1. Introduction

Metamaterial perfect absorbers have been investigated extensively due to their broad potential applications, such as energy harvesting, thermal emitters, detectors and sensing [1–11]. Different types of resonant nanostructures have been proposed to achieve perfect absorption of the incident electromagnetic waves [12–17], where most of them take advantage of the unique properties of metallic nanostructures that support localized surface plasmon resonances (LSPRs). Sandwich structures with a metal nanoantenna-insulator-metal film (MIM) configuration is a common design in previous metamaterial absorbers, where one can tune the resonance wavelengths of the perfect absorbers by changing the size or shape of the top nanoantennas as well as the thickness of the middle dielectric spacer layer [18–27]. Due to the inherent Ohmic losses in metals, MIM-based MPAs often exhibit low quality resonances with a relatively broad bandwidth (>40 nm), which is far from the desired performance in spectroscopy and biosensing fields [28–31].

Although Ohmic loss cannot be completely avoided when using metals, radiative damping of plasmonic modes can be suppressed with rational design of the nanostructures. When metallic nanoparticles are arranged in a periodic array, they can scatter the incident light into diffracted waves. Certain diffractive waves in the plane of the arrays, known as Rayleigh anomaly (RA), can be coupled to the LSPRs of the constituent individual nanoparticles leading to the excitation of surface lattice resonances (SLRs), which can effectively suppress radiative damping and exhibit a narrow resonance bandwidth with a corresponding high quality-factor (Q-factor) [32–35]. In addition, more recent research witnesses a surging interest in all-dielectric nanoparticles or nanostructures made from high refractive index materials with inherent low loss [36,37]. Such all-dielectric nanoparticles or nanostructures can simultaneously support electric dipole (ED) and magnetic dipole (MD) modes providing a more versatile platform to engineering light-matter interactions on the nanoscale [38]. Similarly, when dielectric nanoparticles are arranged in an ordered array, the RA in the array can also be coupled with the ED or MD modes in the nanoparticles giving rise to narrow-band SLR modes, as an alternative method to achieve even higher quality resonances [39].

In this paper, we propose a new ultra-narrow-band perfect absorber consisting of a tungsten disulfide (WS₂) nanodisk array sitting on top of a gold film. In addition to its wide popularity as a 2D material, WS₂ also possess high refractive indices and thus can be used to fabricate Mie resonators [40]. Mode coupling between the MD modes of the WS₂ nanodisks and the RA of the disk array leads to the excitation of SLR modes with ultra-narrow bandwidth. Perfect absorption occurs at the SLR wavelength with the light energy absorbed by the lossy gold film. Ultra-narrow band perfect absorption is demonstrated in the near-infrared wavelength range and full-width at half maximum (FWHM) as small as 15 nm is achieved. Moreover, the SLRs depend strongly on the environmental refractive index, so the proposed perfect absorbers can be used in refractive index sensing and a sensitivity up to 1067nm/RIU is demonstrated.

2. Methods

Figure 1 shows the geometrical configuration of the proposed perfect absorber. WS₂ nanodisks sit on the top of an optically-opaque Au film and form a periodic array, whose pitches are labeled as Px and Py in the x and y direction, respectively, as shown in Fig. 1(a). Figure 1(b) shows the unit cell in the finite difference time domain (FDTD) numerical simulations. The incident light is polarized along the x direction and propagates along the z axis. A broadband planewave is used as the light source. Anti-symmetric and symmetric boundary conditions are applied in x and y directions, respectively, while perfectly matched layer (PML) boundary condition is used in z directions. The thickness of the gold film is set to 200 nm with the transmitted light completely blocked. The reflected light is collected to characterize the optical properties of the WS₂ nanodisks array. The dielectric constants of Au and WS₂ are obtained from the handbook edited by Palik [41] and the work by Ermolaev et. al. [42], respectively.

 

Fig. 1. Illustration of the WS₂ MPA (a) and the unit cell in the numerical simulation (b). The WS₂ nanodisks are arranged in a periodic array on a thick Au film. The geometrical parameters of the WS₂ nanodisk are diameter (D) and height (H). The periods of the array are Px and Py in x and y direction, respectively. The incident light is polarized along the x direction.

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3. Results and discussion

Figure 2(a) shows the reflection and absorption spectra of the WS₂ nanodisk array with the following parameters: Px = Py = 1300 nm, D = 340 nm and H = 200 nm. A very sharp absorption peak is observed at 1348 nm with a FWHM of 15 nm. The absorptivity (A) of the MPA can be calculated by the equation A = 1 – T – R, where T is the transmissivity and R is the reflectivity of the MPA. Here, T = 0 because the transmission of the light is totally blocked by the thick Au film making A and R complementary to each other. When R reduces to 0.002% at this wavelength, the corresponding absorptivity of the MPA reaches 99.998% achieving near perfect absorption within an ultra-narrow band.

