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Abstract
Due to their ability to confine light in a sub-wavelength scale and achieve coherent absorption, plasmonic nanostructures have been intensively studied for solar energy harvesting. Although nanoparticles generating localized surface plasmon resonance (LSPR) have been thoroughly studied for application in a direct absorption solar collector (DASC), nanoparticles exciting magnetic polaritons (MP) for use in a DASC have not drawn much attention. In this work, we report a metal-insulator-metal (MIM) nanodisk that can excite MP peaks apart from the LSPR in the solar spectrum. It was found that the MIM nanodisk generates a broader and relatively more uniform absorption band compared to a pure metallic nanodisk. The MP peaks were also found to cause less significant scattering compared to those associated with the LSPR. We finally showed that the peaks induced by the MIM nanodisk are highly tunable by varying the particle dimensions, making the proposed MIM nanodisk a potential candidate for solar thermal applications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the past few decades, investigations of electromagnetic metamaterials have grown dramatically as researchers have developed the ability to manipulate the propagation of electromagnetic waves by tailoring the material’s radiative properties [1]. Different resonance modes, such as surface phonon polaritons [2], surface plasmon polaritons [3], magnetic polaritons [4,5], hyperbolic modes [6], and epsilon-near-zero modes [7] have been achieved with different metamaterials. Using surface plasmon polaritons (SPP) excitation to confine light at small scale, plasmonic nanostructures can be applied in various ways, including energy harvesting [8], imaging [9], bio-chemical sensing [10], and optoelectronics [11].
For solar thermal harvesting, SiO$_2$/Au core-shells, which exhibit localized surface plasmon resonance (LSPR), were firstly proposed to make a plasmonic nanofluid [8]. By mixing four kinds of core-shells of different dimensions, the thermal efficiency of a direct absorption solar collector (DASC) was improved significantly, to about 70%, at a low volume fraction of 0.05%. Since then, numerous works have investigated the application of plasmonic nanofluids for solar thermal harvesting, using different particle materials, such as Au and Ag [12–14], and different particle shapes, such as nanorods, nanoplates, nanosheets, nanocubes and nanostars [15–23]. Systematic optimizations and new designs have also been proposed [14,21,24,25].
When the LSPR is excited in the nanoparticles, the absorption efficiency at the resonance peak is greatly enhanced, due to the coupling of the incident solar radiation and the collective resonance of the electrons in the metallic particle [8,13,26]. However, because the SPP peak is intrinsically narrow, the absorption band of the nanoparticles is usually limited to a narrow spectrum [8,27]. For this reason, developing a nanoparticle which can further broaden the absorption band is an important goal, which has become a trendy research topic [28–30]. For instance, Liu and Xuan [28] have proposed the Janus nanoparticle, which is composed of two different materials at two sides of a nanoparticle to broaden the solar energy absorption. The asymmetry of the Janus nanoparticle leads to the integration of various resonances in the broad solar spectrum, resulting in an almost full-spectrum absorption with a relatively low nanoparticle concentration.
In addition to volumetric based solar collectors using nanofluids, surface based solar thermal absorbers have also been studied [31–36]. For instance, in Ref. [37], a perfect absorber was proposed by controlling the electric and magnetic resonances of a metamaterial. Afterwards, different types of solar absorbers were studied, including a cross resonator [38], a flexible wide angle terahertz absorber [39] and metal-insulator-metal (MIM) absorber [40]. A typical solar absorber is featured with a metallic grating and a metallic substrate which are separated by a dielectric spacer, i.e., a MIM nanostructure [4,5,41]. Han and Lee [33] have also proposed a tandem grating to explore the interaction of magnetic resonances thus to broaden the absorption band. In addition, Wang, O’Dea, and Wang [42] numerically demonstrated the excitation of a magnetic resonance in a film-coupled nanoparticle metamaterial. The magnetic resonance occurred in the spacer between the Au nanoparticle and the ground Au film. The common mechanism enhancing solar energy absorption is essentially similar in both grating based solar absorbers and nanoparticle modified solar absorbers. That is, upon solar incidence, the solar energy is coupled with a magnetic polariton (MP) excited inside the absorber, leading to the solar energy being resonantly absorbed by the solar absorber.
