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Abstract
Ultrabroadband absorbers are vital for applications such as solar energy harvesting and integrated optoelectronic devices. Herein, we design, fabricate and characterize a novel ultrabroadband and ultrathin absorber based on the encapsulated T-shaped metasurface (ETM). The ETM consists of a 20 nm Cr film and a Cr substrate sandwiched by the T-shaped polymethyl methacrylate (PMMA) arrays. The Cr film provides a robust absorptive surface with improved impedance matching, and ultrabroadband absorption can be achieved via the excitation of the localized surface plasmon (LSP) of this ultrathin film. The average absorption of simulated and experimental results of the ETM in the visible range of 400-800 nm for the TM (TE) polarization are 96.4% (96.3%) and 90.6% (89.4%), respectively. Three-dimensional (3D) power dissipation density distributions of the proposed structure have been investigated, which indicates that the synergistic absorption effect of different parts of the T-shaped ultrathin Cr film contributes to the major absorption enhancement. The absorption of the ETM is very robust to the changes of geometrical parameters and the symmetry of the structure, and it can be maintained almost the same even if T-shaped profiles are changed to L-shaped profiles. Moreover, the absorption performance of the ETM exhibits polarization-insensitive and wide-angle features, which has advantages for many potential applications.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Plasmonic absorbers have received widespread attention due to their unique ability to trap electromagnetic waves, which have potential applications in photovoltaics [1–3], photoelectric detectors [4,5], sensing [6–8], imaging [9,10], and thermal emitters [11,12]. Generally, the typical design scheme for a plasmonic absorber consists of sandwiched metal-insulator-metal (MIM) layers with a patterned metallic surface [13], high-efficient absorption can be realized by exciting electric resonance or magnetic resonance confined in the structure. In addition, by tailoring the shape of the metallic surface of the MIM structure such as nanodisk [14,15], nanosquare [16], nanohole [17], ŋ-shape [18], and nanoring [19,20], single band or multiband absorption enhancement can be obtained. Unfortunately, the absorption bandwidth based on electrical resonance or magnetic resonance is relatively narrow due to its resonance characteristics. For applications such as solar energy harvesting and optical imaging, broadband absorbers with angle and polarization-insensitive performances are highly desired. In order to increase the absorption bandwidth, multi-sized resonators such as multi-sized cylinders [21], squares [22–24], crosses [25,26], trapezoids [27], patches [28,29], grooves [30,31], and rings [32–34] are integrated into the unit cell of the structure, and broadband absorption is feasible due to the overlapping of multiple absorption peaks. However, the absorption bandwidth of the multi-sized absorber is limited by the number of resonators that can be integrated into the unit cell, and the introduction of multi-sized patterns also increases the fabrication difficulty.
In addition, it is noteworthy that hyperbolic metamaterials (HMMs) can also support light trapping over a wide wavelength range due to the hyperbolic dispersion, which originates from the orthogonal elements of the permittivity or permeability tensors having the opposite sign. In recent years, nanostructured HMMs for broadband absorption have attracted extensive attention. These nanostructures are usually composed of metal/dielectric multilayers with graded width such as sawtooth, which absorbs different wavelengths through different widths of the structures with the aid of the slow light effect [35]. Later, many improved metal/dielectric multilayered structures such as pyramids [36,37], conical frustums [38–40], tapers [41,42], spheres [43], cascaded nonorods [44,45], and multilayer metasurfaces [46,47] are also proposed to achieve broadband absorption. Compared with the sawtooth structure, these types of structures contain the two-dimensional (2D) arrays whose width varying with their depths, so they can achieve polarization insensitive light absorption while ensuring broad absorption bandwidth. Although depolarized broadband absorption can be achieved by using these improved structures, a large number of metal/dielectric multilayers are required, resulting in the increase of the bulk size of the devices, and the graded width of the structure also increases the difficulty of manufacturing. Moreover, at optical frequencies, most of the reported broadband absorbers have employed the noble metal, such as gold, silver as one ingredient of the alternating layers [29–33,38–41], which leads to the increase of the manufacturing costs. Therefore, it is crucial to explore high-efficient broadband absorber with good angular-and polarization-performances within a comparatively simple, low-cost and ultrathin architecture.
