1. Introduction

Compared with traditional materials, two-dimensional (2D) materials have exhibited many exceptional and appealing characteristics [1–3]. Quantum confinement in the direction perpendicular to the 2D plane leads to novel electronic and optical properties, such as relativistic carrier transportation, indirect-to-direct bandgap transition and valley polarized light coupling [4–6]. Ultra-small thicknesses allow significant tuning of carrier density by electrostatic gating [7–9]. Naturally passivated surfaces and weak interlayer bonding make it easy to integrate 2D materials with different kinds of systems [10–13]. In this way, 2D materials have received widespread attention for optoelectronic and photonic applications [6,14,15]. However, atomic thicknesses of 2D materials result in poor light absorption and thus severely challenge their practical usage. Many efforts have been paid to address this bottleneck problem by integrating 2D materials with photonic structures to improve light coupling efficiency [16]. Different kinds of optical waveguides, microcavities, photonic crystals and plasmonic structures have been demonstrated to be able to enhance light absorption of 2D materials [13,16–27]. In principle, a photonic structure for this purpose should efficiently convert the incident light into a locally intensified field that overlaps the 2D material. Therefore, previous studies mostly focused on how to achieve significantly enhanced local field at the 2D material. Critical coupling seems to be an ideal case since the incident light under this condition is completely absorbed by the system [26,27]. At the critical coupling status, the reflectance is zero and the incident light is completely absorbed by the structure (partially by the metal and partially by the 2D material). However, if the light coupling structure is absorptive, like a metallic structure, critical coupling is not adequate for 2D material absorptance optimization, since the light power would be largely absorbed by the light coupling structure instead of the 2D material. Therefore, how to further enhance the light absorption in the 2D material and suppress the loss in the absorptive light coupling structure beyond the critical coupling is an important problem. In this work, we reveal that the light polarization at the 2D material is a crucial factor that can significantly influence the light absorption in a 2D material integrated with a light coupling structure, since 2D materials are typically much more efficient to absorb in-plane polarized light than out-of-plane polarized light [4,27]. We demonstrate that making the light polarization in-plane at the 2D material can selectively enhance the interaction between light and the 2D material instead of the interaction between light and the absorptive structure, and thus help the 2D material overwhelm the absorptive structure in the absorption competition. Among all light coupling structures, metallic structures have been extensively employed, since they are more compatible to optoelectronic devices. In many cases, metallic structures could be fabricated together with the contacts in one lithography and lift-off process [24,28,29]. And in some 2D material devices metallic structures have optical and electrical dual-functions [28–30]. The metal-insulator-metal (MIM) structure, as a representative metallic light coupling structure, has generated tremendous research interest, since it provides efficient coupling, insensitive angle dependence, and better compatibility with 2D material optoelectronic devices [28–40]. In a typical MIM structure integrated 2D material device, the 2D material is placed under the patterned top metal layer and on the insulator layer supported by the continuous bottom metal plane. We reveal that this composite structure has two forms: magnetic resonator form and metasurface Salisbury screen form. The magnetic resonator form is well known for the MIM structure to be a perfect absorber [36–39]. In this form, the thickness of the insulator is in deep-subwavelength scale, and the lateral dimension of the top metal patches is in subwavelength scale. The light mode is regarded as a magnetic resonance, where the magnetic dipole induces prominent electric field within the insulator layer and mainly perpendicular to the top and bottom metal. In this case, the enhanced local electric field at the 2D material is mainly out of the 2D plane. Since a lot of 2D materials, such as graphene and transition metal dichalcogenides (TMDs), are much less efficient to absorb the out-of-plane polarized light than the in-plane polarized light, the absorption enhancement of the 2D material in this form is not optimized. Although a critical coupling status can be reached, a large portion of the total absorptance is consumed by the metal instead of the 2D material. Another shortcoming of this form is the limited bandwidth that obstructs absorption of broad-spectrum light. In this work, we propose to switch to the metasurface Salisbury screen form of the MIM structure. In this form, the insulator layer is much thicker than that in the magnetic resonator form, and the dimensions of the patterned top metal layer depend on the optical conductivity of the 2D material. As a result, the induced light field at the 2D material is mainly kept in-plane and the critical coupling status can still be reached, so the light-2D material interaction is prominently enhanced. When the MIM structure in the metasurface Salisbury screen form is integrated with graphene, the peak absorptance of graphene is pushed to nearly 100% in the THz regime and 90% in the mid-infrared regime. Compared with the magnetic resonator form, the metasurface Salisbury screen form increases the absorptance enhancement of graphene by 1.6 to 4.2 times, enlarges the bandwidth of the resonant absorption enhancement by 3.6 to 6.4 times, and reduces the metal loss by 7.4 to 24 times. Concerning monolayer black phosphorus (BP), the MIM structure in the metasurface Salisbury screen form enhances the absorptance of BP at the wavelength of 3.5 µm from 0.44% to 31%, which is 5.4 times higher than that induced by the magnetic resonator form. In addition, the bandwidth is also 1.8 times larger. Moreover, the metasurface Salisbury screen form enhances the averaged absorptance of monolayer MoS₂ in the visible-near infrared range (415 nm to 800 nm) from 7.3% to 68.1%, which is 4.4 times higher than that induced by the magnetic resonator form. The improvement beyond critical coupling is attributed to the in-plane polarized light field that helps the 2D material overwhelm the metal in the light absorption competition. This finding deepens the understanding of photonic structure mediated light-2D material interaction and would benefit the design of light coupling structures for 2D materials, which is relevant to a broad range of researches related to 2D material photonics and optoelectronics.

