurfaces can freely control the amplitude, phase, polarization mode and beam shape of electromagnetic waves in a wide range of spectrum from the visible to the terahertz band [26–28]. Among them, phase gradient metasurfaces received the most research interest [29–32]. Phase gradient metasurface can cause a sudden phase change of the reflected or refracted electromagnetic wave through changing the sub-wavelength sizes of the resonance units and arranging them with a continuously distributed phase shift. The additional wave vector introduced by the phase gradient offers us a chance to manipulate the incident light with control over propagation direction, wavefront form and polarization states.

Mid-infrared (MIR) contains two atmospheric transmission windows, which is also the intrinsic vibration absorption frequency band of most materials in nature. It has numerous applications in medical, military, industrial and other fields. Considering BP exhibits a thickness-tunable direct bandgap from the near infrared to the MIR [33,34] and monolithic integration with traditional electronic materials such as silicon [35], here we propose an all-dielectric gradient metasurface to demonstrate its absorption enhancement in thin layer BP in MIR. By selecting elemental meta-atoms of appropriate size and conducting reasonable arrangements, the gradient metasurface can achieve in-plane convergence. We also investigate the absorption dependence on sizes and thicknesses of BP.

2. Results and discussions

Figure 1 illustrates the proposed gradient metasurface, the structure consists of a series of periodic rings which introduces a constant phase gradient. Due to the opposite phase gradients, when the polarized light is normally incident, it will be coupled into two rows of surface waves propagating toward the center and converges to form an enhanced electric field. The BP is placed at the position where the electric field is enhanced to enhance the absorption. The designed metasurface is lossless since all the materials used in our structure have no absorption in MIR. The unit cell is shown in the inset. It consists of silicon on the top of the middle CaF₂. Perfect electric condition (PEC) is applied at the very bottom. The refractive index of silicon is 3.43 at wavelength of 3.6 µm and the refractive index of CaF₂ is 1.4 [36]. The imaginary part of the refractive index of the Si and CaF₂ are both negligible at this wavelength. The structural parameters are: period P = 500 nm, silicon height H = 1700nm, and CaF₂ thickness h = 250 nm. The length of silicon changes to realize different phase shifts. Each super cell contains five unit cells arranged with a constant phase gradient.

 

Fig. 1. Schematics of the phase gradient metasurface. Inset shows the unit cell which is composed of silicon waveguide and continuous CaF₂ dielectric film followed by the PEC. MIR light is vertically incident with polarization along x-axis.

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The simulation is conducted with finite element method (COMSOL Multiphysics). Scattering boundary conditions are employed in x and y directions. The default finer meshing generation is adopted. The smallest mesh size is 50 nm. BP is set by transition boundary conditions. In the mid-infrared regime, the surface conductivity of BP can be described using the semi-classical Drude model ${\sigma _{\textrm{jj}}} = i{D_\textrm{j}}{\pi ^{ - 1}}{({\omega + i\eta {\hbar^{ - 1}}} )^{ - 1}}$ [37,38], where j = x, y represents the x and y directions, respectively. ${D_\textrm{j}}$ is the Drude weight, ω is the incident light frequency, $\eta $ = 10 meV is the electron relaxation rate, ħ is the reduced Planck's constant. The parameter of ${D_\textrm{j}}$ is described by ${D_\textrm{j}} = \pi {e^2}nm_\textrm{j}^{ - 1}$, where e is the electron charge, n = 9×10¹³ cm⁻² is the electron doping, the BP sheet is treated as a thin layer of 10 nm, m_cx = 0.15 m₀ and m_cy = 0.7 m₀ (m₀ is the static electron mass) are the in-plane electron's effective mass along the x and y directions, respectively [39]. Hence, the equivalent relative permittivity of BP in three directions can be derived by ${\varepsilon _{\textrm{jj}}} = {\varepsilon _\textrm{r}} + i{\sigma _{\textrm{jj}}}{({{\varepsilon_0}\omega t} )^{ - 1}}$, where j = x, y, z represents the x, y and z directions, respectively. ${\varepsilon _\textrm{r}}$ = 5.76 is the relative permittivity of BP [40–42], ${\varepsilon _0}$ is the vacuum permittivity.