In this paper, an ultrabroadband and ultrathin absorber is presented by using a comparatively simple architecture of encapsulated T-shaped metasurface (ETM). The ETM consists of an ultrathin Cr film and a Cr substrate sandwiched by the T-shaped polymethyl methacrylate (PMMA) arrays. In the wavelength region of 400-800 nm, the absorption of the simulated and measured results of the ETM are greater than 96.3% and 89.4%, respectively. Three-dimensional (3D) power dissipation density distributions of the structure show that the ultrabroadband absorption is mainly resulted from the synergic effect of different parts of the ultrathin T-shaped Cr film. In addition, the absorption response of the ETM is insensitive to the variations of the geometric parameters and the structural symmetry, and good absorption performance can be maintained even the polarization angle and the incent angle are significantly altered.
2. Design and characterization
Figure 1 depicts the schematic diagram and the cross-section view of the ETM under the illumination of the transverse magnetic (TM) polarized wave (magnetic field perpendicular to the plane of incidence) with incident angle of θ and azimuthal angle of φ. Herein, Cr is chosen as the absorption metal due to its high imaginary part of the refractive index in visible and near-infrared regions. In addition, Cr has good thermal stability and chemically inactive features [48], and it can be easily deposited using conventional magnetron sputtering system, which facilitates the fabrication of the ETM. The unit cell of the ETM consists of a Cr film and a Cr substrate sandwiched by a T-shaped PMMA. The T-shaped PMMA includes a horizontal bar (along x axis) and a vertical bar (along y axis). The length and width of the horizontal bar are L1 and W1, respectively; the length and width of the vertical bar are L2 and W2, respectively. The height of the T-shaped PMMA is hd, and the T-shaped PMMA is encapsulated by an ultrathin Cr film with thickness of hm. The period of the ETM along the x and y directions are Px=Py=P. The background is air with the refractive index equal to 1. The refractive index of PMMA is 1.49 [49], and the refractive indices of Cr are derived from Palik [50].
Fig. 1. (a) Schematic diagram of the proposed ETM absorber. (b) Cross-section view of the unit cell of the ETM in the xy and xz planes. The parameters are: Px=Py=P=300 nm, L1=180 nm, W1=20 nm, L2=130 nm, W2=30 nm, hm=20 nm, and hd=130 nm.
For a 2D periodic lattice illuminated by plane wave with incident angle θ and azimuthal angle φ, the diffraction angle θmn and azimuth angle ϕmn for the (m,n) diffraction order can be expressed as [51,52]:
For the ETM absorber under normal incidence with φ=0, subwavelength structure is required so as to achieve high absorption efficiency. According to Eq. (1), the subwavelength condition of the ETM that ensures only zero-order diffractive waves in the background can be simplified as:
In simulations, 3D finite-difference time-domain (FDTD) approach was utilized to calculate the absorption spectra of the ETM. Periodic boundary conditions are set in the x and y directions, and perfectly matched layers are used in the z direction. The grid size along the x, y and z axis is set to 3 nm. Because the optically thick Cr substrate blocks the light transmission, the total absorption of the ETM can be reduced as A(λ) = 1-R(λ), where R(λ) denotes the reflection of the structure. Meanwhile, by calculating the power dissipation in a specific volume of the unit cell, the absorption spectra of different parts of the ETM can be obtained by the volume integration as below [53]:
where ε0 is the permittivity of vacuum, ω is the angular frequency, ε is the relative dielectric permittivity of each layer, Imε(ω) is the imaginary part of ε, and E is the electric field.
