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A magnetic coupling metasurface with a structure of a Ag nanograting/space layer/Ag reflector is proposed to achieve broad-band and broad-angular absorption response for 2D materials such as a MoS2 monolayer. By reducing the size of the Ag nanograting and thickness of the spacer into deep subwavelength, strong magnetic coupling effects occur within the metasurface. The magnetic coupling effects can confine large energy density and reduce the metallic optical loss to a relatively low value in the structure. Correspondingly, broadband absorption enhancement is achieved for the MoS2 monolayer. The average absorption within the visible wavelength range reaches as high as 72.7% and the value still remains over 40% when the incident angle increases up to 80°. It is revealed that the magnetic coupling effects are more efficient than both the plasmonic and the magnetic resonant effects to achieve broad-band and broad-angular absorption in ultrathin 2D material absorbers.
© 2016 Optical Society of America
Corrections
8 December 2016: A correction was made to the author listing.
1. Introduction
In recent years, there has been a great deal of interest in studying optical properties of transition metal dichalcogenides, such as MoS2, MoSe2, WS2 and WSe2, since they can be applied to atomic-scale optoelectronic devices like photodetectors, solar cells, and optically pumped lasers [1–5]. However, the absorption of a single sheet of transition metal dichalcogenides is still relatively low due to the small thickness of the materials [4,5]. For example, a monolayer of MoS2 can absorb less than 25% of the normal incidence light and the relatively low absorption limits its potential application in solar energy conversion devices and photodetectors.
To improve light absorption in the MoS2 monolayer, various resonant systems have been proposed to improve the interaction between the MoS2 monolayer and the light [6–10]. Some examples of these systems are chirped-planar-dielectric cavity, nanocavity resonance combined with plasmonic nanoparticles and multiple guided resonances of photonic crystal slabs [8–10]. With these resonant nanostructures, absorption spectra with multiple peaks are obtained for the MoS2 monolayer and an average absorption of 51% is achieved within the visible wavelength [10]. Despite this, an intrinsic shortcoming still occurs for the resonant structures. The off-resonance suppression always leads to a relatively low absorption for the light with wavelength far away from the resonant modes, which prevents the average absorption in the whole range from being further improved. To solve this problem, broad-band light trapping structure should be developed for the MoS2 monolayer so that it can be more efficiently applied to solar energy conversion devices and broad-band photodetectors.
For this purpose, we develop a magnetic coupling metasurface with a structure of metal nanostructure/spacer layer/metal reflector (MDM) to achieve broadband absorption for the MoS2 monolayer. In fact, MDM metasurfaces with localized surface plasmonic resonance (LSPR) and magnetic resonance have been proposed in previous studies to achieve high absorption, and the absorption value has reached as high as 100% [11–15]. In spite of the total absorption achieved, these metasurfaces cannot be efficiently used as light trapping structures to enhance light absorption in 2D materials [14,15]. The reason is that the LSPR and the magnetic resonance raise the optical absorption of the metal in the process of achieving total absorption for the whole metasurface. With the rise in the metallic absorption, light absorption of the 2D materials in the structure is proportionally reduced.
To circumvent the intrinsic metallic absorption, magnetic coupling is introduced into the metasurface to enhance light absorption of the 2D materials such as a MoS2 monolayer. Strong magnetic coupling in the MDM metasurface can be achieved by reducing the size of the Ag nanograting and thickness of the spacer into deep subwavelength. Compared with the plasmonic resonant effects and the magnetic resonant effects in previous studies, the magnetic coupling effects have two advantages: broad-band energy density enhancement and small metallic absorption loss. These advantages render the magnetic coupling effects more efficient to enable broad-band absorption enhancement in the MoS2 monolayer. Correspondingly, the average absorption within the visible wavelength range reaches as high as 72.7%, much higher than the highest value (51%) reported in recent papers [8–10].
2. Structure and method
The magnetic coupling metasurface proposed to enhance light absorption in the MoS2 monolayer has a MDM structure of Ag nanograting/SiO2/Ag reflector, as is shown in Fig. 1. The Ag reflector is assumed to have a thickness of 100nm. SiO2 acts as a spacer layer and its thickness is referred to as d. The thickness, period and strip width of the Ag nanogratings are h, p and w, respectively. The monolayer of MoS2 is inserted between the Ag grating and the SiO2 spacer layer in the MDM metasurface.