Inspired by surface based MIM absorbers which exploit MP resonances, we propose a MIM nanodisk to broaden the absorption band for solar energy harvesting in a DASC. The resonance characteristics of the proposed MIM nanodisk were investigated by analyzing its absorption efficiency, as well as the electric/magnetic field distribution in the near field. The boundary element method (BEM) was employed to calculate the absorption and scattering efficiency over a wide spectrum, and the finite element method (FEM) was employed to obtain the near-field electric/magnetic distribution at resonance conditions. To the best of our knowledge, there have not been any studies employing MIM nanodisk to generate MPs for use in a DASC. The inductance-capacitance (LC) circuit model, which is frequently used for predicting MPs [4,5,43,44], was also applied to confirm the excitation of a MP resonance. Parametric studies were also performed to investigate how the size parameters of the proposed MIM nanodisk affect the overall absorption and scattering spectra.
2. Simulation method and model description
A schematic of the proposed MIM nanodisk is depicted in Fig. 1. Silver was chosen because of its superior (i.e., smaller) loss factor compared with other metals in the visible spectra [45]. A silica disk was used as the spacer dielectric to excite the magnetic resonance [4,34]. The diameter of the nanodisk was set to be $d$ = 60 nm, and the thickness of the top Ag nanodisk ($t_1$), the middle SiO$_2$ nanodisk ($t_2$), and the bottom Ag nanodisk ($t_3$) were all set to be 20 nm, unless further specified.
To calculate spectral absorption and scattering efficiency, the boundary element method was used, which has good computation efficiency [46]. Specifically, the open source MNPBEM toolbox [46,47] was employed in the current study. In the BEM simulation, the boundary element was set to different numbers to check the convergence. For example, the element number of 35 was used to approximate the disk circle to ensure convergence. The finite element method was also employed to analyze the resonance mode, because of its better ability to analyze the electric and magnetic fields [48]. Specifically, the Wave Optics Module in COMSOL Multiphysics was applied. The spectral absorption efficiency obtained from the BEM simulation was also compared with the results of the FEM simulation. The comparison showed the results were consistent, confirming the convergence of the BEM simulations, except for a slight red-shift in the FEM results (about $5\sim 10$ nm).
Because the nanoparticles are randomly oriented when they are dispersed in a base fluid of a DASC, it was necessary to determine the average absorption efficiency of nanoparticles with different orientations. For this purpose, we fixed the orientation of the disk, as shown in Fig. 1 while varying the incidence and polarization directions of the electromagnetic wave. Considering the symmetry of the proposed MIM disk, three components were calculated to obtain the average [12,30], namely, $z$-direction incidence with $x$-direction polarization (i.e., the electric field oscillating along the $x$-direction), $x$-direction incidence with $z$-polarization and $x$-direction incidence with $y$-polarization, with each having the same chance of contribution. The cross-sectional area of a sphere with the same volume as the disk was adopted to calculate absorption and scattering efficiency. The surrounding medium was water. The tabulated data in Ref. [49] were used to obtain the optical constants for bulk Ag, SiO$_2$ and water.
3. Results and discussion
3.1 Resonance modes in a MIM nanodisk
The absorption efficiency of the Ag-SiO$_2$-Ag nanodisk in the three directions (i.e., $z$-incidence with $x$-polarization, $x$-incidence with $z$-polarization, and $x$-incidence with $y$-polarization) is shown in Fig. 2(a). Due to the asymmetric geometry of the MIM nanodisk, its absorption peaks depend on the direction and polarization state of the incident wave. For the $z$-incidence with $x$-polarization, two main resonance peaks occurred at 510 and 600 nm due to the well-known electric and magnetic resonances of the MIM nanostructure, respectively [50]. For the $x$-incidence with $z$-polarization, two obvious peaks appeared at around 350 and 420 nm, as well as a minor peak which appeared near 600 nm. For the $x$-incidence with $y$-polarization, one main peak was located at about 510 nm, and a minor peak appeared near 450 nm. Assuming random distribution in the base fluid, the overall absorption efficiency of the considered MIM disk should be obtained as the average of the three components in Fig. 2(a).
