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Abstract
We numerically study a fan-like metamaterial absorber (FMMA) composed of an ${\rm Au} {\text -} {\rm TiO}_2 {\text -} {\rm Au}$ multilayer with a 3-D finite-difference-time-domain method (FDTD) and verify it experimentally. Our proposed design shows high absorbance, $\gt\!98\%$ numerically, in the visible spectrum, which is due to the excitation of both localized surface plasmons (LSPs) and propagating surface plasmons (PSPs). In particular, the ${\rm TiO}_2$ dielectric spacer sandwiched between the top fan-like nanopatterned structure and the bottom planar Au-film is identified as playing a crucial role in the spectral response of the FMMA. Its introduction excites the PSP mode, which first enhances the absorbance of the FMMA and subsequently redshifts the spectral absorbance with a further increase in the thickness. Moreover, the proposed FMMA, numerically and experimentally, also shows polarization and angle insensitivity in the visible spectrum under normal and selected oblique incidence. These results offer unique potential in sensing applications and devices requiring selective absorption in the visible spectral region.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
Metamaterials (MMs) are artificially engineered materials with special optical properties that are not readily realizable in existing natural materials. Due to their ubiquitous nature, MMs have been utilized enormously in many photonics-based applications to manipulate optical fields in both the visible and the terahertz spectral ranges [1–3]. MM absorbers (MMAs) have become a hot topic in scientific research due to their prospects in the field of solar power generation [4], sensing [5], perfect absorption [6], and thermal electronic devices [7]. These applications are dependent on the small, multi-band, and higher absorbance of MMs.
MMAs have been studied by researchers to exploit the high optical absorbance property for different technological applications [5]. Typically, MMs comprising dense nanorods and tubes [8,9], photonic crystals [10,11], and multilayered planar structures [12] have been demonstrated as high optical absorbing materials. In these designs, noble metals such as gold (Au) and silver (Ag) have been utilized enormously to design these MMs due to their mean free path fermionic property [13]. In the prospects of narrow broadband absorbance with high quality (Q)-factor, metallic nano-arrays [8] and metal-insulator-metal (MIM) thin layers [14] have been exploited. Recently, Xu et al. [7] proposed a dual-band MMA with two absorption bands in the visible and near-infrared (NIR) region with an absorbance reaching 93% to 88%, respectively. They associated the bands in the visible and near-IR to the excitation of surface plasmon resonance (SPR) and localized magnetic polaritons, respectively. Liu et al. also proposed a numerically simulated ultra-wideband MMA with high absorbance from the visible spectrum to the NIR. Their proposal is based on a four-layer structure, silica-titanium-magnesium fluoride-aluminum (${\rm SiO}_2$-Ti-${\rm MgF}_2$-Al), with a high absorbance factor arising as a result of the combined effect of propagating surface plasmon polaritons (SPPs), local surface plasmon resonance (LSPR), and the Fabry–Perot (FP) cavity [15] modes excitation. Moreover, stacked MMAs also exhibit the excitation of long- and short-range SPPs, FP cavity modes, and localized surface plasmons (LSPs) at the resonance wavelength [16,17]. The excitation of these modes [18] has been identified to contribute to the high absorbance in the aforementioned structures.
One of the desired requirements in MMAs is the flexibility to control the response of the structure in addition to the perfect absorbance. For example, polarization-sensitive MMAs can be used for sensing applications and, preferably, polarization selection of an incident electromagnetic field [19]. In this direction, many different mechanisms have been employed to achieve the needed control using liquid crystal MMAs and temperature-sensitive MMAs [20]. However, such devices usually show sharp absorption linewidths offering limited tuning control [21–23] for devices requiring absorption in a wider spectral range such as energy harvesting. Moreover, tuning of the spectral absorbance of MMAs can be achieved by varying the periodicity and the structural parameters. Surprisingly, the role of the dielectric spacer in MMAs has been either limited to supporting FP modes [15] or demonstrated not to influence its spectral absorbance [7]. Our proposed design demonstrates otherwise.
