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Abstract
A method to develop an insulator window film which is able to filter thermal emission while transmitting the visible spectrum of sunlight is proposed. The proposed film is constructed from engineered metallic nano-spheres randomly distributed in ${\rm{Si}}{{\rm{O}}_2}$, as a host medium. The performance of the designed film is investigated using both analytical models and numerical full-wave simulations. The analytical analysis shows that the thermal emission (the wavelengths in the range of 6–16 µm) is suppressed by more than 10 dB when going through the designed film, meaning that more than 90% of the thermal power is filtered by the film. This is while more than 50% of the visible light passes through the film. Similar results are obtained using numerical full-wave simulations. Moreover, to have a more comprehensive study on the ability of our method, the illuminance due to the insulator window film is calculated and compared with illuminance in different places. This comparison shows that the resultant illuminance in a typical room at the distance of 4 m from the designed window is in the range of illuminance required in a typical office room.
© 2022 Optica Publishing Group
1. INTRODUCTION
Among different parts used inside a building, windows have the highest role in heat transfer [1–3]. In other words, most of the heat transfer from inside a building to the outside and vice versa happens through windows [1–3]. On the other hand, to provide thermal isolation, windows cannot be made from dark materials since that stops visible light entering the building. Therefore, developing a smart window that is transparent to the visible light and simultaneously filters thermal radiation can be very useful and will find applications in construction of different buildings. In fact, this window minimizes energy consumption on hot summer days and cold winter days by preventing the heat from entering or escaping from the building, respectively. Figure 1 simply shows how such a window works in different types of weather. As shown in this figure, such a window transfers the visible parts of the incident light while reflecting the infrared and helps save energy in the controlling of the indoor temperature.
Fig. 1. The way a smart window works in different types of weather, helping to save energy in the controlling of the indoor temperature and providing visual comfort for the building.
Several different types of reflective [4,5] and transmissive [6,7] filters with multi-band [4–7] and wideband [8] performance have been designed in the visible and infrared wavelengths [4–8]. Most of these filters are designed to work only in the infrared [4–6,8] or visible [7] regimes, and therefore their performance in both of these regimes has not been considered. One approach for achieving efficient windows has been proposed in [3], where coatings composed of ATO have been used to manage energy exchange. In [9], low emission (low-E) coatings have been designed based on multi-layered dielectric–metal–dielectric structures with layers as thick as a few nanometers. Reference [10] has proposed a glass composed of plasmonic nano-shells made of noble metals to block infrared radiation and transmit visible light that can be a good candidate for cheap optical media and energy-saving windows in warm climates. Another type of coating for saving energy applications has been proposed in [11] based on the electrophoretic deposition technique.
In this work, we propose a method which has an easier fabrication process when compared to previously reported works [4–11]. Moreover, we develop an analytical model here to make the design of these windows more straightforward. In the proposed technique, metamaterials operating based on the Mie theorem are engineered to stop thermal radiation and simultaneously pass the visible light. Metamaterials and their 2D counterparts, metasurfaces, have recently found a wide range of applications such as developing efficient thin-film solar cells [12–15], high-performance antennas [16–18], flat lenses and imaging systems [16,19], absorbers [20–22], invisibility clocks [23–25], realizing photonic topological insulators [26], and wave-front engineering [27,28]. Here, we propose to use them in designing smart windows whose performance has the least dependence on polarization and incident angle of light.
2. PROPOSED SMART WINDOW
In the proposed smart window, to develop our metamaterial environment, we use engineered metallic nano-spheres randomly distributed inside ${\rm{Si}}{{\rm{O}}_2}$ as a host medium. Nano-spheres are designed and engineered to provide a desired reflectance and transmittance in the visible and infrared spectrum. Using the developed analytical model, the properties of this structure are studied and a smart window is designed to filter thermal emission and transmit visible spectrum. The performance of the designed window and accuracy of the proposed analytical model is verified using full-wave numerical simulations. Moreover, we use the luminous efficiency function, which describes the average spectral sensitivity of human visual perception of brightness, as a criterion, to study the amount of visible light passing through the proposed window.