The first step to design the phase gradient metasurface is to achieve the entire 2π phase coverage while maintain the transmittance by sweeping the geometric parameters of unit cell. As shown in Fig. 2(a), periodic boundary conditions are employed in x direction and scattering boundary condition is used along the direction of y-axis. The x-polarized plane wave is normally illuminated on silicon waveguide from the upper direction. With parametric optimization, it is observed that for the range of L from 200 nm to 440 nm, the full 2π phase profile can be achieved as depicted in Fig. 2(b) at the wavelength of 3.6 µm. In this work, we use rectangular silicon waveguide arrays to create a dielectric gradient metasurface, which consists of five unit cells in a super cell and the phase increment is 2π/5 (L₁= 222 nm, L₂= 272 nm, L₃= 330 nm, L₄= 380 nm, L₅= 401 nm).

 

Fig. 2. Geometry and operating principle of the structure. (a) Boundary conditions setup for the unit cell simulations. (b) The reflected phase with different length of Si structure at 3.6 µm. The blue stars represent the selected L for five unit cells with the phase step of 2π/5. (c) Simulated scattered E_x field pattern of the gradient metasurface. (d) Simulated E_x field distributions on the x-y plane for three super cells.

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With proper arrangement of the phase change unit cells, the metasurface offers a phase gradient along the x direction. Anomalous reflection is achieved with the additional phase gradient $d\phi /dx = 2\pi /{L_\textrm{x}}$, where L_x denotes the period of a super cell of the metasurface, $d\phi$ and $dx$ are the phase difference and the distance between adjacent units in a super cell, respectively. According to generalized Snell's law $\sin ({{\theta_\textrm{r}}} )- \sin ({{\theta_\textrm{i}}} )= {\lambda _0}{({2\pi {n_\textrm{i}}} )^{ - 1}}({d\phi /dx})$ [43], where ${\theta _{\textrm{r}}}$ is the reflected light, ${\theta _{\textrm{i}}}$ is the angle of incidence which is 0 degree in our simulation, ${n_\textrm{i}}$ is reflective indices of media which is 1 in our simulation and ${\lambda _0}$ is the operational wavelength, respectively. If the phase gradient $d\phi /dx$ is larger than the wave vector of the incident wave ($2\mathrm{\pi }/{\lambda _0}$), the normally incident light can be converted to surface wave that propagates along the interface. In other word, for subwavelength super period ${L_\textrm{x}} \le {\lambda _0}$, the metasurface introduces an additional wave vector which is larger than that of light in free space along x-axis and compensates the condition for the existence of surface wave. Specifically, we consider a normally incident light at wavelength ${\lambda _0}$ = 3.6 µm and the periodicity of a super cell is L_x = 2500 nm, as shown in Fig. 2(c). To confirm the performance of designed gradient metasurface, a gradient metasurface with three super-cells is simulated using full wave simulation. Figure 2(d) illustrates the x-components of electric field E_x in x-y plane, which clearly shows the existence of surface wave.

Based on the grating structure, we further optimized the structure as circular rings which can induce opposite phase gradients along the x-direction when a linearly polarized plane wave is normally incident on the metasurface. The laws of reflection in dielectric gradient metasurface can be written as:

Where ${\theta _\textrm{i}}$ is the incident angle, ${\theta _{\textrm{r}1,2}}$ is reflection angles, ${k_0} = 2\pi /{\lambda _0}$ is the wave vector in the free space and ${k_{\textrm{m}1,2}} = d\phi /dx$ indicates the gradient of the phase discontinuity along the interface of dielectric structure. Here it should be noted that the reflect angle has opposite sign for the left and right parts.

