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Abstract
A transparent absorber refers to the device which can absorb light strongly within a narrow frequency range but transmit light efficiently outside that range. Because of the contradiction between absorption and transmission, however, the performances of the transparent absorbers are usually compromised. In this work, we propose a transparent absorber based on a sandwiched metal-insulator-metal (MIM) structure, i.e., two perforated ultrathin metal films separated by a central dielectric layer. This structure has the advantage that the narrow-band absorption can be greatly enhanced because of the cooperation of surface-plasmon polariton (SPP) mode and multiple reflections in the dielectric cavity. Moreover, the ultrathin thickness of the stacked metal films enables high transmission when the wavelength of incident light deviates from the SPP resonance. A semi-analytical Fabry-Perot model has been employed to describe the optical properties, which agrees well with the simulation. The dependence of optical properties on the structural parameters has also been studied systematically. In addition, by covering the transparent absorber with an antireflection layer, highly efficient absorption of red (∼87% @ 629 nm), green (∼89% @ 524 nm), or blue (∼68% @ 472 nm) light and high transmission (∼80%) in the transparent region have been suggested. With its excellent visible-wavelength selective absorption, polarization independence, high angle-tolerance, and structural simplicity, the proposed MIM transparent absorber may have potential applications in the display technology and other smart scenarios.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurface-based absorbers (MAs) have attracted increasing interest in past decades due to their extensive potential applications in selective thermal emitters [1–3], photodetectors [4–6], plasmonic sensors [7,8], thermophotovoltaic cells [9], and other optoelectronic devices. Compared with conventional absorbers composed of bulky absorbents and base materials, MAs are artificially constructed with quasi-two-dimensional array of subwavelength meta-atoms, thus being thinner, lighter, and more convenient for system integration. Generally, for the MAs, high absorption within a wide frequency range with high angle-tolerance and polarization-independence is of utmost importance in view of the practical applications.
In some scenarios, there is a need that the absorber is able to achieve extremely high absorption in a narrow frequency band but almost transparent in a wide frequency range outside the absorption band. This means the reflection R and transmission T are simultaneously minimized within the absorption band while the reflection R and absorption A are minimized outside the absorption band (thus R should be suppressed in the whole frequency range). The absorbers of such characteristics are called the transparent absorbers [10–12]. An asymmetric metal-insulator-metal structure based on Fabry-Perot cavity was designed to achieve non-zero transmission outside the absorption band, but the obtained transmission efficiency and bandwidth were found to be relatively low [10]. The transparency in a single nanoparticle array is seriously degenerated due to the higher-order scattering modes [11]. A narrow-band optical absorber based on a Salisbury-like structure, where optical metasurfaces made of plasmonic ellipsoids play the role of the resistive sheet and the ground plane, has been proposed [12]. Such a structure exhibits a high transmission in a rather wide frequency range outside the absorption band, but it is highly polarization dependent.
It is well known that a thick metal film perforated with periodic subwavelength holes can support enhanced optical transmission [13,14]. On the contrary, a perforated ultrathin metal film with the thickness smaller than or comparable to the skin depth exhibits suppressed transmission and enhanced light absorption [15,16]. The latter can be attributed to the resonant excitation of the short-range surface-plasmon polariton (SPP), which is strongly bounded to the metal surface, thus resulting in a large Ohmic loss. The absorption properties of such ultrathin single-layer perforated metal films provide new ideas for the design of selective absorption of electromagnetic waves. However, it was theoretically proved that the upper limit of the absorption efficiency of such an ultrathin structure is 50%, which greatly hinders the practical application of this structure [15]. In this paper, we proposed a sandwiched transparent absorber, consisting of two ultrathin metal films perforated with small holes and separated with a central dielectric layer. Due to the short-range SPP resonance and multiple light reflections in the dielectric cavity, the absorption efficiency is greatly increased while high transmission is maintained outside the absorption band. It is also shown that, by covering the transparent absorber with an anti-reflection layer, the performance of the device can be further optimized (considering the absorption peak locating at the three primary colors). Compared with previous designed transparent absorber based on indium tin oxide (ITO) films, liquid or double-resonance-layer metamaterial [17–21], the novelty of the proposed structure is three-fold. First, by adjusting structural parameters, excellent transparent absorption performance can be achieved at any wavelength in the visible light band, while most of previously proposed transparent absorbers only work in the microwave frequency regime. Second, the ultrathin perforated metal films are used in place of the conventional continuous ITO film or nanoparticle array as the ground plane to improve optical transmission. The designed structure is relatively simple and easy to fabricate. Third, due to the symmetry of the proposed structure, the optical properties are polarization independent and highly angle tolerant. These performances suggest that the proposed designs are promising candidates for the display applications.
