A computational study of a metamaterial (MTM)-on-glass composite is presented for the purpose of increasing the energy efficiency of buildings in seasonal or cold climates. A full-spectrum analysis yields the ability to predict optical and thermal transmission properties from ultraviolet through far-infrared frequencies. An opportunity to increase efficiency beyond that of commercial low-emissivity glass is identified through a MTM implementation of Ag and dielectric thin-film structures. Three-dimensional finite difference time-domain (FDTD) simulations predict selective nonlinear absorption of near-infrared energy, providing the means to capture a substantial portion of solar energy during cold periods, while retaining high visible transmission and high reflectivity in far-infrared frequencies. The effect of various configuration parameters is quantified, with prediction of the net sustainability advantage. MTM window glass technology can be realized as a modification to commercial low-emissivity windows through the application of nanomanufactured films, creating the opportunity for both new and after-market sustainable construction.

Introduction

The design of materials for radiant characteristics often takes into account the spectral dependence in radiative absorption and emission. Natural gas storage tanks are universally painted a shade of white, meant to minimize absorptivity in the visible spectrum during the day, yet maximize emission in the infrared during the night. Positive and negative photoresists are used in combination with a single wavelength of light to produce lithographic effects, and photovoltaic cells are engineered to maximize absorption near the bandgap energies of the semiconductors used. Radiative material properties are famously sensitive, however, and in some cases, ill-defined, often leading to suboptimal application. Further, the most recent decade of research has revealed additional strong dependencies of radiative properties in the near-field in which bulk properties can be dramatically different based on surface structuring at the micro- and nanoscale [18]. This sensitivity is a double-edged sword, creating a difficult challenge for analytical or computational design of a nanostructured surface, yet providing the opportunity to tailor precise, coherent properties to manage radiative energy in intelligent ways. Several recent communications have demonstrated the ability to manipulate the near-field radiative properties of surfaces to meet demands for specialized applications [912]. Metamaterials (MTMs)—synthetic composite materials engineered to produce unique electromagnetic properties—have been proposed for a variety of applications including sensing, solar thermovoltaics, and lensing or manipulation of electromagnetic signature [1316]. Negative-index metamaterials—which exhibit negative values of refractive index at certain wavelengths—have attracted attention as lensing or cloaking devices demonstrated in the microwave and radar range [17,18], though application in the visible range carries significant challenges [19]. In the solar spectrum, metamaterials are typically constructed with metals such as Ag, Au, and Cu featuring plasmonic excitation peaks in this range, however titanium nitride and aluminum oxide structures have also been utilized for broadband absorption [20,21], and metamaterials consisting of a silica/polymer composite have demonstrated radiative cooling through spectral selection in the 8–13 μm atmospheric window range [22,23]. The present study focuses on Ag-based structures due to their ability for effective absorption in the near-infrared range of interest. Also, because of the current use of thin-film Ag coatings on low-emissivity window glass, there is compatibility with the existing process technologies and aftermarket application.

A large fraction of fossil fuel use is dedicated to heating and cooling structures due to seasonal and geographic variations in solar irradiation. The radiative characteristics of common building materials, therefore, represent a fulcrum through which the energy efficiency of a structure can be leveraged. A design is presented here to introduce intelligent radiative properties in window glass, allowing a structure to absorb or reflect near-infrared energy to adapt to the needs of the interior. The variable emissive properties are predicted to substantially enhance the thermal efficiency of windowed structures. By building on recently presented techniques [24,25], the authors have converged on a design for MTM window glass with the capability of reducing winter heating demand by over 150 Watts per square meter of installed material. This efficiency gain—relative to state-of-the-art low-emissivity windows—is expected to create significant long-term cost-savings and reduction in fossil fuel usage for medium- to large-sized structures.