To compare the absorption bandwidth of the ETM absorber with other reported absorbers, we define the relative absorption bandwidth (RAB) as:
where λL and λS are the upper and lower limits of the wavelength region with the absorption greater than 90%. In addition, the average absorption of the structure can be calculated as:The SEM image of fabricated ETM absorber is shown in Fig. 2(a). The ETM is realized through T-shaped PMMA fabrication following with ultrathin Cr film deposition. Comparing with the absorbers based on the MIM [54] or HMMs structures [55], the fabrication procedure of the ETM is comparably simpler. That is, in the fabrication process of the ETM, only metal material is required to be deposited, and the lift-off process is not required as well, the detailed information can be found in Supplement 1, Fig. S1. The ETM was fabricated as follows: Firstly, a 100 nm thick Cr film was deposited on the quartz glass at room temperature as Cr substrate via magnetron sputtering system (MSP-620; Beijing Jinshengweina Technology Co. Ltd., China) with deposition rate of 0.3 nm/s, sputtering power of 200 W and pressure of 1×10−4 Pa, then a 130 nm thick PMMA was spin-coated on the Cr substrate and baked on a hotplate at 180 °C for 170 s. Secondly, the PMMA layer with an area of 180 μm×180 μm was exposed by using thee-beam lithography (JEOL 6300 FS; JEOL Co. Ltd., Japan) with a 7 nm beam size at 100 kV. After the e-beam exposure, the development process was performed to achieve the T-shaped PMMA arrays using amyl acetate for 80 s, and iso-propyl alcohol (IPA) rinse for 70 s. Finally, the T-shaped PMMA arrays were encapsulated by the 20 nm thick Cr film via magnetron sputtering system at room temperature. From the point view of application, an additional remark is that nanoimprint lithography or continuously variable spatial frequency photolithography could be used to fabricate the ETM over a much larger area [56,57].
Fig. 2. (a) SEM images of the fabricated ETM with a zoomed image in the inset. The white scale bar is 600 nm. (b) Theoretical and experimental spectra of the ETM illuminated by TM wave with θ=0 and φ=0.
Figure 2(b) shows the simulated and measured spectra of the ETM illuminated by the TM wave with θ=0 and φ=0. The reflection spectra of the sample are measured by using the angle-resolved microspectroscope (AR-ARM; Ideaoptics Instruments Co. Ltd., China). A 100 W halogen lamp works as a broadband light source. A 100× microscope objective lens with a numerical aperture of 0.9 was used to measure the area of the sample about 80 μm×80 μm. Reflection response R(λ) were normalized to a silver mirror with 96% reflectivity in the designed wavelength region, and the measured absorption of the sample is obtained as A(λ) = 1-R(λ). In Fig. 2(b), it can be seen from the simulation results that the ETM exhibits good absorption performance with two resonant absorption peaks occurred at 401.2 nm and 650.6 nm, and the average absorption of the ETM is Aav=96.4% in the visible range of 400-800 nm. The RAB of the designed ETM is 89.2%, which is comparable with many broadband absorbers such as multisized squares [22,23], multisized grooves [30,31], multisized nanorings [32,33], and multilayered conical frustums [38,40] in the visible and infrared regions, while the ETM has the advantages of simpler architecture and without using noble metals. However, although the measured average absorption of the ETM is high (90.6%) in the range of 400-800 nm, there are some mismatches between the simulated and measured spectra, particularly in the longer wavelength region. The discrepancies may result from fabrication errors, such as the imperfect T-shaped metasurface, the inconsistent permittivity of Cr between simulation and experiment, and scattering due to the rough surface features. Note due to the limitation of detectability of the silicon-based photodetector of our measured system, the measured absorption response is fluctuated significantly beyond the range of 400-1000 nm.
3. Physical mechanism for ultrabroadband absorption
To better understand the physical mechanism for ultrabroadband absorption of the ETM via the 20 nm ultrathin Cr film, the impedance feature of the ETM without the ultrathin Cr film (hm=0) are compared with that of the ETM. According to the impedance theory [58,59], the impedance Z of the ETM can be expressed as follows:
where S11, S21, S12, S22 are S parameters; n, k, and d are the effective refractive index, the wave vector, and thickness of the ETM, respectively. Reflection from the ETM can be calculated as R = [(Z-Z0)/(Z + Z0)]2, where Z0 is the impedance of free space.As shown in Fig. 3(a), for the ETM without the ultrathin Cr film, the impedance of the structure is mismatched with that of the free space, and high reflection is occurred due to the mirror effect from the metallic Cr substrate. However, as shown in Fig. 3(b), the impedance of the ETM can be well improved as the T-shaped PMMA arrays are encapsulated by the 20 nm Cr film, the real part of Z tends to 1 and its imaginary part approaches 0, resulting in ultrabroadband antireflection effect in the wavelength region of interest. Obviously, the introduction of the 20 nm ultrathin Cr film not only provides a more robust surface (surface of T-shaped PMMA can be protected by the Cr film) but also the improved impedance matching, which are responsible for the ultrabroadband absorption of the ETM. Note reflections calculated by using the impedance theory are consistent with the FDTD results in the subwavelength region (λ>P=300 nm), validating the effectiveness of the impedance theory in evaluating the absorption performance of the ETM. However, the impedance theory is invalid as higher diffraction order propagates with λ<P, and significant differences are occurred between the results of the impedance theory and those of the FDTD.