Fig. 1. (a) Schematics of the FMMA. Structural parameters: Au film thickness ($ H $), ${\rm TiO}_2$ spacer thickness ($ t $), top-layer thickness ($ h $), Au nanodisk diameter ($ D $), and Au-triangle side-length ($ l $) and height (${{ T }_h}$). (b) Scanning electron micrograph (SEM) showing the nanopatterned fan-like Au top-layer structure. The solid black line corresponds to the 555 nm period of the FMMA.
In this study, we numerically and experimentally investigated the Au-titanium-dioxide (${\rm TiO}_2$)-Au fan-like metamaterial absorber (FMMA) using 3-D finite-difference-time-domain (FDTD) method. We examine the FMMA in terms of its polarization response and the influence of structural parameters including the spacer thickness, periodicity, and the dimensions of the top-layer structure. The proposed FMMA demonstrates near-perfect absorption in the visible spectrum due to LSP and PSP modes. Moreover, the FMMA shows polarization and angle insensitivity as a result of the symmetry conditions of the structure. Importantly, contrary to other studies, analysis of the ${\rm TiO}_2$ spacer shows two functionalities, namely, increasing the absorbance and facilitating broadband tunability, with full width at half-maximum (FWHM) of 320 nm, over nearly the whole visible spectrum as a result of the emergence of the PSP modes. For the first time, we have proposed the FMMA structure, exploiting the combination of the typically isolated particles utilized in absorber configurations, which shows a strong dependence of the spectral absorbance on the dielectric thickness. The significant influence of the spacer thickness on the absorption band and the ease at which the thickness can be controlled from the fabrication point of view manifest the relevance of the newly proposed FMMA structure. This novel FMMA can have significant applications in sensing, solar power generation, and devices requiring selective absorption in the visible spectral region.
2. METHODS
A. Structure Design and Modeling
The proposed FMMA comprises ${{{\rm Au} {\text -} {\rm TiO}}_2} {\text -} {\rm Au}$ layers with a fan-like nanopatterned structure stacked on top of the ${\rm TiO}_2$ spacer. The top nanopatterned structure consists of a central nanodisk with four equilateral triangles surrounding it. Figure 1(a) shows the schematics of the FMMA. The wavelength-dependent complex dielectric functions for Au and ${\rm TiO}_2$ were calculated based on the complex refractive indices obtained from ellipsometric measurements. The complex permittivities were then utilized in the simulation of the FMMA spectral absorbance (see Fig. S1 of Supplement 1 for the complex permittivities). The combined structures are situated on an infinite ${\rm SiO}_2$ substrate. The absorbance, current density, and electromagnetic field distribution were determined using an in-house developed script command in Lumerical FDTD software. The simulation region dimension is set to a 3-D layout with a period of 555 nm in both $ x $ and $ y $ directions and a perfectly matched layer (PML) boundary condition set in the $ z $ direction. We utilized the conformal variant mesh and increased the simulation time to ensure that the electromagnetic field sufficiently decays. The PML layers were also increased to stabilize the simulation region due to the dispersive nature of the materials used. A plane wave, propagating normal to the interface, at different polarization angles was used as the incident source on the FMMA to calculate the absorbance using a spectral-domain field monitor. Similar calculations were also carried out at selected oblique incidence. The numerically simulated absorbance spectra show a good match with the experimental results for the following parameters: bottom Au-film thickness ($H = 180\;{\rm nm} $), ${\rm TiO}_2$ spacer thickness ($t = 20\;{\rm nm} $), thickness of the fan-like nanopatterned top layer ($h = 20\;{\rm nm} $), nanodisk diameter ($D = 130\;{\rm nm} $), and Au-triangle height (${T_h} = 212.5\;{\rm nm} $). The higher thickness of the bottom Au-film was chosen to exceed the skin depth of gold to decrease the transmittance such that the absorbance of the proposed structure can be approximated as $A = 1 - R$, where $A$ is the absorbance and $R$ is the reflectance spectra. The results also show polarization independence of the spectral absorbance for the FMMA in the region of interest. We also calculated the field distribution at suitable absorption wavelengths to determine the origin of the observed resonance in the FMMA. Further, we performed different parametric sweeps to determine the effect of structural parameters on the spectral absorbance of the FMMA.