2. Results and discussions

Figure 1 presents the MIM-graphene composite either in the magnetic resonator form (Fig. 1(a-c)) or in the metasurface Salisbury screen form (Fig. 1(d-f)). The MIM structure is employed to enhance the absorption of graphene. It basically contains a complete metal plane at the bottom, an insulator spacer and a metal strip array on the top. The geometrical difference between the two forms is mainly about the thickness of the insulator layer and the dimensions of the strip array on the top. In both forms, the graphene is inserted below the top patterned metal layer and on the insulator supported by a complete bottom metal plane. In this scenario, both the two forms (Fig. 1(a), 1(d)) are designed to optimize the absorption of graphene at the wavelength of 400 µm in the THz regime. The metal is assumed to be Au and the insulator to be SU-8. Concerning the magnetic resonator form, the insulator layer has a deep subwavelength thickness (8.26 µm), so the light induced currents in the top and the bottom metal can couple to each other and then induce a magnetic dipole [36–39]. The metal strip width (105.4 µm) defining the magnetic resonance frequency is around half wavelength in the medium of the insulator spacer. The period of the metal strip array is designed to be 183.5 µm. In comparison, the metasurface Salisbury screen form has a much thicker insulator layer (30 µm). The metal strip width (33 µm) and the period (35 µm) are both much smaller than those in the magnetic resonator form. The composite structures were numerically investigated by the finite element method for the spectra of reflectance, graphene absorptance and metal absorptance. The permittivity of Au was described by a Drude model [41]. SU-8 is considered to be transparent in this wavelength range and the dielectric constant is set to be 3.61 [42,43]. Graphene is regarded as a surface current sheet with a frequency dependent complex surface conductivity and zero thickness (see Supplement 1 Sec. 1) [44–46]. Therefore, in our simulations, the graphene only responds to light field polarized parallel to the 2D plane, which is consistent with previous findings [4,27,47]. Without loss of generality, the Fermi velocity of graphene is set to be 8.9×10⁵ m/s, and the carrier mobility to be 1000 cm²/(V·s) [48–50]. The Fermi level E_F of graphene is set to be 0.1 eV for the results in Fig. 1. The incident light is a TM wave. As shown in Fig. 1(b) and 1(c), the MIM-graphene composite in the magnetic resonator form holds a typical magnetic dipole resonance at the wavelength of 400 µm. As shown in Fig. 1(c), the displacement currents in the insulator, as represented by the electric field (pink arrows), form a loop together with the currents in the metal and then induce a magnetic dipole in the y-direction at x = 0 µm in the insulator layer. The zero reflectance at the resonant wavelength (Fig. 1(b)) indicates that all the incident power is absorbed by the composite and a critical coupling status is reached. Although this status is already an ideal case for the composite to be a good absorber, it is not optimized for absorption enhancement of the 2D material. The graphene absorbs 61.5% of the incident power and the rest 38.5% is consumed by the metal parts. The power loss by the metal is unwanted, since it limits the absorptance of the 2D material. Actually, it is the most detrimental problem of all plasmonic systems [31,33,51–53]. In our composite structure, there is a light absorption competition between the graphene and the metal. When the light coupling status is fixed, the one interacting more strongly with the light field would absorb more power [54]. There are several ways to enhance the interaction between the 2D material and the light field, such as increasing the thickness of the material or overlapping the local field better with the material [34,54,55]. In this work, we reveal that for 2D materials typically with very different in-plane and out-of-plane optical properties, creating an intensified local field polarized along the principle absorption axis of the 2D material is crucial to enhance the light-matter interaction and thus the absorptance of the target material. As shown in Fig. 1(c), the local field at the graphene is mostly perpendicular to the 2D plane, so it is poorly absorbed by the graphene since graphene hardly responds to the field perpendicular to the 2D plane. Another problem of the magnetic resonator form is the very limited bandwidth. It is due to the fact that the electric field in a magnetic dipole resonator forms a loop and thus cannot couple to the incident light efficiently [36,56]. As we found, when the MIM-2D material composite switches to the metasurface Salisbury screen form, both the absorptance of the 2D material and the bandwidth of the resonant enhancement are prominently improved. As shown in Fig. 1(e), the peak absorptance of the graphene reaches 98.3% and the full width at the half maximum (FWHM) of this absorption enhancement peak is 6.4 times larger than that of the magnetic resonator (Fig. 1(b)). The critical coupling condition is still satisfied so the incident light is fully trapped (R = 0 at λ = 400 µm). It is worth noting that the absorptance of the metal is suppressed to 1.6%, which is 24 times lower than that of the magnetic resonator (Fig. 1(b)). This prominent improvement is attributed to the fact that the intensified localized field at the 2D material is mainly polarized in-plane (Fig. 1(f)). The field is mostly concentrated inside each slit. The induced charges at the corners of the neighboring metal strips induce an array of in-plane electric dipoles that interact more strongly with the 2D material than with the metal. As a result, the 2D material overwhelms the metal in the absorption competition and then absorbs most of the trapped light. In addition, the metal strip array based MIM structures are polarization dependent. The polarization extinction ratio for the graphene absorptance in the MIM structure as a magnetic resonator is 638 at the resonant wavelength. In comparison, the polarization extinction ratio for the graphene absorptance in the MIM structure as a metasurface Salisbury screen is 812 times higher (see Supplement 1 Sec. 7).