With the dielectric rings structure, the coupled surface waves propagate along the interface of metasurface in opposite directions from the left and right side, and finally converge at the center of the device. We define N as the number of super cells. In order to confirm the electric field enhancement, Fig. 3(a) presents the simulated electric field distribution on x-y plane at the wavelength of 3.6 µm (N=15), x-polarized light is incident along the negative direction of the z-axis. It shows that the metasurface can achieve the convergence of incident electromagnetic wave with high intensity spots at the center of the structure. Electric field distribution on x-z plane shown in Fig. 3(b) further verifies the convergence. Figure 3(c) illustrates the corresponding horizontal cuts of x-y cross section. The distance between the two largest peaks is 3 µm which indicates the position of the strongest electric field intensity in the structure.

 

Fig. 3. Simulated results for the electric field intensity distribution on the gradient metasurface. (a) Electric field distribution of x-y cross section on top of silicon ring structures. (b) Electric field distribution of the cross section on x-z plane. The slice is along the direction of ring diameter. (c) The corresponding normalized electric field intensity along the line at the center of cross section in Fig. 3(a).

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To have a direct look at the absorption enhancement of the all-dielectric metasurface on the BP, a 5 µm×5 µm thin layer BP is placed on top of the metasurface. The absorption is calculated by recording the time-average power flow in the z direction near the structure. As shown in Fig. 4(b), the absorption with metasurface has much higher absorptance 3.77% at 3.6 µm which is nearly 20 times larger than that of BP suspended in air. There is a certain reflection loss in the structure. Multiple reflections are responsible for the energy-loss of higher order diffraction. The number of propagation of multiple reflections and the number of unit cells affect the order of diffraction [44–46]. It is possible to further increase the absorption of BP by increasing the number of unit cells in a period due to the improved diffraction efficiency of the higher-order diffracted beam [47,48]. Besides, more unit cells in a fixed period also mean more accurate phase approximations.

 

Fig. 4. Simulation results for the integration of BP and gradient metasurface. (a) Distributions of the electric field on the (x, y) cross sections of the silicon ring structure with 5 µm×5 µm monolayer BP. (b) Absorption of BP with gradient metasurface and without gradient metasurface, a_BP=5 µm. (c) Absorption of different side length of BP. (d) Absorption of different simulated thickness of BP.

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We also investigated the absorption dependence on the size of the BP. Nine side lengths from 1µm to 9 µm are calculated and shown in Fig. 4(c). As the side length of BP becomes larger, the absorptance increases. However, it gradually saturates as the length reaches 5 µm. Because the peak value of the electric field intensity is contained in the range of 5 µm and the electric field intensity at the edges of the structure decreases. The absorptance is also dependent on the thickness of BP. With fixed side length 5 µm, different thickness from 10 nm to 100 nm is simulated and shown in Fig. 4(d). The parameters of BP for different thickness are derived from the Ref. [33]. As the thickness becomes larger, the absorptance increases monotonically and reaches its maximum 28.57% at h_BP= 80 nm. Further increasing the thickness leads to reduced absorptance. We attribute this to the intensity decrease of surface waves on the normal direction of the metasurface. In experiments, the stability of BP can be effectively improved to a certain extent by covering the surface of BP with a protective layer, surface chemical modification, surface etching, or incorporation of appropriate elements [49–52].

3. Conclusion

In summary, we propose an all-dielectric gradient metasurface design for improving the MIR absorption of thin layer BP by surface wave coupling. The metasurface is demonstrated to converge the incidence into a reduced photosensitive area. By changing the side length and thickness of BP, we have found the optimized structural parameters which can maximize the absorption up to 20 times larger. Such dielectric metasurfaces are compatible with existing semiconductor technologies and are easy to be fabricated, which makes this methodology promising in developing next-generation low-loss and miniaturized infrared detector devices.