B. Sample Fabrication
The FMMA was fabricated on a fused silica (${\rm SiO}_2$) substrate using an electron-beam (E-beam) lithography technique and a lift-off process. After substrate cleaning with acetone, isopropanol (IPA), and oxygen plasma, 2-nm-thick titanium (Ti) was sputtered (Emitech K675X, Emitech) on the substrate as an adhesion layer for a 100-nm-thick thermally evaporated gold film using Univex 300 (Leybold Heraeus, Germany). The 30-nm-thick ${\rm TiO}_2$ spacer was deposited using atomic layer deposition (ALD, TFS 200, Beneq Oy, Finland). To fabricate the fan-like structure on top of the spacer, 300 nm of polymethylmethacrylate (PMMA) was first spin-coated at 3000 rpm for 60 s and pre-baked for 5 mins at 150°C. A 30 nm thick copper was thermally evaporated on the PMMA as a conductive layer for the lithography process. The samples were then exposed using E-beam lithography (EBPG5000${+}$ES HR, Vistec Lithography, Netherlands) with a suitable dose and developed with Methyl Isobutyl Ketone MIBK: Isopropyl Alcohol IPA (1:2) solution after the conductive layer removal. Finally, a 24-nm-thick gold (Au) was then thermally evaporated after the deposition of another 2-nm-thick Ti. The fabrication process was completed with a lift-off process in acetone, IPA, and rinsed in de-ionized water. The scanning electron micrograph (SEM) of the final sample is shown in Fig. 1(b).
C. Characterization
The samples were characterized with an ultraviolet-visible (UV-Vis) spectrophotometer (Lambda 18, Perkin Elmer) with a polarizer inserted in the beam path to measure the FMMA absorbance at different polarization angles (see Fig. S2 in Supplement 1 for details). A similar (${\rm SiO}_2$) substrate was used for the reference measurement.
3. RESULTS AND DISCUSSION
A. Spectral Response of FMMA
Figure 2 shows the spectral response of the FMMA for both the simulated and experimental results. Both the simulated and the measured spectra show relatively strong absorbance within 400–600 nm and a corresponding weaker resonance around 800 nm. However, the FDTD result shows near-perfect absorption, $\gt\!{98}\%$, over the spectra range 400–500 nm with the maximum absorbance slightly blueshifted as compared with the experimentally measured spectra, which has its maximum absorbance of $\gt\!{85}\%$ around 460 nm. The observed deviation of the measured absorbance from that of the FDTD simulation could be due to many reasons. First, the material dispersion data used could contribute to the observed deviation. The accuracy of the extracted dispersion from the ellipsometric data can be influenced by the chosen model as well as the thickness of the sample. Second, imperfections in the fabricated FMMA can be another source of the observed deviation. Nonetheless, despite the deviation, a good approximation of the FMMA spectral response can be observed from the FDTD results.
Fig. 2. Simulated and measured spectral absorbance of the FMMA for unpolarized incident light for the fabricated structural parameters: Au-film thickness $({H}) = 100\;{\rm nm}$, ${\rm TiO}_2$ spacer thickness $({h}) = 30\;{\rm nm}$, and top-layer thickness $({t}) = 24\;{\rm nm}$.