 

Fig. 1. (a) Sketch of the MIM-graphene composite in the magnetic resonator form. p = 183.5 µm, w = 105.4 µm and h = 8.26 µm are the period, the metal strip width, and the insulator layer thickness, respectively. (b) Spectra of reflectance (R), absorptance of the graphene (A_gr), and absorptance of the metal (A_m) for the composite in the magnetic resonator form. A_fr is the absorptance of graphene in free space. (c) Light field distribution on the x-z cross section of the composite in the magnetic resonator form at the resonant wavelength (400 µm). The direction and size of the pink arrow indicate the direction and amplitude of the local electric field, respectively. The surface color denotes |E|/|E₀|. (d-f) Counterparts of (a-c) for the MIM-graphene composite in the metasurface Salisbury screen form with p = 35 µm, w = 33 µm, h = 30 µm. The metal strip thickness for both cases is 80 nm. The incident light is polarized along the x-axis.

Download Full Size | PDF

The metasurface Salisbury screen form is further compared with the magnetic resonator form in a semi-analytical manner about polarization dependent light absorption in the 2D material and that in the metal. Figure 2(a) and 2(b) presents |E_x|²/|E₀|² at the graphene layer in the magnetic resonator and that in the metasurface Salisbury screen, respectively. The x-range in Fig. 2(a) and 2(b) is 183.5 µm, which equals to one period of the magnetic resonator and also equals to more than five periods of the metasurface Salisbury screen. E₀ is the same for both cases. In the magnetic resonator, E_x exists at the corners of the metal strips. In the metasurface Salisbury screen, E_x exists in the slits. The absorption of graphene is derived as $\textrm{Re} ({{\sigma_{gr}}} ){|{{E_x}} |^2}$ for TM waves, so it is proportional to ${{|{{E_x}} |_{\textrm{ave}}^2} / {{{|{{E_0}} |}^2}}}$, as shown in Fig. 2(c). $|{{E_x}} |_{\textrm{ave}}^2$ is the averaged ${|{{E_x}} |^2}$ over the graphene plane, as marked out by the red lines in the insets of Fig. 2(c). The power loss by the metal is proportional to the square of the tangential magnetic field integrated over the metal surface: $\sqrt {{{\omega {\mu _0}} / {2{\sigma _m}}}} \int\!\!\!\int {{{|{{H_y}} |}^2}ds} $ [57], so it is proportional to ${{|{{H_y}} |_{\textrm{ave}}^2} / {{{|{{H_0}} |}^2}}}$ since $|{{H_y}} |_{\textrm{ave}}^2 = {{\int\!\!\!\int {{{|{{H_y}} |}^2}ds} } / S}$. S denotes the area of the metal surface marked out by the red lines in the insets of Fig. 2(d). The results in Fig. 2(c) and 2(d) apparently show that the metasurface Salisbury screen enhances the in-plane polarized field at the graphene and reduces the tangential magnetic field at the metal surfaces in comparison with the magnetic resonator, and thus facilitates the graphene in the absorption competition with the metal. Actually, if the metal in the magnetic resonator is assumed to be perfect conductor with no loss, the absorptance of the graphene becomes 100% despite the light field at the graphene is mainly out-of-plane, since the light field cannot be absorbed by any other material except the graphene (see Supplement 1 Sec. 2). However, metal loss is inevitable, so matching the light field polarization to the main absorption direction of the 2D material for an enhanced light-matter interaction has a significant effect to improve the absorptance of the 2D material and meanwhile reduce the absorptance of the metal. Concerning the bandwidth, the light mode of the metasurface Salisbury screen can be considered as an array of electrical dipoles, while that of the magnetic resonator as an array of magnetic dipoles. Basically, the