 

Fig. 2. Optical properties of the MPA with Px = Py = 1300 nm, D = 340 nm, H = 150 nm. (a) Absorption and reflection spectra of the MPA with an FWHM of 15 nm. The electric near-field profiles in the x-y plane (z = 150 nm) and x-z plane (y = 0 nm) at resonance wavelength of 1348 nm are shown in (b) and (c), respectively. (d) Magnetic field intensity in the x-z plane (y = 0 nm) at 1348 nm. The red dotted lines represent the outline of a WS₂ nanodisk.

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Near-field distribution at the resonance wavelength of 1348 nm was investigated in numerical simulations to understand the characteristics of the resonance mode. Figures 2(b) (x-y plane) and 2(c) (x-z plane) show the near-field distribution of the electric field intensity (color mapping) and orientation (white arrows) at 1348 nm, respectively. At the top surface of the nanodisk [Fig. 2(b)], enhanced electric fields are observed at the center of the disk as well as on the edges along the polarization. As shown in Fig. 2(c), it is clear that the electric field stays mostly inside the WS₂ nanodisk and the field lines form a semicircle suggesting a magnetic dipole mode in y direction, which is also confirmed by the magnetic field distribution shown in Fig. 2(d). At resonance, the x-z cross-section (at y = 0) shows an enhanced magnetic field near the WS₂-Au interface in the center of the disk. As WS₂ shows a high refractive index ∼3 in the near-infrared regime, WS₂ nanodisks supports high-efficiency MD modes that are confined inside the nanostructure. By carefully choosing the pitch of the disk array, the RA mode in the array can couple to the MD modes of the individual WS₂ nanodisks enabling the generation of SLR mode with high Q-factor. Such mode coupling is also manifested by the asymmetric Fano-like profile of the absorption peak (or reflection dip) in Fig. 2(a). The near-field lines in Fig. 2(c) indicate that the electromagnetic near-field of the SLR mode can also slightly penetrate the gold film under the nanodisk converting the incident electromagnetic energy into heat in the gold film and creating a perfect absorption band similar to the SLR resonance. It is also noted that near-field intensity enhancement up to 525 times can be observed at the bottom of the two ends of the nanodisk [Fig. 2(c)] providing attractive sites for potential sensing applications.

Then, we studied the effect of the dimensions of the WS₂ nanodisk (i.e., D and H) on its perfect absorption property and the results are shown in Fig. 3. The period of the array is fixed at Px = Py = 1300 nm. In Fig. 3(a), we can see that the resonance peak exhibits a redshift from 1310 nm to 1580 nm as diameter D increases from 220 nm to 580 nm with height H unchanged (H = 150 nm). The major resonance shift and its corresponding FWHM, together with the absorptivity change, are summarized and shown in Fig. 3(b). As D increases, the absorptivity gradually increases to 100% achieving perfect absorption at D = 340 nm and then slowly decreases with further increase of D. The absorptivity of the MPA only reduces to 93% even when D increases to 420 nm. Figures 3(c) and 3(d) show the effect of height H on the SLR mode-induced absorption. Compared with diameter D, the increase of height just results in a moderate red-shift of the resonance. For both parameters, higher-order modes are observed in the shorter wavelength range for larger values of D or H. There appears a certain range of values for both D and H where near perfect absorption and small FWHM values can be achieved simultaneously. Such dimension tolerance is highly desirable as it can relax the strict requirement for nanofabrication. Furthermore, we find that the FWHM of the resonance can be as narrow as 15 nm with near perfect absorption. Therefore, we can tune the parameters to achieve perfect absorption and, simultaneously, an ultra-narrow-band (high-Q) resonance.

 

Fig. 3. Relationship of the simulated absorption, resonance wavelength and the FWHM) with the geometric parameters of the WS₂ nanodisk. (a) and (b) the dependence of the MPA on diameter D with H = 150 nm. (c) and (d) Dependence of the MPA on the height H with D = 340 nm. All the results were obtained at Px = Py = 1300 nm.