To understand the origin of the band, we examine the field distributions at the absorption wavelength of 428 nm, for one unit cell. Figure 3 illustrates the electric, magnetic, and current field distributions of the FMMA obtained from the simulation. Figure 3(a) depicts the electric field distribution at 428 nm resonance wavelength, which shows a highly localized field at the intersection point of the nanodisk and the adjacent tip of the triangle. From the magnetic field distribution in Fig. 3(b), we observe a strong enhancement of the field at the top surfaces of the nanodisk and Au-triangle as well as at the overlapping boundary of the spacer and the bottom Au-film. Propagation surface plasmons (PSPs) arise at a metal-dielectric interface when an optical field of suitable wavelength couples to the collective oscillations of electrons. LSPs, on the other hand, are excited when the surface plasmons are confined by nanoparticles with a size comparable to or smaller than the excitation wavelength. In the addition to the wavelength, LSP is also influenced by the size and shape of the particle [24]. Notably, as the size of the nanopatterned triangle, central nanodisk, is smaller than the excitation wavelength of the incident light, LSP modes are excited and appear prominent at the edges of these structures. We, therefore, attribute the observations of these two fields to LSP and PSP. Thus, the observed near-perfect absorption achieved by the FMMA is attributed to the excitation of the LSP and PSP. To substantiate these mode assignments, we examine the effects of the structural parameters.
Fig. 3. (a) Electric field, (b) magnetic field, and (c) current density distributions of the FMMA at 428 nm. The arrows represent the direction of the electromagnetic fields, whereas the black dashed lines depict the boundary of the layers and structures. The color bar represents the intensity of the electric field (V/m), magnetic field (A/m), and current density (${\rm A}/{{\rm cm}^2}$) distributions.
Fig. 4. Spectral absorbance of the FMMA structure. (a) Parametric sweep of the lattice period (P) with dashed lines representing the excited PSP mode and (b) for different periods.
First, we consider the influence of the period of the FMMA on its spectral response. Figure 4(a) shows the parametric sweep of the FMMA period and the corresponding absorbance spectra. For easier reference, we also illustrate absorbance spectra for some periods in Fig. 4(b). As the period increases from 555 to 855 nm, we observe that the weaker absorption bands in the longer wavelength range redshifts from 620 to 900 nm approximately. On the contrary, the near-perfect absorbance around 428 nm is insensitive to the variation in the periods. The variation of the weaker narrowband at the longer wavelength is a characteristic response of PSPs [1,25]. The position of the plasmonic resonance peak [25] is determined by
and, for normal incidence, where ${k_{{\rm spp}}}$ is the plasmonic wave vector, $P$ is the period, and $m$ is an integer. From the above Eqs. (1) and (2), increasing the lattice period leads to a corresponding increase in the resonance wavelength of the narrow absorption band as observed in Fig. 4(b) due to PSP. Thus, being insensitive to the period, the near-perfect absorption band at the shorter wavelength can be attributed to the excitation of LSPs.Next, we examine the effect of the top layer, namely, the diameter of the central nanodisk and the height of the triangles as shown in Fig. 1. Figures 5(a) and 5(b) show the corresponding plots. While the overall effect is not appreciable, we observe that both parameters affect the absorbance, albeit in the opposite respect. Increasing the diameter, as seen in Fig. 5(a) slightly redshifts the LSP resonance [22,25], whereas increasing the height of the adjacent triangles slightly blueshifts the absorbance beyond the maximum absorption wavelength. Such observation of the LSP resonance response to the structural dimensions has also been demonstrated in other studies [22,26,27].
Fig. 5. Spectral absorbance of the FMMA for different (a) nanodisk diameters ($ D $) and (b) triangle heights (${{ T }_h}$).
B. Impedance
Having determined the origin of the band based on the structural parameters of the top layer, we examine the impedance of the overall FMMA structure. To achieve this, we implemented the impedance transformation method [28,29]. By using an effective medium theory, the impedance of the proposed design was calculated using the scattering matrix (S) parameters. From the scattering matrix, the impedance relation can be expressed as
To obtain high absorbance, the impedance of the proposed structure at the spectral range of interest should match with the free space impedance. That is, ($Z = {Z_0}$), where ${Z_0}(\omega) = \sqrt {\frac{{\mu (\omega)}}{{\varepsilon (\omega)}}} = 1$, and $\mu(\omega)$ and $\varepsilon (\omega)$ are the effective permeability and permittivity of the structure. Thus, calculating the impedance $Z$, the quantitative relationship between the effective parameters, namely, $\mu(\omega)$ and $\varepsilon (\omega)$, of the structure can be estimated. Since the Au-film at the bottom of the FMMA structure is far thicker than the skin depth of the material, the transmission scattering matrix of the structure is minimal and can be approximated as ${S_{12}} = {S_{21}} = 0$, which reduces Eq. (5) to
Fig. 6. Calculated relative impedance for the FMMA using Eq. (6). ${\rm Re}(Z)$ and ${\rm Im}(Z)$ correspond to the real and imaginary parts of the impedance. The dashed line corresponds to the phase-matched condition where $Z = 1$.