Fig. 3. (a) Impedance and reflection curves of the ETM without the 20 nm ultrathin Cr film, i.e., hm=0. (b) Impedance and reflection curves of the ETM with hm=20 nm. Reflections calculated by using the FDTD are indicated by dashed lines, other parameter are the same as in Fig. 1 with θ=0 and φ=0.
To distinguish the contributions of ultrabroadband absorption from different parts of the ETM, absorption in different parts of the ETM and distributions of power dissipation density at resonant peaks are investigated, as shown in Fig. 4. As can be seen in Fig. 4(a), the absorption of the total structure is mainly resulted from the horizontal and the vertical bars of the ETM in the wavelength region of interest. The average absorption of the ETM is 96.4% in the visible range of 400-800 nm, and the absorption of 87.8% is originated from its horizontal and vertical bars, while absorption from the rest part of the ETM is low. Specifically, the average absorption of 64.9% and 22.9% in the range of 400-800 nm are contributed from the horizontal bar and the vertical bar, respectively; and the vertical bar also contributes a large amount of absorption that is comparable with the horizontal bar in the shorter wavelength region. Figures 4(b) and 4(c) show the 3D distributions of power dissipation density of the ETM at absorption peaks of the shorter wavelength (401.2 nm) and the longer wavelength (650.6 nm), respectively. As can be seen in Figs. 4(b) and 4(c), the light energy is mainly dissipated on the edges of the horizontal and vertical bars of the ETM, and light absorption is enhanced due to the excitation of the localized surface plasmon (LSP) trapped by the patterned metallic film [60,61]. Note due to the excitation of the LSP of the horizontal and vertical bars, a small part of light energy is dissipated at the interface between the air and the Cr substrate around the T-shaped patterns. For the absorption peak at shorter wavelength of 401.2 nm, comparable power dissipation is occurred for both the horizontal and vertical bars of the ETM, which means that both the horizontal and vertical bars play the major role for light absorption enhancement. For the absorption peak at longer wavelength of 650.6 nm, the power dissipation is mainly localized on the edges of the horizontal bar, indicating that the absorption of the horizontal bar dominates the absorption of the total structure. The results of the distributions of power dissipation of absorption peaks are in line with the predictions of Fig. 4(a), confirming it is the synergistic absorption effect of different parts of the T-shaped ultrathin Cr film that contributes to the major absorption of the ETM.
Fig. 4. (a) Absorption of ETM and its absorption distributions indifferent parts of the structure. Distributions of power dissipation density at resonant wavelengths of (b) 401.2 nm, and (c) 650.6 nm. Other parameter are the same as in Fig. 1 with θ=0 and φ=0.
4. Influences of the structural parameters
To evaluate the robustness of the absorption performances of the ETM, influences of the structural parameters (hm, hd, P, Δx) on absorption characteristics of the ETM were firstly analyzed. Figure 5(a) shows absorption spectra of the ETM as a function of thickness of the Cr film hm. As shown in Fig. 5(a), the absorption of ETM without the Cr thin film (hm=0) is less than 40% due to high reflection from the Cr substrate, but the ETM exhibits good absorption performance as long as the T-shaped PMMA is encapsulated by the Cr thin film. Specifically, the average absorption of the ETM can be improved to 96.4% in the visible range of 400-800 nm as hm=20 nm. Figure 5(b) shows absorption spectra of the ETM as a function of thickness of the T-shaped PMMA hd. As can be seen in Fig. 5(b), although the absorption peak at longer wavelength is slightly red-shifted as hd is increased, the absorption performance of the ETM is insensitive to the variation of the thickness of the T-shaped PMMA, and ultrabroadband absorption can be maintained even hd is significantly altered. Similarly, the absorption of the ETM is also robust to the variation of the period P, as shown in Fig. 5(c), however, the decrease of the period enables the LSP modes of adjacent metallic T-shapes to interact sufficiently, leading to the slightly broadened bandwidth of absorption as P is decreased. Figure 5(d) shows absorption spectra of the ETM as a function of shift distance Δx of the vertical bar along x axis. As can be seen in Fig. 5(d), the absorption of the ETM is immune to the variation of the lateral shift Δx, and the absorption can be kept almost the same regardless whether the structure is symmetrical or not. In particular, even if the profile of the ETM is changed from T-shape (Δx=0) to L-shape (Δx=75.0 nm), the absorption performances of the ETM remains almost the same, which is superior to the conventional MIM absorbers since their absorption performances are sensitive to the patterned profiles [62]. As shown in Figs. 4(b) and 4(c), the energy of the incident light is highly confined and dissipated by the horizontal and vertical bars of the metallic T-shapes, thus ultrabroadband absorption can be maintained even the vertical bar is shifted from the center to the edge of the ETM. The absorption performances of the ETM are robust to the changes of geometrical parameters and are independent of the symmetry of the structure, which increases the fabrication tolerance and has advantages in application.