Fig. 1 Structure of the metasurface used in this paper. p, h denote the period and thickness of the Ag grating. w is the width of the Ag strips in the grating.
Finite element method is employed to calculate the optical electric field in the MDM structure [16–18]. With the optical electric field obtained from the finite element method as input parameters, the average energy density enhancement (U/U0) in the region below the Ag grating and light absorption in the MoS2 monolayer can be calculated. U denotes the average energy density in the region with a distance less than 3nm to the Ag nanograting/SiO2 and U0 is the average energy density of the incident wave. Light absorption in the 2D materials is then calculated as , where ε0 is the permittivity of vacuum; λ and I(λ) are respectively the wavelength and intensity of the incident light; n and k denote the refraction index and extinction coefficient of the MoS2 monolayer; E is the optical electric field in the MoS2 monolayer. In the calculation, the refractive index of Ag, SiO2 and MoS2 monolayer are adopted from references [19,20].
3. Results and discussion
3.1 Large and broad energy density enhancement in the magnetic coupling metasurface
The magnetic coupling effects within the MDM structure are first investigated by calculating the average energy density enhancement (U/U0) below the Ag grating. In the calculation, h, p and w of the grating are set as 20nm, 50nm and 30nm; d, the thickness of the spacer layer, is set as 40nm (Device I). In this device, no MoS2 is inserted in the MDM structure yet. The calculated results are shown in Fig. 2(a), where U/U0 shows two peaks at 429nm and 571nm.
Fig. 2 Energy density enhancement (U/U0) and absorption in Ag grips. (a) for Device I; (b) for Device II.
The peak at 429nm is high and narrow. It results from the superposed effects of the LSPR of the Ag strips and the constructive interference between the incident light and light reflected from the Ag reflector. The excitation of the LSPR is confirmed by Fig. 2(a), where a resonant absorption peak is observed in the Ag strips. The LSPR can significantly improve the optical electric field around the corner of the Ag strips and then increase the energy density (see Fig. 3(a)). In addition, the light reflected from the Ag reflector can constructively interfere with the incident light and further amplify the optical electric field density at the short wavelength range [21].
Fig. 3 Optical electric field in the MDM metasurface. (a) and (b) for Device I with wavelength of 429nm and 571nm.(c) for Device II with wavelength of 650nm. |E| is the modulus of optical electric field in the device and |E0| denotes that of the incident light. The red arrows denote the electric displacement. The dotted line denotes the magnetic unit.
To understand the broadband peak at 571nm, we calculate the optical electric field within the MDM metasurface and the calculated results are shown in Fig. 3 (b). It is observed that the electric displacement shows a nearly parallel and inverse direction in the Ag grating and the Ag reflector. The antiparallel electric displacement is further analyzed by investigating another MDM device with larger unit size (p = 300nm, h = 80nm, Device II). In this device, the electric displacement circulates within the magnetic unit which is formed by the Ag strip, the spacer, and the Ag reflector for the light with wavelength of 650nm, as is shown in Fig. 3(c). The circulation of the electric displacement indicates that magnetic resonance occurs, and the magnetic resonance leads to a high energy density enhancement (see Fig. 2(b)) [22,23]. In the case of Device I, however, the period is as small as 50nm. The neighboring two magnetic units are so close that they couple with each other and the electric displacement current can flow from one to the other (see Fig. 3(b)). As a result, the circulation of the electric displacement within a single magnetic unit disappears. Instead, the electric displacement current in the Ag grating and the Ag reflector flows to infinity in an antiparallel direction and forms a loop at infinity. Magnetic coupling occurs and it confines large optical electric field between the Ag strips, leading to broad-band enhancement in the energy density below the grating.
In addition to the broadband energy enhancement, it is found in Fig. 2(a) that light absorption of the Ag strips is below 20% at the long wavelength range where magnetic coupling effects are the main forces of enhancing energy density. The relatively low metallic absorption occurs because more optical energy is confined between the Ag strips and less is confined within the corners of the Ag strips (Fig. 3(b)). Correspondingly, the light absorption in Ag strips is relatively low. In contrast, at the wavelength range where LSPR or magnetic resonance occurs, more energy is confined within the Ag strips (Fig. 3(a) and 3c)), leading to a relatively high absorption peak in the Ag strips. Based on these findings, it can be concluded that the magnetic coupling has two advantages: broad-band energy density enhancement and small metallic absorption loss when it is used to improve the absorption capability of ultrathin absorbers.