Figure 6 shows the impedance ($Z$) of the FMMA structure over all the visible range, calculated from the ${S_{11}}$ scattering parameter, which is directly obtained from the reflection coefficients, using Eq. (6). It is observed that, for wavelengths (400–500 nm), the impedance is close to unity and the calculated reflectance also shows a minimum in this range corresponding to the maximum absorbance observed in the spectral response of the FMMA. This indicates a phase-matching condition between the medium and the impedance of free space. The value of the reflectance spectra approaches zero depicting high absorption at this resonance wavelength.
C. Polarization and Angle of Incidence Insensitivity
Here, we examine the influence of the probing light on the spectral response of the FMMA. To achieve this, different polarization angles of the incident optical source were set to determine the spectral response of the FMMA. The results for both the simulation and experiment are shown in Figs. 7(a) and 7(b) for the different polarization angles. It is evident that both results are comparable and that the FMMA is polarization insensitive.
Fig. 7. Spectral absorbance of the FMMA structure showing polarization insensitivity: (a) simulated and (b) measured absorption spectra.
Figures 8(a) and 8(b) show the absorbance of the FMMA at a selected oblique incident angle for both TM and TE polarization, respectively. While the FMMA structure is overall not sensitive to the selected angle of incidence for both polarizations, the case of the TM polarization appears less sensitive, especially at the regions of very high absorbance as compared to the TE polarized case.
Fig. 8. Spectral absorbance of the FMMA structure for selected oblique incidence: (a) TM and (b) TE.
Figure 9 shows the electric field distributions of the FMMA for the TE, TM, and 45° polarization angle at the 428 nm absorption wavelength. For TE and TM, orthogonal to each other, the fields are localized around the structures, namely, the central nanodisk and two of the triangles, as expected. At 45° polarization, much of the field is only localized around the nanodisk and the adjacent spaces between the triangles. These observations strongly indicate the excitation of LSPs and PSPs, and that the polarization of the incident light does not influence the spectral response of the FMMA. Further, this effect is envisaged to result from the high geometrical symmetry of the FMMA structure in both $ x $ and $ y $ directions.
Fig. 9. Field distributions (${x} {\text -} {y}$ plane) at different polarization angles for normal incidence for (a) TM, (b) TE, and (c) 45° at 428 nm. The white double arrows indicate the polarization directions of the input light.
D. Tunability
To consider the role of the ${\rm TiO}_2$ spacer region, we vary its thickness. Figure 10(a) shows the thickness sweep of the ${\rm TiO}_2$ and the spectral absorbance, whereas Fig. 10(b) also depicts the spectra response of the FMMA without and with the ${\rm TiO}_2$ spacer for thickness up to 40 nm.
Fig. 10. Spectral absorbance of the FMMA showing tunability from the visible to the near-infrared (NIR) range with the variation of the ${\rm TiO}_2$ spacer thickness ($t$). (a) Simulated parametric sweep of spacer thickness $t$. (b) Absorbance spectra of FMMA with and without the ${\rm TiO}_2$ spacer layer.
Fig. 11. (a) Electric field distributions in the ${x} {\text -} {y}$ plane, (b) electric field distributions in ${x} {\text -} {z}$ plane, (c) magnetic field distributions in ${y} {\text -} {z}$ plane, and (d) current density in ${x} {\text -} {z}$ plane with ${\rm TiO}_2$ spacer thickness, $t = 0$, 10, 20, 30, and 40 nm, respectively, at the following wavelengths: 422, 400, 426, 492, and 584 nm.