2. Results and discussions
To make a comparison, Figs. 1(a) and 1(b) show the schematic views of the single-layer perforated metal film and the sandwiched transparent absorber, respectively. Here, the thickness of the metal films is t, comparable with or smaller than the skin depth of the metal (t<δ); the periodic circular holes are milled in the metal film with the lattice constant of p and radius of r; the dielectric substrate of the single-layer metal film and the dielectric spacer of the sandwiched absorber have a permittivity of ɛd; and the thickness of the dielectric spacer in the transparent absorber is h. A linearly polarized light with the magnetic field along the y axis is incident upon the structure, where the incident angle is θ (but due to the structural symmetry, the performance of the absorber is actually polarization independent).
Fig. 1. Unit cell of (a) the single-layer perforated metal film and (b) sandwiched transparent absorber; (c, e) spectra of transmission, reflection and absorption for the two types of plasmonic structures; (d, f) electric field (Ez) distributions at the absorption peaks (λ=519 nm) for the two structures (xz-plane). Here, the incident light is incident normally upon the structures with the magnetic field along the y axis. The structural parameters are set as p = 90 nm, r = 20 nm, t = 8 nm, h = 90 nm.
To study the optical properties of the proposed transparent absorber, numerical simulations based on the finite-difference time-domain (FDTD) method have been performed [22]. In the simulations, the periodic boundary conditions were used in the x and y directions and open boundary condition was employed in the z direction. To ensure high transmission of light (when the wavelength deviates from the SPP resonance), the ultrathin metal film was assumed to be silver, which has a low absorption in the visible and infrared region. In the optical frequency range, the dispersion of silver film can be described by the Drude model ${\mathrm{\varepsilon }_\textrm{m}}\textrm{ = }{\mathrm{\varepsilon }_\infty }\mathrm{\ -\ \omega }_\textrm{p}^\textrm{2}\mathrm{/\omega (\omega +\ i\gamma )}$ [23], where ɛ∞=5, ωp = 1.37×1016 rad/s. It should be pointed out that the surface dispersion effect occurs when the metal nanoparticle size or the film thickness is smaller than the mean free path of electrons in the bulk metals, which results in an additional size-dependent damping factor in the optical response [24,25]. The damping factor of the ultrathin metal film is about 3∼4 times as large as that of bulk metals [26]. Thus, taking into account the additional optical losses from surface dispersion, a larger value of γ=1.2×1014 Hz is used in this study (for the bulk silvers, γ=4×1013 Hz). The permittivity of the dielectric is ɛd = 2.25. The electric field of the incident light was set as E0 = 1 V/m.
Without loss of generality, the structural parameters are set as p = 90 nm, r = 20 nm, t = 8 nm, and h = 90 nm; the incident light is normally incident on the plasmonic structure. Figure 1(c) presents the simulated transmission, reflection and absorption spectra (400∼750 nm) for the single-layer perforated metal film. It is shown that, near the wavelength 519 nm, a narrow transmission dip (∼30%) and reflection peak (∼43%) appear in the spectra. Correspondingly, an absorption peak with the absorption efficiency ∼27% is obtained at the same wavelength. Figure 1(d) plots the electric field (Ez) distribution in the xz-plane for the absorption peak. It is clear that the electric field is enhanced and highly localized near the metal surface. The field pattern shows that the free charges accumulated at the upper and lower metal surfaces are symmetric, i.e., of the same sign. These features correspond to the short-range SPP mode. Near the center of the metal film, a strong parallel electric-field component Ey will be induced by the free charges, thus leading to a large Ohmic loss or absorption of light. One can also notice that, outside the absorption band, the transmission efficiency is high (70–80%) in a wide range. Nonetheless, the absorptivity (∼27%) of the single-layer structure is too low to work as an efficient transparent absorber.