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As we mentioned above, the perfect absorption of this metasurface takes place within the SLR band. Thus, the resonance behavior of the MPA can also be tuned by the period of the WS₂ nanodisk array. The spectral positions, where Rayleigh anomalies occur under normal incidence, can be obtained from the following equation:

Figure 4(a) shows the reflection spectra of the MPAs with different Px while other parameters of the WS₂ nanodisk arrays are kept fixed: D = 340 nm, H = 150 nm. It can be seen that the resonance wavelength exhibits a distinctive redshift to the longer wavelength as Px increases. In the simulation, the environmental refractive index is set to be 1. According to Eq. (1), the position of (±1, 0)-order RAs can be simplified as Px. When Px = 900 nm, the RA is weakly coupled with the MD resonance of the WS₂ nanodisk resulting in a weak SLR mode and correspondingly lower absorption. The coupling becomes visibly stronger as Px continues to increase, accompanied by the redshift of (±1, 0) RAs and bandwidth narrowing. A sharp dip with the narrowest FWHM of ∼15 nm appears when Px increases to ∼1300 nm. As Px increases further, the RA spectrally move away from the MD mode narrowing the spectrum and weakening the SLR mode intensity. It should be noted that the stronger resonance is shifted from the position of RAs and the SLR mode arises on the longer-wavelength side of their associated diffraction orders [33]. Figure 4(b) shows the relationship between the SLR-induced absorption and Py. In contrast to Px, the variation of Py does not cause a significant shift of the resonance wavelength, which is consistent with the analysis above that the MD mode radiates in x direction. The reflection dip position only exhibits a blueshift of 15.7 nm when Py varies from 900 to 1600 nm.

 

Fig. 4. Reflection spectra of the MPA when (a) Px or (b) Py changes while the other one keeps fixed at 1300 nm. (c) Ultra-narrow-band perfect absorption can be achieved by varying different parameters of the array. (d) Energy absorption distribution in the x-y plane at z = - 3 nm inside the gold film.

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As shown in Figs. 3 and 4(a) and 4(b), each geometry parameter of the nanodisk and the array affects the resonance wavelength and intensity to various extents, which actually offers a straightforward means to rationally design and tune the MPA with an ultra-narrow FWHM in a wide wavelength range. Figure 4(c) displays such a capability of several ultra-narrow-band MPAs at various wavelengths ranging from 900 nm to 1700 nm. The FWHM of these absorbers is ∼15 nm and perfect absorption is achieved for all these MPAs.

For the proposed MPA consisting of WS₂ nanodisk arrays and an underlying gold film, the energy absorption occurs almost inside the latter as shown in Fig. 4(d), where the energy is mainly dissipated in the gold under the nanodisks. As the imaginary part of the refractive index of WS₂ is close to zero in this wavelength range, there is nearly no energy dissipation inside the disk. Figures 2(c) and 2(d) suggests field penetration into a superficial part of the gold enabling energy loss near the top surface of the Au film directly under the nanodisks, which is clearly shown in Fig. 4(d).

A perfect absorber with an ultra-narrow FWHM can find potential applications in many fields such biosensing and narrow-band thermal emitters [43–45]. According to Eq. (1), the SLR modes depend strongly on the refractive index changes of the environment. Therefore, the proposed perfect absorbers can be employed as refractive index sensors in biological applications. Figure 5(a) shows the evolution of the reflection spectra of the MPA with the refractive index variation of the surrounding medium. When the ambient refractive index increases from 1 to 1.06, the resonance wavelength shows a redshift about 64 nm while the absorptivity remains above 92.7% and the FWHM of the resonance stays almost the same. Figure 5(b) shows the linear dependence of the resonance wavelength on the environmental refractive index. The MPA is highly sensitive to external refractive index variations with a sensitivity up to 1067 nm/RIU, which is much higher than those of some common plasmonic structures [12,46].

 

Fig. 5. (a) Evolution of the reflection spectra of the MPA under different environmental refractive indices. (b) Linear relationship is established between resonance wavelength and the environmental refractive index.

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It is noted that the proposed perfect absorbers can be fabricated using similar lithography tools as demonstrated in Ref. [40], where plasma etching was used to fashion WS₂ nanodisks from WS₂ multilayer flakes. In addition to mechanical exfoliation, WS₂ thin films can also be prepared via sputtering for the fabrication of large-area nanodisk arrays.

In summary, we have proposed and numerically analyzed a metamaterial perfect absorber consisting of periodic WS₂ nanodisks on top of a gold film. We utilized the high refractive-index and low loss properties of WS₂ in the near infrared. By rationally choosing the geometrical parameters of the nanodisk array, ultra-narrow-band SLR mode can be excited via the coupling between the RA of the array and the MD modes of individual WS₂ nanodisks. The electromagnetic field penetration in the gold film converts the incident light energy within the SLR band into heat readily creating an effective ultra-narrow-band perfect absorber in the near infrared. It is anticipated that such ultra-narrow-band MPAs can find potential applications for biosensors as well as for narrow-band thermal emitters.