Fig. 2. Absorption efficiency $Q_a$ of (a) Ag-SiO$_2$-Ag nanodisk, and (b) Ag nanodisk for the three directions (i.e., $z$-incidence with $x$-polarization, $x$-incidence with $z$-polarization, and $x$-incidence with $y$-polarization). The geometric parameters of the Ag-SiO$_2$-Ag nanodisk are $d = 60$ nm and $t_1 = t_2 = t_3 = 20$ nm.
For comparison, the absorption efficiency of a single Ag nanodisk was also determined, and is plotted in Fig. 2(b). The diameter and the height of the Ag nanodisk were 60 nm and 20 nm, respectively. It was observed that the absorption peaks associated with the Ag nanodisk occurred at similar positions, except that in the Ag nanodisk, the peak near 600 nm disappeared for the $z$-incidence with $x$-polarization, and the minor apophysis near 600 nm also disappeared for the $x$-incidence with $z$-polarization. Those two peaks disappeared because a single Ag nanodisk cannot support magnetic resonances. In other words, the proposed Ag-SiO$_2$-Ag nanodisk generates more absorption peaks due to the excitation of the magnetic resonance. Besides, the Ag nanodisk absorption peaks near 510 nm were sharper and higher than the corresponding peaks of the Ag-SiO$_2$-Ag nanodisk. Comparatively, the more uniform distribution of absorption efficiency in terms of both wavelength and magnitude makes the Ag-SiO$_2$-Ag nanodisk more beneficial for broadband absorption of solar radiation [51]. For quantitative comparison of the photo-thermal conversion by two particles (i.e., MIM nanodisk and Ag nanodisk), the solar-weighted absorption coefficient $A_m$ [30] is evaluated for a water-based nanofluid. It turns out that at the particle concentration of $f_v=10^{-5}$, the corresponding $A_m$ of the MIM nanodisk increases from 0.687 to 0.925 when the thickness of the nanofluid increases from 2 cm to 10 cm, but that for the Ag nanodisk changes from 0.6258 to 0.8795. This indicates that excitation of the MP in MIM nanodisks certainly increases the solar thermal conversion. Note that to further increase the solar thermal conversion efficiency, different sizes of MIM nanodisks can be mixed together so that broader absorption band can be achieved, as will be discussed later.
In addition, the absorption spectrum of a bare Ag nanodisk with a rounded edge (the radius of curvature at the top and bottom edge was set to 3 nm), was evaluated (not shown here). It was found that the absorption spectrum of the Ag nanodisk with rounded edges had the same pattern as the Ag nanodisk with normal edges (without rounding) for all three incidence cases, except for a slight shift of some peaks. This indicates that none of the peaks in Fig. 2 was caused by the edge effect or lighting rod effect of an edged nanoparticle [30].
Next, we will further elucidate the resonance mode of each peak in Fig. 2(a) with the electric/magnetic field distributions. Specifically, we plot the time-averaged electric-field (or magnetic-field) energy density normalized by that of the incident wave. Figures 3(a) and 3(b) show, respectively, the electric- and magnetic-field energy density for the Ag-SiO$_2$-Ag nanodisk at $\lambda =510$ nm. A sharp absorption peak exists in Fig. 2(a) for the $z$-incidence with $x$-polarization. It is clear from Fig. 3(a) that the electric field at the corners near the interfaces of the Ag and SiO$_2$ disk as well as near the interface between the Ag disks and the environment medium is greatly enhanced. As to the magnetic field in Fig. 3(b), it is enhanced in both the upper and lower parts of the SiO$_2$ disk as well as the top and bottom of the Ag disks. The direction of the electric vectors are also aligned with the incident electric field direction, consistent with the characteristics of an electric resonance [52]. Since the enhanced electric field is localized at the interface corners, this electric resonance can be specified as LSPR. For comparison purpose, the field distributions for the bare Ag nanodisk are plotted in Figs. 3(c) and 3(d). Key features of the electric and magnetic field distributions around the Ag nanodisk are very similar to those of the Ag-SiO$_2$-Ag nanodisk, suggesting that the absorption peak at 510 nm in Fig. 2(b) is also due to LSPR. On the other hand, the magnitude of the electric field in Fig. 3(c) is higher than that in Fig. 3(a).
