1. Introduction
Buildings need to provide a pleasant living environment and at the same time to minimize the electricity requirements for lighting and cooling. Recently there is an increasing architectural trend towards more use of glass. Conventional glass, in hot climates, transmits most of the solar infrared radiation. This increases the electricity consumption for cooling.
The household sector in Sudan consumes about 46% of the total energy consumption [1] . The consumption of electricity for lighting and cooling is about 3.5 × 106 MWh per year.
The shape of a building influences the solar energy that it receives. The solar radiation incident on a building affects the energy requirement for lighting and cooling. By improving the glazing performance of windows, it is possible to reduce the electricity consumption. For more energy saving, the spectral selectivity of the glazing has to be modified. At present, this has been achieved by using eitherelectrochromic or thermotropic devices. The optical properties of these materials are either electrically adjustable or thermally self-adjusting.
Electrochromic windows change light transmission in response to an external applied voltage. The transition from clear to opaque could take 3 - 5 minutes, for a small window [2] . Hong and Chen [3] used nano-Prussian blue analogue/ PEDOT/PSS: composites for a 10 × 10 cm2 WO3 electrochromic window. A maximum transmittance modulation of 61.6% at a voltage of 1.6 V was obtained. Kim and Taya [4] used V2O5 and poly (3,3-dimethyl-3,4-dihydro-2H-thieno [3,4-b][1,4]dioxepine) coatings. The window demonstrated electrochemical stability after over 150,000 cyclic switches, and that the response time for a 25 × 25 mm2 window was 5 seconds for coloration and 4 seconds for bleaching. Similarly, Kim et al. [5] obtained highelectromatic contrast andoptical cyclic stability, when they used electrochromic windows based on anodic electrochromic polymesitylenes containing 9H-carbazole-9-ethanol moieties. Fernandes et al. [6] used glass/ ITO/WO3/electrolyte/ITO/glass layered configuration. That resulted on visible average transmittance variation and optical density change of 41.6% and 0.39%, respectively. Hee et al. [7] concluded that electrochromic windows are more suitable for applications in residential areas in cold climate regions. Brooke et al. [8] investigated the effect of oxidant on the performance of conductive polymer films. They concluded that the oxidant Fe(Tos)3 produced superior device performance with respect to optical switching, switch speed and optical relaxation. Kim et al. [9] prepared transparent conductive ZnInSnO-Ag-ZnInSnO multilayer films for polymer dispersed liquidcrystal based smart windows. They obtained a lower operating voltage and a higher cutoff rate of infrared light, compared to ITO or ZITO-based smart windows. Khandelwal et al. [10] fabricated electrically switchable broadband infrared reflectors using polymer stabilized cholesteric liquid crystals. They predicted that their reflector can save more than 12% of energy compared to double glazing window and 9.3% compared to static infrared reflector. One of the drawbacks of electrochromic windows is their need for external biases to operate. Wang et al. [11] introduced a self-powered window. Aluminum was used to reduce Prussian blue to Prussian white in potassium chloride electrolyte. For self-recovering of the device to the blue appearance, the aluminum and Prussian blue electrodes could be disconnected. Lim et al. [12] studied the performance of tungsten-oxide-based electrochromic window. The results showed that the transmittance of visible light varied from 64% in the clear state to very low values in the colored state. They also concluded that there is little additional benefit from placing low emissivity coating on the electrochromic window.
Thermochromic windows switch from a clear state in low temperature to a diffuse reflective state in high temperature. The results of Long et al. [13] indicated that, in hot climate, the use of VO2 window decreases the energy consumption for cooling compared to the case with ordinary window. Zheng et al. [14] designed TiO2(R)/VO2(M)/TiO2(A) multilayer film to work as a smart window with antifogging and self-cleanig functions. Koo et al. [15] fabricated CeO2-VO2 bilayer to improve the optical properties of VO2 window. The CeO2 was employed as an antireflection layer of the VO2 film. Kamalisarvestani et al. [16] studied the spectral selective properties of thermochromic windows and the effect of doping of VO2 coatings with different dopants.VO2 could be the most promising thermochromic material, but its drawback is the preparation cost and the stability. Batista et al. [17] concluded that tungsten was the most effective dopant on the reduction of the semiconductor-metal transition temperature of VO2. More energy could be saved by using VO2 double window. Long and Ye [18] suggested that an appropriate phase transition temperature is needed to make the VO2 remains principally in its metallic state with low solar transmittance for summer application and in its semiconductor state with high solar transmittance for winter application. Zhou et al. [19] combined a VO2 thermochromic window with solar cells operated by the scattered radiation from the window. However, the efficiency of the cell was too low to justify the additional cost.