3.2 Broad-band and broad-angular absorption enhancement for the MoS2 monolayer
In light of the two advantages observed above, the magnetic coupling effects are utilized to enhance light absorption in a MoS2 monolayer. For this purpose, a MoS2 monolayer is inserted below the Ag nanograting in Device I and the device has a structure of Ag nanograting/MoS2/SiO2/Ag reflector. The calculated results are shown in Fig. 4(a). It is observed that light absorption of the MoS2 monolayer is higher than 65% in the wavelength range of 420nm-680nm. Moreover, the average absorption within the wavelength range of 420nm-700nm is about 72.7%, about 7.3 times that (about 9.9%) of a MoS2 monolayer in free space. There are mainly two factors contributing to the broad-band absorption enhancement for the MoS2 monolayer. As is discussed in previous section, in the short wavelength range, the superposed effects of the LSPR and the constructive interference significantly improve the energy density below the Ag grating and increase light absorption in the MoS2. At the long wavelength range, the magnetic coupling effects lead to a broad enhancement for the energy density and improve light absorption of the MoS2 monolayer in a broad wavelength range.
Fig. 4 (a) Absorption spectrum for the MoS2 monolayer inserted in Device I and II. Black line for the MoS2 in Device I; red dotted line for the MoS2 in Device II; blue dashed line for a bare monolayer MoS2. (b) Absorption spectrum for the MoS2 monolayer inserted in Device I (black line) and in Device I without Ag grating (red dashed line).
More specifically, it is observed in Fig. 4(a) that absorption reaches a high value of 84% at the wavelength of 617nm, higher than the peak value (75%) at the short wavelength of 450nm where U/U0 is even much larger. In the short wavelength range, absorption is relatively lower because the intrinsic optical loss in the Ag strips is also increased by the LSPR, which in turn reduces light absorption in the MoS2. The LSPR even causes a reduction in light absorption in the MoS2 monolayer. In Fig. 4(b), light absorption of the MoS2 in Device I is lower at the short wavelength range below 428nm when compared with that of the device in which no Ag grating is capped (i.e. no LSPR occurs). At the long wavelength range, however, increase in light absorption of the MoS2 is mainly caused by the magnetic coupling effects of the Ag strips. The magnetic coupling effects can improve light absorption in the MoS2 with less absorption in Ag strips, resulting in a relatively higher absorption in the MoS2 monolayer. The advantage of the magnetic coupling effects is further verified by calculating light absorption of the MoS2 inserted in the magnetic resonant Device II. Figure 4(a) demonstrates that light absorption of the MoS2 is lower in Device II than in Device I because the magnetic resonance in Device II can also raise the absorption loss in the Ag grating, which proportionally reduces light absorption in the MoS2 monolayer. Apparently, the magnetic coupling effects are more efficient to achieve higher and broader absorption response than the LSPR and the magnetic resonance.
For deeper insights into the effects of magnetic coupling on light absorption in the MoS2 monolayer, further investigation is carried out by calculating light absorption in the MoS2 monolayer with varied thickness of the spacer (d) and period of the grating (p). Device I with a MoS2 monolayer inserted are utilized for the calculation as strong magnetic coupling occurs in the device. The calculated results are shown in Fig. 5.
Fig. 5 (a) Absorption in the MoS2 monolayer as a function of the wavelength and thickness of the spacer layer. (b) Average absorption of the MoS2 monolayer as a function of the spacer layer. (c) Absorption in MoS2 monolayer when d is set as 40nm and 250nm. (d) Optical electric field in the MDM metasurface with d equal to 250nm. The wavelength is set as 620nm. |E| is the modulus of optical electric field in the device and |E0| denotes that of the incident light. The red arrows denote the electric displacement.
Figure 5(a) and 5(b) demonstrate the calculated light absorption as a function of the thickness of the spacer layer (d). In the calculation, p, w and h are set as 50nm, 30nm and 20nm, respectively. From the figure, it is observed that light absorption shows an oscillating behavior when d increases. This happens because the reflected light from the metal reflector interferes with the incident light and forms a field background that oscillates. For large d of 250nm, absorption peak occurs in the MoS2 monolayer but the peak is narrower than that for d equal to 40nm. When d is set as 250nm, coupling between the Ag grating and the Ag reflector is weak and magnetic coupling does not occur since the electric displacement is predominantly aligned along one direction, as is shown in Fig. 5(d). In this case, however, the plasmonic coupling (i.e., electrical coupling) still occurs between the Ag strips since their distance is very small, confining large optical field between the Ag strips and leading to the absorption peak for the MoS2. As far as small d (i.e., d = 40nm) is concerned, strong magnetic coupling effects occurs between the Ag nanograting and the metal substrate, and the entire nanostructure can be assumed as a homogeneous effective medium25. As a result, large absorption is achieved simultaneously for the light with wavelength ranging from the blue to the red. Broad-band absorption enhancement is achieved.