Fig. 3. Local field distributions at $\lambda =510$ nm for $z$-incidence and $x$-polarization: (a) time-averaged square of the electric field and (b) magnetic field at $y = 0$ for the Ag-SiO$_2$-Ag disk; and (c) time-averaged square of the electric field and (d) magnetic field at $y = 0$ for the Ag disk. The arrows indicates the electric field vector when the phase = 0 degree.
The electric and magnetic field distributions for the Ag-SiO$_2$-Ag disk at $\lambda =600$ nm for the case of $z$-incidence with $x$-polarization [refer to Fig. 2(a)] are plotted in Fig. 4. As seen from Fig. 4(a), the electric field in the SiO$_2$ disk area is greatly enhanced, especially near the corners at the Ag-SiO$_2$ interface. The electric vectors circulate clock-wise in the SiO$_2$ disk, forming an eddy current. In Fig. 4(b), the magnetic field is also greatly enhanced in the SiO$_2$ disk and confined in this dielectric region. The distribution of the electric and magnetic fields indicates a diamagnetic response in the MIM disk [43,53], suggesting that the absorption peak at $\lambda =600$ nm is caused by magnetic resonance. It is now obvious that the MP resonance can also contribute to the generation of the absorption peak for the proposed MIM disk, broadening the absorption band accordingly.
Fig. 4. Local field distributions at $\lambda = 600$ nm for the Ag-SiO$_2$-Ag disk for $z$-incidence with $x$-polarization: (a) time-averaged square of the electric field and (b) magnetic field at $y = 0$. The arrows indicates the electric field vector when the phase = 0 degree.
For the case with $x$-incidence with $z$-polarization, the electric and magnetic field distributions corresponding to three absorption peaks at 350 nm, 420 nm and 600 nm [see Fig. 2(a)] are shown in Fig. 5. For the peak at 350 nm in Fig. 5(a), the electric fields in the Ag disks are enhanced, especially near the Ag-SiO$_2$ interfaces and at the particle edges. The magnetic field shown in Fig. 5(b) attenuates gradually along the incident direction. Note that the investigation of the Ag sphere particle shows a LSPR peak at 350 nm regardless of the particle size, as long as the diameter is below 100 nm [30,54]. Therefore, the peak here at 350 nm can be attributed to the LSPR, which is caused by the intrinsic Ag property. Note that it was also found that the variation of diameter does not cause any shift in the peak at 350 nm in the case of $x$-incidence with $z$-polarization (not shown here), indicating this resonance peak is dimension independent, consistent with the LSPR characteristics in the elctrostatic limit [42]. An interesting phenomenon is that the directions of the electric vectors in the SiO$_2$ disk are opposite, i.e., the directions are upward in the left part while downward in the right part.
Fig. 5. Local field distributions for the Ag-SiO$_2$-Ag disk at the peaks for $x$-incidence with $z$-polarization at $y = 0$: (a) time-averaged square of the electric field and (b) magnetic field at $\lambda =350$ nm; (c) time-averaged square of the electric field and (d) magnetic field at $\lambda =420$ nm; and (e) time-averaged square of the electric field and (f) magnetic field at $\lambda =600$ nm. The arrows indicates the electric field vector when the phase = 0 degree.