Fig. 5. Absorption spectra of the ETM as functions of (a) thickness of the Cr film hm, (b) height of the T-shaped PMMA hd, (c) period P, and (d) the shift distance Δx of the vertical bar along x axis. Other parameter are the same as in Fig. 1 with θ=0 and φ=0.
We further discuss the influences of the length and width of the horizontal and vertical bars (L1, W1, L2, W2) on absorption performance of the ETM, as shown in Fig. 6. As can be seen in Fig. 6(a), the variation of L1 almost does not change the absorption of the resonant peak in shorter wavelength, but the absorption of the resonant peak in longer wavelength can be significantly improved with the increase of L1. As indicated in Fig. 4(c), the energy of light in the longer wavelength region is mainly dissipated on the edges of the horizontal bar, thus the absorption of the resonant peak in longer wavelength is more sensitive to the variation of L1. Similarly, as shown in Fig. 6(b), although the absorption of the ETM is robust to the variation of the width W1 of the horizontal bar, the absorption of the resonant peak in longer wavelength is more sensitive to the variation to W2 comparing with the resonant peak in shorter wavelength. Figures 6(c) and 6(d) show the influences of the length L2 and width W2 of the vertical bar on absorption spectra of the ETM. As can be seen in Figs. 6(c) and 6(d), the absorption of the ETM is very robust to the variations of L2 and W2. Although a 50 nm change is introduced in the length or width of the vertical bar, the ultrabroadband absorption features can be maintained. However, because a large amount of light energy of the resonant peak in shorter wavelength is dissipated via the vertical bar, the absorption peak of the shorter wavelength is slightly altered as L2 or W2 is varied. Additionally, the broadband absorption performances of the ETM can be maintained even if multiple structural parameters are significantly altered, indicating good fabrication error tolerance of the structure. The detailed information can be found in Supplement 1, Fig. S2 and Table S1.
Fig. 6. Absorption spectra of the ETM as functions of (a) length of horizontal bar L1, (b) width of horizontal bar W1, (a) length of vertical bar L2, (b) width of vertical bar W2. Other parameter are the same as in Fig. 1 with θ=0 and φ=0.
5. Polarization and angular performances
We analyzed the influence of the change of polarization angle on the absorption performance of the ETM absorber under normal incidence. As shown in Fig. 7(a) and Fig. 7(b), it can be seen that the measured spectra are in good agreement with the theoretical results. As the polarization angle is changed from 0° to 90°, the absorption performance of the ETM almost does not change, and the measured average absorption is 85.9% even φ is increased to 90° in the range of 400-800 nm. Therefore, the ETM absorber has excellent polarization insensitivity characteristics.
Fig. 7. Absorption curves of the ETM under different polarization angles. Other parameter are the same as in Fig. 1 with θ=0. (a) Theoretical and (b) measured absorption spectra of the ETM.