Simulations reveal the opportunity to access a large portion of the near-infrared spectrum using a nanoscale base layer of Ag (currently used in commercial low-emissivity window glass) with an additional, patterned, Ag layer to create a periodic, metamaterial configuration. MTM window glass is capable of reflecting the near-infrared and far-infrared energy from the sun in its “summer” configuration, while selectively absorbing solar near-infrared energy in the “winter” configuration. By tuning the radiative properties to this specific wavelength band, the glass retains its ability to reflect far-infrared energy (λ > 1500 nm) emitted by heated interior spaces, thereby maximizing the energy efficiency of the window through adaptable design. It is shown that the effect is nontrivial, representing an opportunity for thermal efficiency enhancement in any windowed structure.

Model Development

Commercially available, high-efficiency, low-emissivity window glass was simulated for algorithm verification and baseline comparison to MTM glass. The finite difference time-domain (FDTD) method solves Maxwell's curl equations at the nodes of a discretized spatial grid [26]. A commercial simulator, FDTD Solutions (Lumerical), was used for the investigation, which employs the Yee algorithm to solve for both electric and magnetic field components in time and space [27]. FDTD Solutions is a three-dimensional Maxwell equation solver built to accurately simulate wavelength scale optical and photonic devices, with an efficient parallelization algorithm making it well suited for the massively parallel simulations presented here. Absorbing (perfectly matched layer), periodic, and Bloch-type boundary conditions are used to simulate macroscale surfaces with small, periodic domains with characteristic lengths on the order of 100 nm to 1.0 μm. Grid-independence investigations determined minimum spatial resolution for accuracy, which ranged from 2.5 Angstroms in the wave propagation direction to 1.0 nm in the lateral directions. Simulations presented here were performed on a combination of parallel systems, with the majority of the work utilizing the Ranger cluster at the Texas Advanced Computing Center (TACC), distributed across approximately one thousand processing cores for tractable full-spectrum calculation.

Finite difference time-domain simulations established baseline configurations for both standard and low-emissivity glass. While standard (bare) glass windows allow virtually all optical wavelengths and a portion of near-infrared solar energy to enter the structure, a significant portion of near- and far-infrared energy is absorbed by the window glass, which is opaque at longer wavelengths. Low-emissivity windows typically make use of chemical vapor deposition techniques to apply between 5 and 20 nm of silver in a uniform, thin film. The Ag thin-film in low-emissivity glass allows transmission of the majority of visible radiation, while reflecting much of the unwanted infrared energy during mild or warm periods, as well as reflecting and retaining infrared thermal energy from the interior of structures during cold periods. The absorption/reflection of the thin-film in the visible range is minimal, allowing the windows to appear transparent; however, the Ag layer efficiently reflects near- and far-IR energy, up to > 90% beyond 1.5 μm wavelength. Figure 1 presents the reflectivity spectrum between 400 nm and 2.5 μm of bare glass and commercial low-emissivity glass with a 10-nm-thick Ag thin-film coating. The computational results agree with curves presented by various manufacturers.

Spectral integrations to be presented were compared to the state-of-the-art low-emissivity baseline to determine the net advantage of MTM window glass designs. The opportunity for improvement lies within the near-IR band, which contains nearly 50% of all solar energy, yet virtually none of the energy emitted from the interior of heated structures. The reflection of near-IR energy is, therefore, desirable only during periods of warm environmental temperature, when energy is used to cool the interior of the structure. During periods of cold environmental temperatures, commercial low-ε window glass reflects near-IR energy wastefully to the environment. Window glass with the ability to modify its emissive and reflective properties based on external temperature can make use of this wasted solar energy during colder conditions, thereby boosting energy efficiency by tapping into a fraction of the spectrum containing over 400 W/m2.