For the resonance peak at 420 nm in Fig. 5(c), the electric field in the SiO$_2$ disk is magnified to some extent, and the electric field near the disk interfaces and edges are especially stronger. The electric vector direction in the SiO$_2$ disk is opposite to that in the Ag disks (i.e., downward in the Ag disks and upward in the SiO$_2$ disk). It can be observed in Fig. 5(d) that the magnetic field in the left part of the SiO$_2$ disk area is especially enhanced, along with the closely connected upper and lower Ag disk areas. The investigation of a single Ag disk indicated that the electric and magnetic fields (not shown here) of the single Ag disk were similar to that of a Ag-SiO$_2$-Ag disk, except that a symmetric magnetic field along the $x$-axis was generated. This confirms that the two electric resonances inside the Ag disks are spatially overlapped in the Ag-SiO$_2$-Ag case, where only a small distance (i.e., the thickness of the SiO$_2$ disk) exists between the two Ag disks. Since this resonance is merely dependent on the Ag nanodisk itself [refer to Fig. 2(b)], it is attributed to electric dipoles (ED) resonance, which only requires collective polarization in the material(i.e., $z$ polarization in the Ag disk) with the electric field of the incident light [55].
For the minor peak at 600 nm in Fig. 5(e) and 5(f), the electric field in the SiO$_2$ disk region is obviously more highly enhanced than in the Ag disk regions. Again, the electric field at the corners is stronger compared to other positions. The electric field gets weaker along the incidence $x$ direction. The magnetic field in Fig. 5(f) is enhanced slightly at the left side of the Ag disks and on the right side of the SiO$_2$ disk. Since this resonance is dependent on the SiO$_2$ disk, and considerable energy is confined in this SiO$_2$ region, the resonance is attributed to magnetic resonance. Note also that the MP resonance for the $z$-incidence with $x$-polarization occurs at 600 nm as well. However, a diamagnetic response pattern similar to the one in Fig. 4(a) was not clearly observed here. This is probably due to the other parts of the current loop lies in the air to the left of the disk. This has also been observed in Ref. [55] for a SiO$_2$ nanocylinder, where the resonance is attributed to magnetic dipole (MD) resonance.
Finally, we consider the $x$-incidence with $y$-polarization case, with Fig. 6(a) and 6(b) for the peak at $\lambda =450$ nm and Fig. 6(c) and 6(d) for the peak at $\lambda =510$ nm. Note that these two peaks both occurred in a pure Ag disk [refere to Fig. 2(b)], implying they are related to electric resonances. The peak at 450 nm can be attributed to the ED resonance, which can be excited by the collective polaritons in the Ag disk. The electric field and magnetic field at $\lambda$ = 510 nm here resemble that of the peak at 510 nm in Fig. 3 for $z$-incidence with $x$-polarization, and these two peaks at the two different incident directions also have the similar magnitude as shown in Fig. 2, thus the resonance at $\lambda$ = 510 nm here is also attributed to the LSPR.
Fig. 6. Local field distributions for the Ag-SiO$_2$-Ag disk for $x$-incidence and $y$-polarization at $x = 0$: (a) time-averaged square of the electric field and (b) magnetic field at $\lambda =450$ nm; and (c) time-averaged square of the electric field and (d) magnetic field at $\lambda =510$ nm. The arrows indicates the electric field vector when the phase = 0 degree.
The investigation of the near-field electric and magnetic field distributions clearly indicated that the absorption peaks are caused by both electric (including LSPR and ED) and magnetic (including MP and MD) resonances. Compared to the single Ag disk, the addition of the SiO$_2$ disk in between the two Ag disks results in a broader absorption band, and also lowers the sharp resonances near 510 nm and lifts up the relatively low peaks near 350 and 420 nm. Therefore, the proposed Ag-SiO$_2$-Ag disk is more suitable for broadband solar energy absorption [51].
3.2 Verification of the MP excitation using the LC-circuit model
As analyzed based on the local field distribution, the peak at $\lambda$ = 600 nm for the $z$-incidence with $x$-polarization is associated with the magnetic polariton. In this section, we applied the widely used LC-circuit model to predict the magnetic resonance peak, thus to further verify the MP excitation.