It is noted that light absorption in the MoS2 monolayer is low in the whole visible wavelength range when d is set as 140nm (Fig. 5(a)). This happens because for the visible light the MoS2 monolayer is positioned far away from both the first-order and second-order electric maximum caused by the constructive interference between the incident light and the light reflected from the metal. As a result, the average absorption in the MoS2 monolayer reaches the minimum. Generally, low absorption band occurs for the MoS2 monolayer when d is increased from 100nm to 200nm due to the destructive interference, and the average absorption remains at a relatively low value.
Figure 6(a) and 6(b) demonstrate the calculated light absorption as a function of the period of the grating (p). In the calculation, d, w and h are set as 40nm, 30nm and 20nm, respectively. It is observed that light absorption within the short wavelength range of 420nm-450nm only varies slightly when the period increases. Light absorption at the wavelength larger than 500nm, however, decreases rapidly when the period increases. This is because increase in p can raise the gap between the Ag strips, which reduces the coupling between the Ag strips. As a result, the displacement current cannot flow from one strip to another and magnetic coupling does not occur. The optical electric field confined within the gaps decreases and light absorption of the MoS2 monolayer is reduced, as is shown in Fig. 6(c), 6(d) and 6(e).
Fig. 6 (a) Absorption in the MoS2 monolayer as a function of the wavelength and the period of grating. (b) Average absorption of the MoS2 monolayer as a function of the period of grating. (c), (d) and (e) denote the optical electric field when p is set as 50nm, 100nm and 200nm, respectively. The wavelength of the incident light is assumed to be 600nm. |E| is the modulus of optical electric field in the device and |E0| denotes that of the incident light.
The calculations above demonstrate that the magnetic coupling occurs only when both the distance between the Ag strips and the distance between the Ag grating and the Ag reflector are very small. The magnetic coupling, together with the superposed effects of the LSPR and the constructive interference, can lead to a high average absorption of about 72.7% in the MoS2 monolayer. Apart from the discussion concerning the normal incident light, the angular response of the structure is also investigated. For this purpose, we calculate the optical absorption as a function of the wavelength and the angle of incidence. The calculated results are shown in Fig. 7(a) and the average absorption is shown in Fig. 7(b). It is observed from Fig. 7(a) that the absorption band and absorption efficiency of MoS2 are almost independent of the incident angle. This indicates that the strength of magnetic coupling can be maintained for TM-polarized incident light with all incident angles due to the unchanged direction of the magnetic field [15]. Specifically, the average absorption remains higher than 70% when the incident angle increases to 50°. The value is still lager than 40% even when the incident angle is increased up to 80°.
Fig. 7 (a) Absorption in the MoS2 monolayer as a function of the wavelength and incident light. (b) Average absorption of the MoS2 monolayer as a function of incident angle.
3.3 Universality of the broad-band and broad-angular absorption enhancement
The calculation so far has demonstrated that the magnetic coupling metasurface can be used to achieve broad-band and broad-angular absorption enhancement for the MoS2 monolayer. In this section, we examine whether the magnetic coupling metasurface can be widely used to achieve broad-band and broad-angular absorption enhancement for various 2D materials. Light absorption in a monolayer of 2D materials such as MoSe2 and graphene is first calculated when they substitute MoS2 as the thin absorber. In the calculation, the device is assumed to have a structure of Ag nanograting/2D material/SiO2/Ag reflector. The refractive index of MoSe2 and graphene are adopted from references [19,25]. In the device, d, h, p and w are set as 40nm, 20nm, 50nm and 30nm, respectively. The calculated results are shown in Fig. 8. It is observed from Fig. 8(a) that absorption in MoSe2 is larger than 58% in the wavelength range of 420nm-825nm under normal incidence. The average absorption within the wavelength range of 420nm-840nm reaches a high value of 73.6%, about 8.5 times that (about 8.6%) of the MoSe2 monolayer in free space. In addition, the average absorption remains over 61% when the incident angle increases to 60° (see Fig. 8(b)), indicating broad-angular response.