In contrast, Fig. 1(e) shows the simulation results for the sandwiched structure. Both transmission dip (∼8%) and reflection peak (∼23%) occur at the same wavelength λ=519 nm, but the efficiency is significantly reduced. Consequently, the peak absorptivity (at 519 nm) is promoted to ∼70%, which is much larger than that of the single-layer structure. Moreover, the transmission efficiency can be maintained near 70∼87% outside the absorption band. Therefore, the sandwiched structure may behave as an efficient transparent absorber. Figure 1(f) plots the electric field distribution at λ=519 nm. One can see that the electric fields near the two ultrathin metal films are also localized and enhanced, with the field patterns similar to that of the single-layer structure. This characteristic along with the same absorption peak demonstrates that the enhanced absorption in the sandwiched structure also originates from the short-range SPP mode (note that the SPP fields of the two metal films do not overlap or couple with each other, thus the resonance frequency of SPP mode is unchanged). However, due to the retardation and absorption effect, the SPP resonance on the second metal film is later and weaker than that of the first film. We emphasize that the main mechanism here is different from that of unpatterned ultrathin metal/dielectric/metal structure, where the absorption or transmission peak results from the Fabry-Perot resonance in the dielectric layer [27,28]. It is worth noting that outside the absorption band the transmissivity of the sandwiched structure around 650 nm (Fig.1e) is higher than that of the single-layer structure (Fig.1c), which can be attributed to transmission modulation resulting from the Fabry-Perot effect and will be explained in detail below.
Besides the short-range SPP resonance, the dielectric cavity defined by the upper and lower perforated metal films may also play an important role. When the incident light impinges the first perforated metal film, the SPP may be excited which absorbs part of the light energy. Similarly, the transmitted (propagating) light reaches the second metal film, which also induces the SPP resonance and light absorption. Moreover, because of the multiple internal reflections, some remaining light will travel back and forth in the dielectric cavity, thus giving rise to multiple SPP excitation and enhanced absorption. Such a propagation process may be described with the following semi-analytical formulas:
Here, r and t are the reflection and transmission coefficients of the sandwiched structure; r1 and t1 are the corresponding coefficients at the individual air/metal/dielectric interface (from air to dielectric); and r2 and t2 are the coefficients at the individual dielectric/metal/air interface (from dielectric to air), as denoted in Fig. 2(a). These coefficients include both amplitude and phase information. The accumulated propagation phase of the light in the cavity is $\mathrm{\delta =\ 2\pi }{\textrm{n}_\textrm{d}}\mathrm{h/\lambda }$, where nd is the refractive index of the dielectric and λ is the light wavelength in vacuum.
Fig. 2. (a) Sketch for the calculation of reflectivity and transmissivity of the sandwiched structure; (b, c, d, e) simulated amplitude and phase of r1, t1, r2 and t2 as a function of wavelength (inset shows the structure for simulation); (f) comparison of semi-analytical results (the symbols) and numerical simulations (the lines) for transmission, reflection, and absorption spectra of the sandwiched structure.
The amplitude and phase of r1, t1, r2, and t2 used for theoretical calculation can be acquired numerically from the single-layer perforated metal film and the results are shown in Figs. 2(b)-(e), respectively. One can see that the single-layer ultrathin perforated metal film is almost transparent except that a minimum of transmission coefficient and a maximum of reflection coefficient occur near the SPP resonance. Also, at the SPP resonance, the reflection phase of r1 and r2 is close to π. Based on these results, the reflectivity $\textrm{R = |r}{\textrm{|}^\textrm{2}}$, transmissivity $\textrm{T = |t}{\textrm{|}^\textrm{2}}$, and absorptivity A = 1-R-T of the sandwiched structure may be obtained. Figure 2(f) gives the semi-analytical results (the symbols) obtained by using Eqs. (1), which exhibit a good agreement with the pure numerical simulations (the lines). According to Eqs. (1), the transmission coefficient t of the sandwiched structure is proportional to the product of t1 and t2, thus inducing a very low transmission at the SPP resonance and being transparent in the other wavelength regions. We find that at the SPP resonance wavelength a strong Fabry-Perot effect is not present, as the internal reflection coefficient is small (at 519 nm, $|{{\textrm{r}_\textrm{2}}} |\mathrm{\sim 0}\textrm{.35}$ and ${|{{\textrm{r}_\textrm{2}}} |^\textrm{2}}\mathrm{\sim 0}\textrm{.1}$) and the position of absorption peak is almost independent of the thickness of the dielectric spacer (which will be shown in the following). Nonetheless, the reflection coefficient r of the sandwiched structure benefits not only from the direct reflection r1 but also from the weak multiple reflection of the cavity, which may be partly canceled at the SPP resonance. Thus, a narrow band of absorption enhancement and a wide band of transparency can be achieved. The result demonstrates that the optical properties of the sandwiched structure are indeed associated with the SPP and cavity effect: the SPP effect is dominant and the cavity effect is secondary but also important.