Both electrochromic and thermochromic windows suffer from high cost, low transmission of visible light and slow response time. In tropical regions, the ideal window is the one which transmitsall the visible light to reduce the lighting load, and reflects all the infrared radiation to reduce the cooling load, with 0.78 μm cutoff wavelength.
In this paper we studied the potential of usingthin layers of periodic structure as a glazing with spectrally selective properties. The proposed structure is for hot climates. It consists of alternating layers of Si/SiO2. The performance of the glazing was studied by using rigorous coupled-wave analysis method. The optimized structure was prepared by using magnetron sputtering technique.
2. Simulation
Rigorous coupled-wave analysis (RCWA) is formulated in the 1980s by Moharam and Gaylord. It is used for analyzing the diffraction of electromagnetic waves by periodic gratings [20] . RCWA is used in this study to calculate the radiative properties (reflectance and transmittance) of the periodically multilayer surfaces. It analyzes the general diffraction problem by solving Maxwell’s equations accurately in each of the three regions (input, multilayer, and output), based on Fourier expansion [21] . In RCWA, diffraction efficiency for each diffraction order is calculated with incident wave properties regardless of feature size, structural profiles, and dielectric function of the materials. The dielectric function of the materials is expressed as, 
where n is the refractive index and k is the extinction coefficient. The accuracy of the solution computed depends solely upon the number of terms retained in space harmonic expansion of electromagnetic fields, which corresponds to the diffraction order. Any linearly-polarized incidence can be decomposed into the transverse electric (TE) and transverse magnetic (TM) mode. The normalized electric field of incidence 
can be expressed as:
(1)
The electric field in region I (Figure 1) is the superposition of the incident wave and the reflected waves; therefore
(2)
Similarly, the electric field in region II (
) is the a superposition of all transmitted waves
(3)
The magnetic field in region I and II can be obtained from Maxwell’s equation H
(4)
(5)
where 
represents the frequency and 
the magnetic permeability of vacuum. The electric and magnetic field components in region M (Figure 1) can be expressed as a Fourier series:
(6)
(7)
where 
and 
are vector components for the jth space-harmonic electric and magnetic field in region M (multilayer region), respectively. Due to the structure periodicity, the relative dielectric function in region M, 
and its
inverse
, can also be expanded in Fourier series:
(8)
![]()
Figure 1. The proposed selective filter components.
![]()
(9)
where ![]()
and ![]()
are the jth Fourier coefficient for the ordinary and inverse of![]()
, respectively.
3. Optimization of the Thicknesses
3.1. Optimization of Si Thickness
The glazing consists of ITO layer deposited on one-dimensional (ID) four pairs of Si/SiO2 layers on top ofa1mm-glass sheet, Figure 2. The geometric parameters
![]()
Figure 2. The proposed selective filter for TM wave with different d1 thicknesses. (a) shows the reflectance and (b) the transmittance.
used to illustrate the wavelength selective filter are the thicknesses of the layers.
The wavelength-dependent dielectric optical constants of ITO, silicon and silicon dioxide were obtained from Ref. [22] . The thickness of ITO was 0.1 μm and that of Si was d1 = 0.1, 0.15 and 0.2 μm. The thickness of SiO2 was fixed at d2 = 0.4 μm. The normal reflectance and transmittance for the proposed selective filter were calculated numerically by using RCWA method in the wavelength range from 0.3 μm to 3 μm.
The normal reflectance and transmittance of the glazing, at normal incidence TM waves, is shown in Figure 2. The results show that the optimum thickness of the Si is 0.15 μm. It gives low reflectance (less than 30%) for wavelengths less than 0.8 μm and reflectance of nearly unity for higher wavelength values. This would transmit most of the visible light (to reduce the lighting load) and reflects nearly all the infrared (to reduce the cooling load).