To further examine the omnidirectional absorption performance of the ETM, we studied the absorption properties as a function of incident angle θ. As can be seenin Fig. 8(a), the designed absorber shows wide-angle absorption features for TM polarization, and the average absorption in the visible region of 400-800 nm is 83.6% even θ is increased to 60°. Interestingly, for absorption response of the ETM at oblique incidence, an absorption hollow is occurred in the shorter wavelength region accompanying with a sharp absorption peak, and the absorption peak is red-shifted with the increase of θ. The sharp absorption peak of the ETM in the shorter wavelength region is known as the Wood anomaly (WA) [63,64], which occurs at oblique incidence as the evanescent (−1,0) diffraction order propagates at grazing angle (propagating along the surface of the ETM). According to Eqs. (1)–(2), the relation between the location of the sharp absorption peak λp (wavelength of the WA) and the incident angle θ can be reduced as λp=P(sinθ+1) for the (−1,0) diffraction order with φ=0. For example, the location of the sharp absorption peak can be calculated as λp=450.0 nm as θ=30°, and it red-shifts to λp=559.8 nm as θ is increased to 60°, which are consistent with the result in Fig. 8(a). Note the occurrence of the WA decreases the absorption of the ETM below the cutoff wavelength of the (−1,0) diffraction order, resulting in the absorption hollow in the shorter wavelength region at oblique incidence. Figure 8(b) shows the angular absorption spectra of the ETM under TE polarization (electric field perpendicular to the plane of incidence). Similarly, for the absorption response of the ETM under TE polarization, the absorption hollow is also occurred in the shorter wavelength region at oblique incidence, but the absorption hollow is more striking comparing with that of the TM polarization. This is because that the reflection of the (−1,0) diffraction order of the ETM for the TE polarization is larger comparing with that of the TM polarization, the absorption of the TE polarization in the shorter wavelength region is lower.
Fig. 8. Absorption spectra of the ETM at different incidence angles. Other parameter are the same as in Fig. 1 with φ=0. (a) and (b) are the theoretical absorption for TM and TE polarizations, respectively. (c) and (d) are the measured absorption for TM and TE polarization, respectively.
Figures 8(c) and (d) show the measured angular absorption responses of the ETM for TM and TE polarization, respectively. As shown in Figs. 8(c) and 8(d), at normal incidence, the measured average absorptions in the range of 400-800 nm are 90.6% and 89.4%, respectively. The measurement results indicate that the fabricated ETM possesses wide-angle absorption performance, and high absorption can be maintained even θ is increased to 30° for both TM and TE polarizations. Some differences between experimental measurements and theoretical results are mainly originated from fabrication imperfections and the inconsistent permittivity of Cr between simulation and experiment. Notably, the absorption hollow associated with the WA in the shorter wavelength region does not be observed in the measured spectra for both TM and TE polarizations. This is because the diffraction efficiency of the ETM from the (−1,0) diffraction order cannot be detected by using our measured system, and the measured absorptions will be larger comparing with those of the theoretical results in the shorter wavelength region. Note although the absorption hollow cannot be observed in experiment, the average absorption of the ETM is also decreased with the increase of θ for both TM and TE polarizations. To clearly show the influence of the incident angle on the absorption performance of the ETM, the average absorption of the theoretical and experimental results within the visible range of 400-800 nm are presented in Supplement 1, Table S2.
6. Summary
In conclusion, a novel ultrabroadband and ultrathin absorber based on the ETM is designed, fabricated and characterized. The ETM consists of an ultrathin Cr film and a Cr substrate sandwiched by the T-shaped PMMA arrays. The ultrathin Cr film provides a robust absorptive surface with improved impedance matching, and ultrabroadband absorption can be realized due to the excitation of the LSP confined in the patterned ultrathin Cr film. In the visible wavelength region of 400-800 nm, the absorption of the theoretical and measured results of the ETM are larger than 96.3% and 89.4%, respectively. The 3D power dissipation density distribution of the proposed structure indicates that the horizontal and vertical bars contribute to the major absorption in the shorter wavelength region, while the major absorption is arising from the horizontal bar in the longer wavelength region, and ultrabroadband absorption can be achieved due to the synergistic absorption effect of the different parts of the T-shaped ultrathin Cr film. The absorption of the ETM is insensitive to the variations of the geometric parameters and the structural symmetry, and it can be maintained almost the same even if the profile of the ETM is changed from T-shape to L-shape. Additionally, the absorption response of the ETM exhibits polarization-insensitive and wide-angle features. The measured results validate that the ETM absorber has excellent polarization insensitivity characteristics, and the measured absorption can be maintained high even θ is increased to 30° for both TM and TE polarizations. The strategy of using the encapsulated metasurface to enhance absorption combines the advantages of low-cost metal materials within the compact architecture, and it can be generalized for designing more complex nanostructures, which may facilitate many potential applications related to light absorption enhancement.
Funding
Major projects of the Science and Technology Commission of Shanghai Municipality (17JC1400800); National Natural Science Foundation of China (61975155).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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