Although the Fabry-Perot effect is not dominant, a transmission modulation associated with the cavity can be induced, especially in the transparent region. With Eqs. (1), the ratio of the transmission efficiency between the sandwiched (TMIM) and single-layer (TSL) structures is expressed as
The SPP resonance is dependent on the structure sizes of the plasmonic system. Consequently, by changing the structural period, hole size, film thickness, etc., the optical properties of the single-layer metal film such as the transmission and reflection coefficients can be adjusted. Accordingly, the properties of the sandwiched structure may be manipulated. In Fig. 3, the transmission and absorption spectra of the sandwiched structure for different parameters have been simulated and presented.
Fig. 3. Transmission and absorption spectra of the sandwiched structure for different parameters: (a, b) thickness of metal film; (c, d) thickness of dielectric spacer; (e, f) hole radius; and (g, h) incident angle. Insets in (e, f) depicts the electric field (Ez) distribution in the xy-plane at the two absorption peaks (λ1 = 519 nm, λ2 = 468 nm) for the sandwiched structure with hole radius r = 30 nm.
Figure 3(a, b) presents the transmission and absorption spectra for different thickness of the metal film (t = 5, 8, 16, 24 nm), where p = 90 nm, r = 20 nm, and h = 90 nm. It is found that, when t decreases from 8 nm to 5 nm, the narrow-band absorption and wide-band transparency are well maintained, except that the position of absorption peak is redshifted from 519 nm to 595 nm. The redshift is associated with the SPP wavevector that is a function of metal film thickness, where the decrease of thickness t will enhance the electromagnetic coupling between the two surfaces of a metal film and thus the effective index of short-range SPP mode is enlarged. On the contrary, when the thickness t increases from 8 nm to 16 nm and 24 nm, the absorption peak exhibits a blueshift and the absorption efficiency degenerates gradually. Moreover, the transmission efficiency at longer wavelength is reduced significantly because of the skin effect of the thick metal film. This is the reason for using the ultrathin metal film in this work.
Figure 3(c, d) gives the effect of thickness h of dielectric spacer on the transmission and absorption spectra (where p = 90 nm, r = 20 nm, t = 8 nm). An important finding is that both position and efficiency of absorption peak (or transmission dip) are not sensitive to the thickness h, which is significantly different from the unpatterned metal/dielectric/metal structure [27,28]. The semi-analytical results (not presented here) based on Eqs. (1) also confirm the finding. This facilitates the fabrication and practical application of the device. The result demonstrates that the Fabry-Perot resonance is not the main mechanism of enhanced absorption. When the thickness h is larger enough (e.g., h = 130 nm), however, the efficiency of absorption peak and transmissivity in the transparent region will be degenerated obviously. Upon deviation from the SPP resonance, the effect of Fabry-Perot resonance is enhanced. With increasing thickness of the dielectric cavity, the Fabry-Perot resonance may appear in certain wavelength. Near the Fabry-Perot resonance, the phenomenon of constructive or destructive interference occurs, such that the reflection strengthens or weakens and the transmission exhibits the opposite behavior. For example, when the thickness h is increased to 130 nm, $\mathrm{2\delta +\ 2}{\mathrm{\varphi }_\textrm{2}}\mathrm{\ =\ 4\pi }{\textrm{n}_\textrm{d}}\mathrm{h/\lambda +\ \pi =\ 2}\mathrm{.73\pi }$ at λ=450 nm, resulting in increased reflection and decreased transmission. On the other hand, when the thickness is very small, the performances will also degenerate due to the coupling between the two adjacent metal films, as shown in Fig. 3(c, d).
In Figs. 3(e, f), we show the spectra of transmission and absorption for different hole radius (where p = h = 90 nm, t = 8 nm). With the radius varying from 15 nm to 30 nm, no significant changes are observed for the original absorption peak and transmission dip. However, when r is larger than 25 nm, a secondary absorption peak and transmission dip (at about 468 nm) appears and grows gradually. With the simulations, this peak is found to stem from the localized plasmonic resonance on the short metal patch between two adjacent holes [see inset of Fig. 3(f)], which is different from the field distribution of absorption peak at 519 nm [inset of Fig. 3(e)].