Fig. 8 (a) Absorption for the MoSe2 monolayer when incident angle is varied. (b) Average absorption for the MoSe2 monolayer as a function of incident angle. (c) Absorption for graphene film with different layer number (N). (d) Average absorption in graphene film as a function of N.
As far as graphene is concerned, Fig. 8(c) demonstrates that the maximum of the absorption spectrum reaches a high value of 55%. This value is larger than those obtained in pervious studies where metal nanostructures are used to enhance absorption in graphene. More importantly, light absorption is larger than 20% in the broad wavelength range of 400nm-800nm without any oscillating behavior, while for the broad absorption spectrum achieved by the multi-resonant nanostructures in former studies, the value of absorption is observed to oscillate dramatically [14,15]. Correspondingly, the average absorption reaches a relatively higher value of 41.9%, about 18 times that of graphene in free space. This value is also much higher than that presented in previous research where multi-resonant nanostructures are used to broaden the absorption response [14, 15]. The average absorption can be further increased by inserting multi-layer graphene films in the MDM structure. As is shown in Fig. 8(c) and 8(d), light absorption in graphene films rises with the increase in the layer number (N) of the graphene and the average absorption is improved up to 75% when N is equal to 5.
In addition to MoS2, MoSe2 and graphene, broad-band and broad-angular absorption enhancement can also be achieved when other 2D materials such as WS2 and WSe2 are used as the ultrathin absorber in the magnetic coupling MDM metasurface, as is shown in Fig. 9. The average absorption reaches a high value of 60% in a broad-angular range. These findings confirm the conclusion that the magnetic coupling MDM metasurface is a general approach to improve light absorption of various monolayer 2D materials in both broad wavelength range and broad angular range.
Fig. 9 (a) Absorption for the WS2 monolayer when incident angle is varied. (b) Average absorption of the WS2 within the wavelength range of 420-700nm as a function of incident angle. (c) Absorption for the WSe2 monolayer when incident angle is varied. (d) Average absorption of the WSe2 within the wavelength range of 420-800nm as a function of incident angle.
Finally, we investigate the effects of the metal material on the light absorption of the 2D material. In the calculation, Au or Al substitutes Ag as the grating and metal reflector in the device. d, h, p and w of the device are set as 40nm, 20nm, 50nm and 30nm, respectively. The 2D material is assumed to be a MoS2 monolayer and the calculated results are shown in Fig. 10. For the Au device, light absorption of the MoS2 monolayer is significantly improved in the red wavelength range due to the magnetic coupling effects, but relatively low absorption is achieved in the blue wavelength range due to the absorption loss in Au. As far as the Al device is concerned, light absorption in the whole wavelength range is significantly improved and an average value of 52.3% is achieved due to the magnetic coupling effects, which are also accompanied by the superposed effects of the LSPR and the constructive interference between the incident light and the light reflected by the metal reflector. This finding is similar to the case for the Ag-device discussed in previous sections. However, the average absorption in Al device is still lower than that in the Ag device since the plasmonic enhancement effect of the Al is relatively weaker than that of Ag.
4. Summary
In conclusion, we propose a magnetic coupling metasurface to achieve broad-band and broad-angular absorption enhancement for a MoS2 monolayer. It is revealed that the magnetic coupling effects are more efficient to achieve higher and broader absorption response than the LSPR and the magnetic resonance. For the MoS2 monolayer, the average absorption within the visible wavelength range of 420nm-700nm reaches as high as 72.7% and the value still remains over 40% even when the incident angle increases up to 80°. Similar results can also be achieved for other 2D materials such as MoSe2, WS2, WSe2 or graphene. The results shall strike a new path for applying metasurface to enable broad-band and broad-angular absorption response for 2D materials.
Funding
Guangdong Natural Science Funds for Distinguished Young Scholar (Grant No: 2014A030306005); Natural Science Foundation of Guangdong Province, China (Grant No. S2013010012854, 2016A03031339); Foundation for High-level Talents in Higher Education of Guangdong Province, China (Yue Cai-Jiao [2013]246, Jiang Cai-Jiao[2014]10); Development Program for Outstanding Young Teachers in Guangdong University (Yue Jiaoshi [2014]108); The Science and Technology Program of Guangzhou (No.201607010176), Special Funds for the Cultivation of Guangdong College Student.
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