In the absence of the ${\rm TiO}_2$ spacer, in Fig. 10(b), the FMMA shows a broader and lower response with an absorbance maximum of 60%, approximately, for simulation and measurement. However, it is evident that the presence of the 10-nm-thick ${\rm TiO}_2$ already enhances the absorbance [15] $\gt\!{90}\%$ but further broadens the bandwidth. Contrary to Liu et al. [15], who observed a subsequent decrease in absorbance with increasing spacer thickness, further increase in the ${\rm TiO}_2$ thickness from 10 to 40 nm leads to a corresponding increase in absorbance to near-perfect, $\gt\!{98}\%$, and redshifting of the FMMA spectral response with a maximum bandwidth of 320 nm. This tunes the spectral response of the FMMA from 400–500 nm to 550–700 nm. Thus, the ${\rm TiO}_2$ spacer region of the FMMA plays a double role in enhancing the spectral absorbance and tuning of the response. From the heat map, it can be inferred that the absorption of the FMMA can be tuned further from the visible through to the NIR region, ${\gt}$780 nm, and also exhibits higher-order modes (HOMs). However, such HOMs do not contribute to the spectral response of the FMMA due to the relatively thin layer of the dielectric spacer. In the case of [15], the observed decrease in the response of the four-layer structure was attributed to the inability to excite the SPR as the spacer thickness increases, whereas, in the present study, we observe an enhancement of both LSP and PSP as we shall see below. The observed tunability in our proposed FMMA, thus, offers flexibility in many absorber-related applications including sensing and light-harvesting since one can select the spectral range of interest to absorb the whole or specific range of wavelengths in the visible spectrum.
To further investigate the role of the ${\rm TiO}_2$ spacer and the physical mechanism supported by the FMMA, we examine the corresponding electric (in the $x {\text -} y$ and ${x} {\text -} {z}$ planes), magnetic (in the ${y} {\text -} {z}$ plane) field distributions, and the current densities (in the ${x} {\text -} {z}$ plane) for the various thicknesses. Figure 11 show the indicated plots at the corresponding absorption wavelengths: 422, 400, 426, 492, and 584 nm.
Fig. 12. (a) Measured spectral absorbance of the fan-like metamaterial (FMMA) structure without ${\rm TiO}_2$ spacer showing polarization insensitivity. Field distributions (${x} {\text -} {y}$ plane) at different polarization angles for normal incidence for (b) TM, (c) TE, and (d) 45° at 422 nm. The white double arrows indicate the polarization directions of the input light.
As previously stated, due to the strong symmetry of the FMMA structure, the incident polarization leads to the localization of the fields near the structure. Such observation is also evident in Fig. 11(a), in the absence of the ${\rm TiO}_2$ spacer. A closer look at the magnetic field in Fig. 11(c) shows that it is localized at the top of the triangular structures, confirming the excitation of LSP modes. In Fig. 10(b), the measured absorbance sharply decreases to below 20% around 600 nm covering the absorption of interband transitions in gold between 5 d-Fermi levels and 5 d-6s energy levels. Thus, in the absence of the spacer layer, the spectral response of the FMMA is additionally supported by the material’s interband transition [30–32].
Before proceeding further, we examine the spectral response of the FMMA structure without the spacer, but briefly. Figures 12(a) and 12(b)–12(d) show the measured spectral absorbance for different polarizations of the incident light and the field distribution in the ${x} {\text -} {y}$ plane for the TE, TM, and 45° polarization angle, respectively, at 422 nm. From Fig. 12(c), as evident in Fig. 7, we observe a similar polarization-insensitive response of the FMMA structure as exhibited when the spacer is present. In particular, the electric field distribution in Figs. 12(b)–12(d) also shows a dominant localization of the field almost all around the central nanodisk and the surrounding Au-triangles, a strong indication of LSP excitation as predicted.