A high angle-tolerance is of great importance in the optical device’s potential applications such as transmission displays and sensing. Figure 3(g, h) presents the simulation results with the incident angle θi varying from 0 to 80° with a step of 20°. One can see that, with the increase of θi, the original absorption peak (or transmission dip) splits into two peaks (or dips). The larger the θi, the larger the separation between the two peaks or dips (but the wavelength shift of the peak is less than 30 nm). This can be understood with the SPP resonance condition ${\textrm{k}_\textrm{0}}\mathrm{sin\theta \pm }{\textrm{G}_\textrm{m}}\mathrm{\ =\ \pm }{\textrm{k}_{\textrm{SPP}}}$, where k0 is wave vector of incident light, θ is incident angle, and Gm is reciprocal lattice vector. For a certain incident angle, there are two solutions of kSPP that satisfy the resonance condition, thus corresponding to two resonances or absorption peaks. It is worth noting that the peak absorptivity and wide-band transmissivity are still kept high even if the angle of incidence θi reaches 60° (when θi is larger than 80°, the performance will be reduced significantly). Thus, an angle-insensitive device can be constructed with the proposed sandwiched structure.
The performance of the sandwiched structure could be further promoted. For instance, the reflection of light may be suppressed by coating the system with an anti-reflection layer. Such a thin overlayer can also prevent the metal film from being corroded. Figure 4(a) shows the schematic view of an improved structure, where an anti-reflection overlayer with the thickness g and a dielectric substrate are added to the sandwiched structure (the refractive index of overlayer and substrate is assumed to be the same as that of the dielectric spacer). Here, we take respectively the absorption peak at three primary colors, e.g., red (630 nm), green (520 nm) and blue (460 nm) light, as an example. By adjusting the structural parameters (such as the thickness of overlayer g and spacer h), the improved structure may be used to realize efficient absorption of red, green and blue light, while being transparent in other wavelength regions. Figures 4(b)-(d) show the numerically obtained transmission, reflection, and absorption spectra for the structures with the absorption peak at red, green and blue light, respectively (the structural parameters are present in the caption of Fig. 4). The absorptivity for red light (at center wavelength λ0 = 629 nm), green light (λ0 = 524 nm), and blue light (λ0 = 472 nm) is 87%, 89% and 68%, respectively. Outside the absorption band, the transmission efficiency is nearly 80%.
Fig. 4. (a) Schematic view of the improved structure; (b)-(d) transmission, reflection, and absorption spectra with the absorption peak locating at red (p = 115 nm, r = 25 nm, g = 75 nm, h = 100 nm), green (p = 65 nm, r = 15 nm, g = 70 nm, h = 65 nm) and blue (p = 40 nm, r = 12 nm, g = 40 nm, h = 40 nm) light, respectively; (e) spectra of selective absorption of red light with overall perforation except the substrate [the structure parameters are the same as that of (b)]. Here, the metal film thickness is fixed as t = 8 nm.
In Figs. 4(b)-(d), the holes perforated only in the metal films are considered. How about the optical properties of the structure with overall perforation in the metal films, dielectric overlay and spacer (except the substrate)? The simulation suggests that such a realistic structure can still possess a good performance. Taking the selective absorption of red light as an example, Fig. 4(e) presents the simulation results for the structure of overall perforation [with the same structural parameters as those in Fig. 4(b)]. As can be seen, the absorption peak maintains a high absorptivity of 75%, accompanied by a small blueshift of peak position from 629 nm to 600 nm. Moreover, the transmissivity outside the absorption band is still around or larger than 80%. Similar results can be obtained for the green and blue light. The improved structure and simulation results indicate the feasibility of fabrication and potential applications.
3. Conclusions
In summary, a kind of sandwiched plasmonic structure, i.e., two ultrathin perforated metal films separated with a dielectric layer, has been proposed to construct a transparent absorber. Compared with the single-layer perforated metal film which has a low absorptivity, the sandwiched structure has greatly enhanced absorptivity in the absorption band, while maintains high transparency in other wavelength regions. The main mechanism of absorption enhancement can be attributed to the short-range SPP resonance on the two metal films and the multiple reflections in the dielectric cavity. The dependence of transmission and absorption spectra on the structural parameters has been investigated. Furthermore, we suggest that the performance of the transparent absorber can be optimized by coating the structure with an anti-reflection overlay. Considering the selective absorption at three primary colors, the improved structure shows the absorptivity reaching 87%, 89%, and 68% for red, green and blue light, respectively (a high transmission about 80% is maintained in the rest of visible bands). The outstanding properties of the proposed sandwiched transparent absorber, including excellent transparent absorption in visible frequencies, low structure complexity, adjustable absorption bands, high angular tolerance (60°) and polarization independence, are expected to find potential applications in modern display techniques.
Funding
National Natural Science Foundation of China (12174193).
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.
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