In the Ag-SiO$_2$-Ag nanodisks, the two parallel Ag nanodisks and one SiO$_2$ nanodisk can form an equivalent LC circuit depicted in Fig. 7(a). The total inductance $L$ in the equivalent curcuit consists of the mutual inductance between two parallel nanodisks $L_m$ and kinetic inductance $L_e$, respectively. Here, $L_m$ is equal to the parallel combination of the inductance for each (differential) section along the $y$-axis, as indicated on the right in Fig. 7(a). Thus, the total inductance $L$ can be simply calculated from $L = 0.5 L_m + L_e$. In this equation,
Fig. 7. (a) Equivalent LC-circuit model for the MIM nanodisk. Predicted MP resonance conditions (b) with varying $d$ when $t_2 = 20$ nm and (c) with varying $t_2$ when $d = 60$ nm.
For the base configuration (i.e., $d = 60$ nm and $t_1 = t_2 = t_3 = 20$ nm), the MP resonance peak for the $z$ incidence with $x$ polarization with the BEM simulation was at 610 nm, while that predicted by the LC-circuit model was about 580 nm, which reasonably agrees with the BEM result. This confirms once again the occurrence of the MP resonance peak. Changing $d$ or $t_2$ has an influence on $\omega _{MP}$, and the corresponding change in resonance peak $\lambda _{MP}$ is shown in Fig. 7(b). The increase in $d$ leads to an increase in the resonance peak, and the increase in $t_2$ results in the decrease of the resonance peak. This trend is similar with that from BEM simulations (not shown here). For the case when $t_2$ = 10 nm in Fig. 7(c), the $\lambda _{MP}$ predicted by the LC-circuit model and the simulated MP resonance wavelength using the BEM simulation were nearly the same at 670 nm. However, it is noted that there was a relatively large discrepancy when the thickness of the SiO$_2$ (i.e., $t_2$) decreased to several nanometers. This is probably due to the fact that the numerical parameter $c$ (i.e., 0.5 here) is underestimated. That is, as $t_2$ becomes very small, the charge distributions becomes more uniform, which leads to $c$ increasing to nearly unit [45], larger than the applied value of 0.5. Similarly, when $t_2$ is above 10 nm, the applied $c$ = 0.5 is overestimated, leading to a smaller $\lambda _{MP}$ compared to the BEM simulation results. Therefore, when using the LC-circuit model, the selection of $c$ is very important, and $c$ is heavily dependent on $t_2$. Overall, the derived LC-circuit model in this study resulted in fairly good agreement with the rigorous electromagnetic simulation.
3.3 Effects of light scattering and geometric parameters
In order to apply the proposed nanoparticles in a DASC, two more factors are considered here. The first is the light scattering by nanoparticles, which also has an impact on the collector performance besides absorption. While scattering may result in a photon being scattered out of the collector (i.e., decreasing the absorption of the solar energy), it can also be beneficial because the light scattering can increase the optical length of a photon [56]. Therefore, controlling scattering is also important. Here, the scattering albedo of the MIM nanodisk is investigated.
Figure 8 shows the scattering albedo of the MIM nanodisk with the base configuration (i.e., $d = 60$ nm and $t_1 = t_2 = t_3 = 20$ nm) in blue. It is clear that the scattering is significant along the spectrum of interest. Especially, the scattering albedo is as high as 0.6 in the range of 470 $\sim$ 550 nm. Note that the LSPR resonance occurs at $\lambda$ = 510 nm. Whereas, the scattering is not significant near the magnetic resonance peak (i.e., 600 nm), implying that the MP related resonance can prevent too high scattering compared to the LSPR, which is beneficial for effective solar energy absorption. To unveil the reason for a less significant scattering effect at the MP resonance compared to that at the LSPR resonance, the heat dissipation density [48] in the MIM nanodisk has been investigated for the $z$-incidence with $x$ polarization case. Although not shown here, the calculation indicates that the heat dissipation is especially strong near the top surface of the upper Ag disk with the LSPR, while the strongest heat dissipation occurs near the interface of the upper Ag and SiO$_2$ disks inside the MIM nanodisk with the MP resonance. The less significant scattering at the MP resonance can thus be attributed to the fact that strong heat dissipation occurs inside the MIM nanodisk rather than at the MIM nanodisk outer surface as for the LSPR resonance case.