The introduction of ${\rm TiO}_2$ and increasing its thickness (t) from 10 to 40 nm show a corresponding strong enhancement of the electric field as seen in Fig. 11(a) (last four columns). For $t = 40\;{\rm nm} $ spacer thickness, a prominent field enhancement is observed in the $x {\text -} y$ as well as in the ${x} {\text -} {z}$ planes. In particular, we also observe strongly enhanced fields at the top layer and ${\rm TiO}_2$ intersection point, which leads to the localization of partially resolved fields in the ${\rm TiO}_2$ dielectric spacer below the central nanodisk. Such observation is typical of the emergence of higher-order LSP modes [25] where more than one odd-number magnetic mode is confined within the dielectric layer. However, the 40-nm-thick ${\rm TiO}_2$ is not optimum to allow full resolution of such modes. We, therefore, envision interesting field distribution with a further increase in the ${\rm TiO}_2$ spacer thickness. The enhanced electric field around the Au-triangle as compared to the circular nanodisk, especially for the case of the 40-nm-thick spacer, is likely due to the increased number of sharper corners of the triangle [33] and the reduced symmetry of the structure [27].
Similarly, in Fig. 11(c), we observe, in addition to the enhanced magnetic field at the top of the patterned structures, enhancement of the magnetic field between the bottom Au-film and the ${\rm TiO}_2$ spacer, which is attributed to the propagating surface plasmons (PSPs). The PSP is also observed to increase with the ${\rm TiO}_2$ spacer thickness. In particular, the magnetic field for the 40-nm-thick ${\rm TiO}_2$ spacer is predominantly enhanced above the Au-triangle as well as at the interface of the ${\rm TiO}_2$-Au-film bottom layer. Combining the field distributions for the case of $t = 40\;{\rm nm} $ in Figs. 11(b) and 11(c) as well as the presence of the fields in between adjacent Au-triangles in Fig. 11(a), we conclude that the near-perfect absorption obtained in Fig. 10(b), as the ${\rm TiO}_2$ spacer thickness increases, can be attributed to the excitation and enhancement of both LSP and PSP modes. Hence, the excitation of PSP, in addition to LSP, as a result of the introduction of the ${\rm TiO}_2$ spacer is responsible for the enhancement and redshifting of the spectral response of the FMMA. For absorbers utilizing thin films instead of periodic structures for the top layer, pure FP modes with high finesse are supported [21–23]. However, our simulation results, not shown here, indicate that such modes cannot be excited in our FMMA due to the smaller thickness of the dielectric layer. Although such sharp resonances are useful for applications such as filtering, they are not desirable for energy harvesting. Thus, our proposed FMMA with a wider bandwidth becomes useful for such applications.
4. CONCLUSION
We propose and demonstrate an easy-to-fabricate MMA in the visible spectrum with an average numerical absorbance of $\gt\!{98}\%$ mainly due to the excitation of both PSP and LSP modes. Examining the role of the spacer reveals two functionalities; namely, varying the spacer thickness of the FMMA initially enhances the absorbance leading to high absorbance due to LSP excitation and at the same time offers tunability across the visible spectrum due to the emergence of PSP. Thus, when required, flexibility in selective absorption can be achieved offering another dimension to be exploited in energy harvesting and sensing applications. The proposed FMMA additionally exhibits polarization insensitivity, which is attributed to the high symmetry and the consequent induction of similar polarizability in the structure.
Funding
Academy of Finland (320165, 320166).
Acknowledgment
This work is part of the Academy of Finland Flagship Programme, Photonics Research and Innovation (PREIN), decision 320166 and 320165. Author contributions: conceptualization, B. O. A., P. B.; simulation, F. L., I. I.; fabrication, M. B.; characterization, I. A. O, L. A.; writing of original draft, I. I.; reviewing and editing, I. I, F. L, B. O. A., P. B.; supervision, B. O. A., P. B. All authors have read and approved the final version of the manuscript.
Disclosures
The authors declare that there are no conflicts of interest related to this paper.
Data Availability
Data underlying the results are presented in the paper.
Supplemental document
See Supplement 1 for supporting content.
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