Filtering thermal emission is one of the crucial parts of the smart window. Thermal emission is the electromagnetic radiation emitted by heated surfaces and objects [29]. This radiation covers a wide range of wavelengths from the far-infrared to visible and ultra-violet wavelengths, and its intensity depends on the temperature [29]. To model thermal emission, here we use Planck’s law, formulated in 1900 by Max Planck [30]. In this regard, energy radiated by a blackbody at different wavelengths is described as [29,30]
where $c$ is the speed of the light, $T$ shows temperature in Kelvin (K), $\lambda$ is the wavelength of the electromagnetic wave in the free space, and finally $h$ and ${{{k}}_B}$ are Planck and Boltzmann constants, respectively. In Fig. 2, thermal radiations for objects at different temperatures of 25°C (298 K), 37°C (310 K), 47°C (320 K), and 57°C (330 K) are shown. This temperature range models the temperature variation on a typical summer day. According to Fig. 2, most of the thermal radiation energy in these temperatures, is related to wavelengths in the range of 6–16 µm. Therefore, a smart window that filters this range of wavelengths, can provide a desirable thermal isolation.To design such a filter, here we have used composite materials consisting of potassium nano-spheres [31,32] randomly distributed inside silica (${\rm{Si}}{{\rm{O}}_2}$) as the host medium (see Fig. 3). Needing transparency to visible light forced us to use potassium nano-spheres due to having low absorption at these wavelengths. The imaginary part of the permittivity at visible wavelengths has been shown for different materials in Fig. 4 based on the calculations and measurements reported in [33–35]. According to this figure, potassium has a lower absorption at visible wavelengths, and that is why we have chosen potassium nano-spheres as the building blocks of the proposed smart window. As shown in the structure of Fig. 3, potassium nano-spheres, with a radius of R, have randomly distributed in the ${\rm{Si}}{{\rm{O}}_2}$ layer. One of the most important aspects in the realization of the insulation film as a smart window is the synthesis process of nano-spheres. In this synthesis process, the shape or the size of the metallic nano-spheres may be slightly varied; however, based on Mie theory, slight variations of the nano-spheres in radius or geometrical shape cause only minor changes in the wavelength of the Mie resonances without major effects on the transmission spectrum of the proposed structure [12,36]. Therefore, in the following, we investigate the proposed smart window through modeling resonators as nano-spheres with a specific radius of R.
Fig. 3. Schematic of the designed smart window in which the metallic nano-spheres are randomly distributed in the ${\rm{Si}}{{\rm{O}}_2}$ as a host medium.
Fig. 4. Imaginary part of permittivity of potassium is compared with other materials, at visible wavelengths.
The constitutive parameters, (${\varepsilon _{\text{eff}}}$, ${\mu _{\text{eff}}}$), of such a film can be modeled using Clausius–Mossotti formulae [37,38]:
Here, we plan to design a smart window that filters a wide range of wavelengths. Therefore, in some wavelengths the radius of nano-spheres can be comparable to the wavelength. Therefore, to have a more accurate model, in addition to dipolar contribution, we also consider quadrupolar contribution ${\alpha _{\textit{Eq}}}$, ${\alpha _{\textit{Mq}}}$ of nano-spheres as [39]
After calculating the effective permittivity and permeability of the designed structure, the transmission coefficient, $T$, can be easily calculated as
Using Eqs. (3)–(6), we can calculate the transmission of the insulation film at infrared wavelengths, particularly in the range of 6–16 µm. In this calculation, for the permittivity of potassium, the Drude model with the plasma and collision frequency of ${\omega _p} = {{5}} \times {{1}}{{{0}}^{15}}\;{\rm{rad}}/{\rm{s}}$ and $\gamma = {{2}} \times {{1}}{{{0}}^{13}}\;{\rm{1/s}}$, respectively, is used. Furthermore, the refractive index of the ${\rm{Si}}{{\rm{O}}_2}$, the host medium, is considered as 1.45 in this calculation. To study the effect of different geometrical parameters on the performance of the proposed structure, the transmission of the insulation film for various values of the radius of nano-spheres, their filling factor, and the thicknesses of the film is shown in Fig. 5. As discussed before, we are interested in the films that filter the wavelengths in the range of 6–16 µm and simultaneously transmit visible light. Since we have used metallic nano-particles in our structure, a film with the lowest possible value of radius and filling factor of metallic nano-spheres, and a minimum thickness of film, will transmit the visible light better. Considering this fact and the results of Fig. 5, the radius, $R$, filling factor of the metallic nano-spheres, and the thickness of the film, $d$, are chosen to be 1150 nm, 0.236, and 15 µm, respectively. Therefore, as shown in this figure, the transmission of the optimum structure, for the wavelengths in the range of 6–16 µm is less than ${-}{{10}}\;{\rm{dB}}$, meaning that more than 90% of the power at these wavelengths is filtered and only less than 10% of the power goes through the designed structure. Also, the designed film has a high blocking factor around the wavelength of 9 µm, which has the highest thermal emission at the solar irradiance according to Fig. 2. Therefore, the designed smart window acts as a good thermal filter.