former couples with the incident light more efficiently than the later, so it corresponds to a larger bandwidth. Consequently, although the MIM-graphene composites in both forms are at the critical coupling status, the metasurface Salisbury screen form is more favorable for enhancing light absorption of a 2D material. For simplicity, the top metal layer of the MIM structure in the above analysis is assumed to be a metal strip array, which can be simulated in a two dimensional manner. In fact, the advantage of the metasurface Salisbury screen form over the magnetic resonator form is not limited to the metal strip array. For MIM structure with metal square array, similar results are also obtained through three dimensional simulations, and they are independent of the polarization of the incident light (see Supplement 1 Sec. 3).

 

Fig. 2. (a) and (b) Distributions of |E_x|²/|E₀|² along the x-axis at the graphene of the composite structures in the magnetic resonator form (p = 183.5 µm, w = 105.4 µm, h = 8.26 µm) and in the metasurface Salisbury screen form (p = 35 µm, w = 33 µm, h = 30 µm), respectively. The span in the x-direction is 183.5 µm (one period of the magnetic resonator) for both (a) and (b). (c) Spectra of |E_x|²_ave/|E₀|² for the magnetic resonator (green line) and the metasurface Salisbury screen (blue line). |E_x|²_ave is the averaged |E_x|² over the graphene sheet. (d) Spectra of |H_y|²_ave/|H₀|² for the magnetic resonator (green line) and the metasurface Salisbury screen (blue line). |H_y|²_ave is the averaged |H_y|² over the metal surfaces marked by the red lines.

Download Full Size | PDF

Conventional Salisbury screen is composed of a thin resistive sheet, a dielectric spacer of the quarter wavelength thickness and a metal ground plane. When the input impedance of the structure matches the free-space impedance, total absorption by the resistive sheet is achieved. This structure is favorable for enhancing absorption of 2D materials, since the light field is completely parallel to the 2D plane. However, in order to achieve high absorptance of the 2D material, impedance matching (or critical coupling) needs to be satisfied as well. Concerning the MIM-graphene composite in the metasurface Salisbury screen form, the impedance matching condition is analyzed by a circuit model. As shown in Fig. 3(a), the graphene together with the metasurface is considered as a shunt resistance (${R^{\prime}_{eff}} = {{{{R^{\prime}}_g}} / f}$), a shunt inductance ($j{X^{\prime}_{eff}} = {{j{{X^{\prime}}_g}} / f}$), and a shunt capacitance (${1 / {j\omega {C_m}}}$). ${R^{\prime}_g} = {R_g} + {{X_g^2} / {{R_g}}}$ and $j{X^{\prime}_g} = j({{X_g} + {{R_g^2} / {{X_g}}}} )$, where ${R_g} + j{X_g}$ denotes the sheet impedance of the graphene [58]. $f = {w / {(p - w)}}$ means the ratio of the metal strip width to the slit width, and it is a key parameter to adjust the impedance of the metasurface integrated graphene. ${C_m}$ describes the capacitance of the slit array. When the incident light passing through the metasurface integrated graphene, it propagates in the dielectric layer for a distance of h and gets reflected by the bottom metal layer. By assuming the metal as perfect conductor for simplicity, the dielectric layer and the metal plane is viewed as a shorted transmission line and modeled as a reactance $j{X_d} = j\sqrt {{{{\mu _0}} / {{\varepsilon _0}{\varepsilon _{dr}}}}} \tan ({{k_d}h} )$. ${\varepsilon _{dr}}$ represents the relative permittivity of the dielectric and the ${k_d}$ is the wave number in the dielectric. Then, the impedance matching (i.e. critical coupling) condition writes [58]