Metamaterial window glass has been conceived for this purpose. The reflection of near-IR energy can be modified through the unique, near-field properties of nanopatterned Ag. MTM glass makes use of the surface plasmon polariton mechanism inherent to nano- and micro-sized Ag objects in IR-vis radiation fields. Local field enhancement—also referred to as anomalous absorption—is used to capture energy selectively in the near-IR portion of the solar spectrum during periods of cold temperature. On a warm day with sunlight, the design requires rotation of the MTM window assembly for elimination of the plasmon coupling in the near-infrared, resulting in performance similar to standard low-emissivity glass. Figure 2 presents a “unit cell” of a conceptual MTM glass segment in which the standard low-emissivity glass is represented by the substrate upon which a 10 nm Ag layer is deposited. The contemporary high-efficiency, commercial design is modified by the inclusion of two additional thin-film layers. An intermediate dielectric film with properties similar to SiO2 provides separation in the range of 50–200 nm for a final, periodically patterned Ag layer. The design shown in Fig. 2 utilizes 100 nm × 100 nm Ag squares of thickness 10 nm and 200 nm period, arranged in a “chessboard” pattern. The dimensions of the Ag base layer thickness, dielectric intermediate layer thickness, and square side length were initially selected based on a review of functional dependence of absorption on wavelength for gratings and nanospheres, and refined through iterative simulation.

Results and Analysis

Three-dimensional FDTD simulations were performed for winter and summer configurations. Electric field distributions are shown in Fig. 3 for the discrete wavelength of 700 nm, at the edge of the visible spectrum. It is evident that strong, localized coupling exists in case (a) in which the MTM glass is presented to the environment in the winter configuration (patterned layer facing out). The local electromagnetic field is enhanced by more than a factor of twenty. Case (b) demonstrates the reduced coupling—and hence reduced absorption—when the MTM layer is presented in the summer configuration (patterned layer facing interior of structure). There is very little field enhancement, with only small volumes of the chessboard pattern exhibiting local enhancement.

Full-spectrum predictions of reflectivity, absorptivity, and transmissivity are presented in Fig. 4 for both configurations discussed in Fig. 3. The calculations indicate that the MTM glass in the summer configuration dramatically increases the absorption in the spectral region between 600 and 1000 nm. This additional energy would now largely be convected to the interior of the structure when used in common dual-pane designs, reducing the heating demand of the building in which the windows are installed.

The net energy effect of an MTM glass design must be calculated by integrating the product of the reflectivity and the solar intensity over the wavelength range of interest. The ASTM Reference Spectra (1.5 air mass) direct + circumsolar data are used here. FDTD results of the product of an MTM glass design and the reference spectra are presented in Fig. 5. The design consists of a 20 nm thick Ag base layer on glass, followed by dielectric layer of width 20 nm, followed by a square-patterned Ag layer 5.0 nm thick, with square side dimension 100 nm, and period of 350 nm. Curves for both summer and rotated winter configurations illustrate the energy capturing mechanism of the MTM glass. It should also be noted that buildings located in climates which enjoy—or suffer from—cold weather year-round may simply maintain a static configuration, which maximizes the sustainability benefit of MTM window glass without any physical transition.

Figure 5 presents a prediction of comparable performance by low-e and MTM glass in the summer configuration. With rotation to winter configuration, however, simulations predict a dramatic absorption enhancement in the near-IR band. Numerical integration of the curves yields a total absorption of 74.7 W/m2 for the baseline low-e window, but an additional 94.6 W/m2 of near-IR captured by the MTM glass for the specified design (+126%).

Simulations imply that a tinting effect may occur in some designs due to increased absorption in the optical range, primarily at the red end of the spectrum. Therefore, an esthetic trade exists in which the amount of change in visible transmission counters the amount of change in near-IR reflection. Any metric would be subjective, but a reasonable transmission threshold can be applied, while maximizing near-IR absorption within this constraint. Figure 6 presents the reflected spectral intensity for an MTM design consisting of a 20-nm-thick Ag base layer on glass, followed by dielectric layer of width 100 nm, followed by a square-patterned Ag layer 5.0 nm thick, with square side dimension 200 nm and period of 400 nm. A substantial effect is predicted with rotation from summer to winter configurations; however, the effect is consistent through the visible and near-infrared. The enhanced absorption in the visible range greatly contributes to the thermal efficiency, boosting the energy capture to 214.6 W/m2, but reducing visible transmission to approximately 30%, or roughly equivalent to a set of sunglasses. Combined, Figs. 5 and 6 illustrate the sensitivity of the radiative properties to small changes in MTM design.