3.2. Optimization of SiO2 Thickness
Figure 3 shows the normal reflectance and transmittance of the glazing for normal incidence TM waves. The thickness of Si was taken to be 0.15 μm, while that of SiO2 was changed, d2 = (0.2, 0.3 and 0.4) μm. The results show that the optimum thickness for SiO2 is 0.4 μm.
The glazing not only reduces the electricity consumption during daytime, but it also acts as an insulator during the cold nights of winter. It reflects the heat back inside the room. In the desert, the air temperature drops to less than 10˚C during the night. When the room temperature is about 30˚C, which corresponds to a peak wavelength of about 10 μm, there would be very little heat loss through the windows, Figure 4.
3.3. Effect of Angle of Incidence
The effect of the angle of incidence on the reflectance and transmittance is shown in Figure 5. It is seen that increasing the angle of incidence from 0˚ to 60˚ makes little difference on the reflectance and transmittance. The glazing seems to be suitable for all seasons and for both direct and diffuse radiation.
4. Experimental Work
The fabrication of the window and the measurements of its optical properties were performed at the laboratories of the Faculty of Science, University of Witwatersrand (Wits), South Africa. The filter consists of ITO layer deposited on four pairs of Si/ SiO2 layers on top of a 1mm-glass sheet. The magnetron sputtering system, shown in Figure 6, was used to deposit a thin film from sputtering targets onto substrate.
The silicon (S) and silicon dioxide (SiO2) were used as sputtering targets. The sputtering power and pressure were kept at 100 W and 140 W for silicon and silicon dioxide, respectively, and operation pressure at![]()
. The base vacuum level was![]()
. The argon gas flow rate was kept at 20 (standard cubic centimeters per minute) and controlled by amass flow meter. The
![]()
Figure 3. The glazing with different SiO2 thicknesses. (a) shows the reflectance and (b) the transmittance.
transmittance and reflectance of the filter were measured by a system consisting of a powering system, light source, stepper motor, photo-detectors and analog to digital converter.
5. Experimental Results
The measurement of the reflectance and transmittance are shown in Figure 7. The optimum thicknesses of ITO, Si and SiO2 were found to be 0.1 μm, 0.15 and o.4 μm, respectively. The measurements have also shown that the filter transmits about 78% of the visible light and reflects nearly all the infrared. These results are almost typical to that obtained by the simulation.
![]()
Figure 4. The optical properties of the glazing in the infrared range makes it a potential insulator during the cold nights.
![]()
Figure 5. The performance of the glazing for different incidence angles. (a) reflectance and (b) transmittance.
![]()
Figure 6. The sputter deposition system at laboratories of the faculty of science, University of Witwatersrand (Wits), South Africa.
6. Conclusions
In summary, we have used Rigorous coupled-wave analysis (RCWA) to design a relatively simple and efficient glazing for hot climates. The glazing consisted of ITO and four periodic pairs of Si/SiO2, deposited on a glass sheet.
RCWA was used to calculate the reflectance and transmittance of the different thicknesses of the layers. The optimum thicknesses of ITO, Si and SiO2 were found to be (in both simulation and experimental work) 0.1 μm, 0.15μm and 0.4 μm, respectively. The glazing transmitted 78% of the visible light and reflected almost all the infrared radiation from the sun. The optical properties of the glazing hardly depended on the angle of incidence of solar radiation. This makes it ideal for all hours of the day. During the night, in winter, it could act as an insulator to reflect the heat back inside the room. It satisfies the conditions for comfort in both the hot days of summer and the cold nights of winter.
The preparation of the filter and the testing were performed at the laboratories of the Faculty of Science, University of Witwatersrand, South Africa. Indium tin oxide (ITO), silicon (Si) and silicon dioxide (SiO2) were used as sputtering targets. The magnetron sputtering system was used to deposit a thin film from sputtering targets onto the substrate.
The experimental results were found to be in good agreement with the simulation results.
It can be concluded that the proposed filter has the advantage that it is relatively simple, efficient, and compared with commercial smart windows, it does not need any external source of energy to control its optical properties. It can be
![]()
(a)![]()
(b)
Figure 7. Reflectance and transmittance of the filter.
used in hot climates in buildings and vehicles.