Equation (1) means that the effective resistance of the metasurface integrated graphene should be equal to the free-space impedance. Apparently, the metasurface is used to reduce the effective resistance of graphene to match η₀. Equation (2) is easier to satisfy since the thickness or the refractive index of the dielectric layer could be adjusted independently of the metasurface. For highly doped graphene, ${R^{\prime}_g}$ is small enough to match η₀ so metasurface is not needed [59]. As shown in Fig. 3(a) and 3(b), when E_F is equal to 500 meV, the graphene Salisbury screen structure without the metasurface can lead to a near unity absorptance of graphene at the designed wavelength. When the doping level is not high enough, the metasurface should be employed to reduce the shunt resistance for impedance matching. The lower the doping level is, the larger the duty cycle of the metal strip array should be, since more metal is needed to reduce the resistance. For E_F=300 meV, the absorptance of the graphene approaches 100% when the period of the metasurface (p) is designed to be 40 µm and the width of each metal strip (w) to be 23 µm. In this case, f is equal to 1.35, which means that the shunt resistance of the graphene should be reduced by 1.35 times to match the free-space impedance (η₀). For E_F=100 meV, the absorptance of the graphene approaches to unity at p = 35 µm and w = 33 µm. f is equal to 16.5, indicating that the shunt resistance of the graphene is reduced by 16.5 times to match the free-space impedance (η₀). For comparison, when the MIM-graphene composite is in the magnetic resonator form, the peak absorptances of the graphene are 0.62, 0.61 and 0.46 for E_F=100 meV, 300 meV and 500 meV, respectively (Fig. 3(c)). Therefore, the metasurface Salisbury screen form is more effective than the magnetic resonator form to enhance the absorptance of the graphene at different doping levels since it can provide mainly in-plane light field at the 2D material and critical coupling.

 

Fig. 3. (a)#Sketch of the MIM-graphene composite in the metasurface Salisbury screen form, and the equivalent circuit model. (b) Absorptance spectra of graphene at different Fermi levels in the metasurface Salisbury screen. The dimensions of the structure are optimized for the graphene Fermi level of 100 meV (p = 35 µm, w = 33 µm, h = 30 µm), 300 meV (p = 40 µm, w = 23 µm, h = 54 µm) and 500 meV (no strip array, h = 67 µm). (c) Absorptance spectra of graphene at different Fermi levels in the magnetic resonator. The dimensions of the structure are p = 183.5 µm, w = 105.4 µm, h = 8.3 µm. The thickness of the metal strips is 80 nm for both forms.

Download Full Size | PDF

The superior performance of the metasurface Salisbury screen form compared to the magnetic resonator form is valid in the mid-infrared and the near infrared regime as well. The mid-infrared version of the MIM structure is made of Au and ZnSe. Concerning the magnetic resonator form designed for the resonance at the wavelength of 10 µm, the graphene absorbs only 21.3% of the incident power, while the metal consumes 78.7% (Fig. 4(a)). In comparison, the absorptance of the graphene in the metasurface Salisbury screen reaches 88.5% and the metal loss is suppressed to 10.6% (Fig. 4(b)). Although both forms of MIM-graphene composite operate at the critical coupling status, the absorptance of graphene in the metasurface Salisbury screen is 4.2 times higher than that in the magnetic resonantor and the metal loss is 7.4 times lower. In addition, the band width of absorption enhancement (FWHM of the absorptance peak) is broadened by 3.6 times. The near infrared version of the MIM structure is made of Au and SiO₂. At the resonant wavelength of 1.55 µm, the magnetic resonantor results in the absorptance of graphene as 36.2% and the metal loss as 63%. In comparison, the metasurface Salisbury screen increases the absorptance of graphene to 72.3%, suppresses the metal loss to 27.2% and enlarges the band width by 2.61 times. Therefore, switching from the magnetic resonator form to the metasurface Salisbury screen form can further improve the 2D material absorption, enlarge the bandwidth of enhancement, and suppress the metal loss. Since metal gets less conductive as the wavelength becomes shorter, the metal loss suppression by the metasurface Salisbury screen form is less effective than that in the far infrared regime. In the simulation, the permittivities of Au, ZnSe and SiO₂ all come from the experimental data [60–63].