Fig. 5. Analytically calculated transmission of the insulation film, (a) for different radii of nano-spheres when the filling factor and thickness are set at 0.236 and $d = {{15}}\;\unicode{x00B5}{\rm m}$, respectively; (b) for different filling factors of metallic nano-spheres when the radius and thickness are set to be $R = {{1150}}\;{\rm{nm}}$ and $d = {{15}}\;\unicode{x00B5}{\rm m}$, respectively; and (c) for different thicknesses of insulation film when the filling factor and radius are set at 0.236 and $R = {{1150}}\;{\rm{nm}}$, respectively.
Using metallic nano-spheres of different sizes may increase the operation bandwidth of the insulation film. However, it increases the fabrication complexity. Therefore, here to avoid more complexity in the fabrication process, we have covered the desired bandwidth (wavelengths in the range of 6–16 µm) using nano-spheres of the same size (as shown in Fig. 5). To provide more detailed information about the proposed structure, the effective refractive index of the insulation film is shown in Fig. 6, showing a high imaginary part ($k$) at the wavelengths of 6–16 µm.
Fig. 6. Real and imaginary parts of insulation film calculated by using the Clausius–Mossotti model.
3. NUMERICAL ANALYSIS AND DISCUSSION
Now, to verify the achieved analytical results, we perform full-wave numerical simulation using CST software, which solves Maxwell equations using the finite-element method (FEM). The simulated structure is shown in Fig. 7. As shown in this figure, the simulated environment includes 125 potassium nano-spheres (with a radius of 1150 nm) randomly distributed in a ${\rm{Si}}{{\rm{O}}_2}$ layer (with thickness, depth, and width of 15 µm). This is equivalent to a filling factor of 0.236. In this simulation, a normally incident plane wave is used for excitation, and periodic boundary conditions have been used in both the $x$ and $y$ directions (see Fig. 7).
The results of this simulation are shown in Figs. 8(a) and 8(b) [dB: ${{20}}\log_{10}$ (transmission or reflection)]. These figures show the transmission and reflection of the designed film, respectively, for the wavelengths in the range of 5–29 µm, and for both TE and TM polarizations of the incident wave. For the sake of comparison, the analytically calculated transmission is also shown in Fig. 8(a). As illustrated in this figure, a good agreement is observed between numerical and analytical results confirming the accuracy of the analytical model. As shown in Fig. 8(b), for both TE and TM polarizations of the incident light, we have a high reflection for the most wavelengths in the range of 6–16 µm, and therefore, only a small part of radiation is absorbed by the window, and most of it is reflected back.
Fig. 8. (a) Transmission and (b) reflection of the simple bar of silica calculated by the full-wave simulator and the proposed insulation window film, calculated with the analytical model and full-wave simulator.
One of the methods for verifying the performance of the designed window in visible wavelengths is the multiple-scattering method [41–45]. The multiple-scattering method proposed in [41–45] studied periodic distribution or a cluster of particles with specific locations in a homogenous medium. In our work, the emerging random distribution of infinite metallic nano-spheres in a host medium with finite thickness may be altered in several cases in different fabrication processes. This behavior is in contrast to [41–45], which investigate nano-spheres in a cluster with specific locations. Thus, we used a fast method of Clausius–Mossotti formulae to model the permittivity and permeability of the structure and then calculated the transmission and reflection of the insulation film. Moreover, to investigate the structure in the visible wavelengths, we study periodic nano-spheres with periodic boundary conditions through the FEM method, which is impossible by the multiple-scattering method due to emerging in a layer with finite thickness. In this regard, we simulate the structure shown in Fig. 9(a). It should be noted that the setup shown in Fig. 7 cannot be used in visible wavelengths, since a very high number of meshes (for achieving accurate results) should be used at these wavelengths. Therefore, for numerical simulation at these wavelengths, we use a periodic distribution of metallic nano-spheres represented in the setup of Fig. 9(a). Although this periodic arrangement of nano-spheres is not possible during the fabrication process, the performance of the structure in the random but dense distribution does not have considerable differences from the periodic one [12].
Fig. 9. (a) The simulation setup used for full-wave numerical analysis in the visible wavelengths of light, (b) numerically calculated transmission of the insulation window film at the visible wavelengths.
As shown in Fig. 9(a), the unit cell used in this simulation contains three metallic nano-spheres in the $z$ direction, and periodic boundary conditions are used in the $x$ and $y$ directions to model an infinite structure in those directions. For the excitation, a Floquet port was used to generate the plane wave, and the total transmission was calculated by the summation of the first 10 diffracted modes. Figure 9(b) shows the results of this simulation. As shown in this figure, the designed structures have a high transmission (more than 50% at most of the wavelengths) at the visible range of the spectrum and therefore provide good transparency at these wavelengths. It should be noted that due to the setup used in this simulation, which is symmetric and uses only few numbers of nano-particles, the results shown in Fig. 9(b) are the same for both polarizations of incident light. In the real structure composed of a random distribution of nano-particles, the different responses for TE and TM polarizations are inevitable. Nevertheless, the proposed random but dense arrangement of nano-spheres, as polarization-insensitive resonators, represents close behaviors for both polarizations [12,46].