Fig. 8. Scattering albedo of the two MIM disks: one with $d = 60$ nm and $t_1 = t_2 = t_3 = 20$ nm, and the other with $d = 30$ nm and $t_1 = t_2 = t_3 = 10$ nm.
In order to reduce the scattering albedo, the dimension of MIM nanodisk was reduced to half (i.e., $d = 30$ nm and $t_1 = t_2 = t_3 = 10$ nm). The corresponding scattering albedo is shown in Fig. 8 in red. Distinctly, the scattering was reduced by a great deal. For instance, the scattering albedo at the LSPR peak at $\lambda$ = 510 nm was decreased significantly from 0.62 to 0.18 by 71%. Except the region around 450$\sim$550 nm, the scattering albedo all decreased to below 0.1, making absorption more dominant than scattering.
The second factor is the tunability of the absorption efficiency (usually done by changing the geometric parameters). The sizes $d$, $t_1$ and $t_2$ were varied to evaluate the corresponding $Q_a$, and the calculated results are shown in Fig. 9. Note that the effect of $t_3$ on $Q_a$ was the same as that of $t_1$; thus not repeated here. The geometric parameters are seen to have an obvious effect on the absorption efficiency of the MIM nanodisk. The variation in $d$, $t_1$ and $t_2$ shifted the absorption peaks and altered the magnitude of $Q_a$ significantly. In Fig. 9(a), the increase in $d$ results in a decrease of all the resonance peaks. For instance, the highest peak value is almost 6 when $d = 50$ nm but decreases to only about 2 when $d = 80$ nm. The distribution of $Q_a$ also becomes more uniform along the visible spectrum, which is beneficial for broadband solar energy absorption.
Fig. 9. Average absorption efficiency $Q_a$ for the Ag-SiO$_2$-Ag nanodisk with varying (a) $d$, (b) $t_1$ and (c) $t_2$. The base configuration is $d=60$ nm and $t_1 = t_2 = t_3 = 20$ nm.
The effect of the thickness of the Ag nanodisk (i.e., $t_1$) and SiO$_2$ nanodisk (i.e., $t_2$) on the average absorption efficiency $Q_a$ is shown in Fig. 9(b) and 9(c), respectively. It shows that the variation in both $t_1$ and $t_2$ influences the peak positions significantly. A smaller $t_1$ or $t_2$ leads to a further separation of the MP peaks from the other electric related resonance peaks. This indicates again the significance of the MP peak in broadening the absorption in the proposed MIM nanodisk.
The parametric study indicates that by changing the geometric parameters, the absorption band and peak values can be effectively tuned. In particular, the nanodisk diameter $d$ can be used to tune the magnitude of the peaks, and the nanodisk thicknesses $t_1$ and $t_2$ are effective for tuning the separation of the resonance peaks. In practice, optimization might help obtain a suitable design for the Ag-SiO$_2$-Ag nanodisk that can enhance solar energy absorption.
4. Conclusion
In this study, a Ag-SiO$_2$-Ag nanodisk has been proposed for solar energy absorption. The investigation of the absorption spectra of the MIM nanodisk showed that multiple absorption peaks occur due to both electric (i.e., localized surface plasmon and electric dipole) and magnetic (i.e, magnetic polariton and magnetic dipole) resonances. Compared to a single Ag nanodisk, the MIM nanodisk broadened the absorption band by exciting magnetic resonance peaks. The equivalent LC-circuit model also confirmed the excitation of MP. It was found that the scattering caused by the magnetic resonance was less significant than the electric resonance. In addition, the parametric study determined that the proposed MIM nanodisk could be sensitively tuned with varying its geometric parameters. The findings in this study can facilitate the utilization of MIM nanodisks which combine both electric and magnetic resonances for solar thermal applications.
Funding
National Research Foundation of Korea (NRF-2019R1A2C2003605).
Disclosures
The authors declare no conflicts of interest.
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