 

Fig. 4. (a) and (b) Spectra of reflectance, absorptance of the graphene and absorptance of the metal for the mid-infrared-version MIM-graphene composite in the magnetic resonator form and for the composite in the metasurface Salisbury screen form, respectively. The structural parameters of the magnetic resonator are p = 2806 nm, w = 1626 nm, h = 126 nm, and metal strip thickness equal to 80 nm. The structural parameters of the metasurface Salisbury screen are p = 527 nm, w = 517 nm, h = 430 nm, and metal strip thickness equal to 20 nm. (c) and (d) Spectra of reflectance, absorptance of the graphene and absorptance of the metal for the near-infrared-version MIM-graphene composite in the magnetic resonator form and for the composite in the metasurface Salisbury screen form, respectively. The structural parameters of the magnetic resonator are p = 550 nm, w = 217 nm, h = 15 nm, and metal strip thickness equal to 40 nm. The structural parameters of the metasurface Salisbury screen are p = 138 nm, w = 128 nm, h = 40 nm, and metal strip thickness equal to 20 nm. The Fermi level of graphene is 100 meV. The insets present the field distributions (|E|/|E₀|) on the x-z cross-section at the resonant wavelengths.

Download Full Size | PDF

Significant difference between in-plane polarized light absorption and out-of-plane polarized light absorption is common in a lot of 2D materials. Black phosphorus (BP) is famous for the in-plane anisotropy [64,65]. Actually, the difference between the in-plane permittivities (ε_x, ε_y) and the out-of-plane permittiviy (ε_z) is much larger [66]. As shown in Fig. 5(a) and 5(b), in the wavelength range from 2 µm to 5 µm, the imaginary part of ε_z approaches 0 [64,66], indicating that the absorption of out-of-plane polarized light is very inefficient. BP has received a lot attention due to the tunable band gap, the high mobility and potential optoelectronic applications in the mid-infrared regime [67–69]. However, the absorption of BP needs to be improved before practical usage. And tuning the local field polarization along the x-direction in the 2D-plane is important for absorption enhancement of BP. As shown in Fig. 5(c), the light absorption of monolayer BP in air at 3.5 µm is only 0.4%. The polarization of the incident light is along the most absorptive direction (x-direction). When the BP layer is integrated with the MIM structure in the magnetic resonator form (p = 1500 nm, w = 730 nm, h = 40 nm) as shown in Fig. 5(d), the absorptance of the monolayer BP is enhanced by 14.5 times to 5.8% at the critical coupling status. However, 94.2% of the incident power is consumed by the metal. When the form of the MIM-BP composite structure is switched to the metasurface Salisbury screen (p = 406 nm, w = 396 nm, h = 55 nm) as shown in Fig. 5(e), the absorptance of the BP is further enhanced to 31%, which is 77.5 times higher than that of the BP in air, and the metal loss is reduced to 69%. In addition, the metasurface Salisbury screen also enlarges the bandwidth of the absorption enhancement by 1.8 times. The MIM structure is made of Au and SiO₂ [60,63,70].

 

Fig. 5. (a) and (b) Real and imaginary parts of the diagonal elements of the permittivity tensor of BP. (c) Absorptance spectrum of monolayer BP in air. (d) Spectra of reflectance (R), absorptance of the BP (A_BP) and absorptance of the metal (A_m) for the MIM-BP composite in the magnetic resonator form (p = 1500 nm, w = 730 nm, h = 40 nm). (e) R, A_BP, and A_m for the MIM-BP composite in metasurface Salisbury screen form (p = 406 nm, w = 396 nm, h = 55 nm). The metal strip thickness is 20 nm for both cases.