Also, we studied the impact of the distribution and size of nano-spheres on the transmission of the proposed structure. The results of this investigation have been shown in Fig. 10(b). As shown in this figure, the structures with a random distribution and the nano-spheres of radius with a deviation of 50 nm from the radius of 1150 nm have transmissions more the 0.5 in most of the wavelengths of visible light, proving that random distributions can also provide transparency to the sunlight. This important feature of low dependency of insulation film performance on the distribution and size of the metallic nano-spheres originates from the dense distribution of nano-particles also observed in [12,47].
Fig. 10. (a) Different structures used to study the impact of the distribution and size of nano-spheres on the transmission of the proposed structure, (b) numerically calculated transmission of the structures shown in part (a).
Fig. 11. Numerically calculated transmission of the proposed smart window at different angles of incidence for (a) TM and (b) TE polarizations of the electromagnetic wave.
Now to have a comprehensive investigation on the ability of the insulator film to pass visible wavelengths, the luminous efficiency function, which describes the average spectral sensitivity of human eyes, is used. The luminous efficiency function can be calculated as [48]
Table 1. Illuminance for Building Room with $2\;{\rm{m}}^2$ Area of the Proposed Insulation Window Film and Other Different Places in the Direct Radiation of the Sunlight
To have a better comparison, we have shown illuminance at different places in the direct radiation of sunlight in Table 1. As shown in this table, the illuminance of the insulation window in a building room at a distance of 4 m from the window is close to the average illuminance we have in a typical office room. Therefore, the designed smart window provides an acceptable illuminance while filtering thermal emission.
Fig. 12. Transmission of the insulation film in different angles of the incident at the visible light range.
Table 2. Average Reflectance for the Designed Insulation Film at the Wavelength Range of 6–16 µm and Visible Light
Table 3. Comparing the Features of the Proposed Smart Window and Other Previous Works
Finally, to have a comprehensive investigation, we study the performance of the proposed structure for oblique incidence (10–60 deg), and also for both TE and TM polarizations of the incoming wave. The results of this numerical study are shown in Fig. 11. As shown in Fig. 11, the transmission coefficient is less than ${-}{{10}}\;{\rm{dB}}$ in the operation bandwidth of the film, representing the performance is independent of the incidence angle. The transmissions of the proposed structure in the visible regime for different angles of incidence are shown in Fig. 12. As shown in this figure, the response is different for different angles of incidence. However, for most of the angles shown in the figure, we have a transmission whose average is above 50%. Moreover, to evaluate the performance of the designed film more accurately, the average reflectance defined as the average (over the interested wavelength range) of ratio of reflected power intensity to the incident power intensity for different incident angles is calculated and shown in Table 2. According to the results shown in this table, as the incident angle increases, the reflectance at the wavelength range of 6–16 µm decreases, and in contrast, it increases in the visible light range. In other words, as the incident angle increases, the performance of the designed film deteriorates. However, the film shows an acceptable performance for incident angles up to 60 deg.
Table 3 compares our designed film with other works in terms of rejected and transmitted bands, thickness, and dependency to the angle of incidence. As shown in this table, most of the previous structures did not investigate the performance of smart windows at the tilted angle of the incident light. However, as we know, most of the time, solar radiance is not normal to the Earth. The other important point is the rejected band, which in previous works does not exactly match with the range of wavelengths of higher thermal energy based on Fig. 2. Another advantage of this work is its uncomplicated fabrication process since it can be easily fabricated using the solgel method [50]. In this method, metallic spheres are distributed homogeneously into the liquid form of ${\rm{Si}}{{\rm{O}}_2}$, and then the resultant sol-solution is deposited on the glass layer using spin coating.
4. CONCLUSION
In conclusion, a new method was proposed to design an insulation window film (smart window). We showed that when potassium nano-spheres with an engineered radius and filling factor are randomly distributed inside a ${\rm{Si}}{{\rm{O}}_2}$ layer as the host medium, a good filter can be developed that stops the thermal emission and transmits visible light. We developed an analytical model based on Mie theory and circuit modeling, to easily design such a window. The accuracy and performance of the developed model were verified using full-wave numerical simulations. The numerical results showed that the designed window reduces the thermal power by more than 10 dB, while providing an illuminance (luminous flux per unit area) of 501 lux in a typical room at the distance of 4 m from the window. Therefore, it was numerically and analytically proved that the designed smart window filters thermal radiation while providing acceptable illuminance in a typical room.
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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