Download Full Size | PDF

Molybdenum disulfide (MoS₂) is another promising 2D material. Since the background carriers can be extremely depleted due to the atomic thickness and the band gap around 1.9 eV to 1.3 eV [71,72], MoS₂ has been proposed for many high-performance optoelectronic devices in the visible-near infrared band. As shown in Fig. 6(a) and 6(b), the in-plane and out-of-plane optical properties of MoS₂ are very different [71,73]. Basically, MoS₂ is much more weakly respond to the out-of-plane polarized than to the in-plane polarized light. Like other 2D materials, the light absorption of 2D-MoS₂ is quite limited by the small thickness. As shown in Fig. 6(c), the absorptance of the monolayer MoS₂ in air is 0.9% at the wavelength of 705 nm and it is averagely lower than 7.3% in the visible-near infrared range (415 nm to 800 nm). Therefore, enhancing the light absorption of MoS₂ has become a key issue for all those applications. The polarization of the incident light is along the x direction. When the MoS₂ layer is integrated with the MIM structure in the magnetic resonator form (p = 350 nm, w = 40 nm, h = 5 nm) as shown in Fig. 6(d), the absorptance of the monolayer MoS₂ is enhanced by 59.1 times to 53.2% at the wavelength of 705 nm. However, and the metal loss is as high as 42.2%. The MoS₂ absorptance enhancement band is quite limited (FWHM∼27 nm) so the averaged absorptance of the MoS₂ over the visible-near infrared range (415 nm to 800 nm) is 15.5%. When the form of the MIM- MoS₂ composite structure is switched to the metasurface Salisbury screen (p = 41 nm, w = 31 nm, h = 26 nm) as shown in Fig. 6(e), the absorptance of the MoS₂ at the wavelength of 705 nm is further enhanced to 68.2%, which is 75.7 times higher than that of the MoS₂ in air. In addition, the metasurface Salisbury screen enhances the averaged absorptance of the MoS₂ over the visible-near infrared range (415 nm to 800 nm) from 15.5% to 68.1%. The metal in the MIM structure is made of Ag and SiO₂ [63,74].

 

Fig. 6. (a) and (b) Real and imaginary parts of the diagonal elements of the permittivity tensor of MoS₂. (c) Absorptance spectrum of monolayer MoS₂ in air. (d) Spectra of reflectance (R), absorptance of the MoS₂ (A_MoS2) and absorptance of the metal (A_m) for the MIM-MoS₂ composite in the magnetic resonator form (p = 350 nm, w = 40 nm, h = 5 nm, metal strip width equal to 50 nm). (e) R, A_MoS2, and A_m for the MIM- MoS₂ composite in metasurface Salisbury screen form (p = 41 nm, w = 31 nm, h = 26 nm, metal strip width equal to 20 nm).

Download Full Size | PDF

3. Conclusion

In conclusion, the polarization of the light field at the 2D material is revealed to be a crucial factor for light absorption enhancement of a 2D material integrated with a light coupling structure, especially with an absorptive light coupling structure. 2D materials are typically much more efficient to absorb in-plane polarized light than out-of-plane polarized light. Making the light polarization in-plane at the 2D material, as a pivotal strategy other than critical coupling, can selectively enhance the interaction between light and the 2D material instead of the interaction between light and the absorptive light coupling structure, and thus help the 2D material gain advantage over the metallic structure in the absorption competition. Concerning a popular light coupling structure, i.e. the MIM structure, it is demonstrated to have two forms: magnetic resonator form with the light mode mainly polarized out-of-plane and metasurface Salisbury screen form with the light mode mainly polarized in-plane. By investigating the MIM structures integrated with three representative 2D materials (graphene, BP and MoS₂), we revealed that the metasurface Salisbury screen form is always much more effective than the magnetic resonator form to enhance the light absorption of a 2D material, as it corresponds to a higher absorptance of the 2D material, a larger bandwidth and lower metal loss. This advantage of the metasurface Salisbury screen form is attributed to the in-plane polarization of its light mode. Based on an equivalent circuit model, the metasurface Salisbury screen is designed to ensure critical coupling as well. The influence of the light field polarization is expected to be significant over many 2D materials similar to graphene, BP and MoS₂. Therefore, our finding in this work would benefit the design of light coupling structures for 2D materials, which is relevant to a broad range of researches related to 2D material photonics and optoelectronics.