This sensitivity requires an understanding of the effect as a function of relevant parameters, including MTM layer size, period, and spacing. Figure 7 presents a set of points predicting the energy capture of an MTM window in its winter configuration, as a function of MTM layer coverage of the Ag base layer. MTM square width and thickness are held constant at 100 nm and 5 nm, respectively. A peak exists at roughly 50% coverage, with the design accessing nearly 120 W/m2 of low-e reflected energy. Likewise, when holding the MTM period constant at 200 nm while varying MTM square width, a similar trend is observed in Fig. 8. Depending on the optical properties desired, however, it may be preferable to shift the design off-peak to allow for increased transmission in the range of λ = 400–700 nm.

Figure 9 presents the results of simulations revealing the strong spectral dependence on the thickness of the dielectric layer separating base and nanopatterned Ag layers. As the patterned layer is moved away from the base Ag layer, the enhanced absorption shifts from the near-IR into the visible range, with the total energy absorbed generally increasing. Figure 9 implies a very specific mechanism for tuning not only total energy absorbed, but the optical quality of the finished product, including tint and coloration. Applications of this mechanism extend beyond improvements in energy efficiency to decorative and functional products.

A final parameter of interest is the response of MTM glass to various incident angles, as the sun sweeps through the sky. High-fidelity simulations predict only mild sensitivity through a cone angle of 90 deg (−45 to 45 deg incident angles), accounting for virtually all expected irradiation during the day. The spectra for a winter configuration of the design presented in Fig. 4 with an incident radiation angle 30 deg off-normal are given in Fig. 10. The results indicate a modest decrease in overall visible transmission relative to normal incidence, primarily in the red portion of the spectrum, coupled with designed absorption in the near-infrared, leading to over 100 W/m2 of harvested energy that currently available products reflect to the atmosphere. High reflectivity beyond 1.5 μm retains the functionality of low-e glass, preventing radiative loss of interior heat through the window, creating the potential for practical application as a building material. Fabrication of prototype MTM glass samples can be accomplished with the available step-and-flash imprint or other lithography methods and roll-to-roll patterning for aftermarket installation. Future work anticipates prototype characterization with a UV-vis-IR spectrometer, visual inspection for induced scattering, and thermal monitoring.

Conclusions

Design options for ultrahigh efficiency metamaterial window glass are presented. Commercial, low-emissivity window designs utilizing Ag thin-films are extended to include a nanopatterned Ag layer and intermediate dielectric assembled into a metamaterial composite. Massively parallel full-spectrum FDTD simulations predict that a significant net sustainability effect is derived from the MTM window glass's reflection of most near-infrared energy in a summer configuration, while capturing a large portion of this near-IR energy in a winter configuration through nonlinear radiative coupling. Baseline simulations are verified against performance of existing low-e glass, with MTM designs predicted to harvest up to 220 W/m2 with high sensitivity to spectral band and resulting transmission. Dependence on design parameters of the chessboard-style nanopattern is presented, with the broadest absorption band present at patterned layer coverage of approximately 50%. Selection of a narrow absorption band can be accomplished by adjusting the characteristic dimension of the square pattern, the periodicity, and distance from base Ag layer. Values of 100 nm, 350 nm, and 20 nm, respectively, are shown to harvest ∼94 W/m2 in the winter configuration, while retaining high visible transmission in both seasonal configurations. Based on the predicted absorption values, installation of MTM window glass should improve the energy efficiency of any windowed structure with heating requirements.

Funding Data

  • National Aeronautics and Space Administration (NASA) (Contract No. NNX12CG39P).

  • U.S. National Science Foundation (Grant No. CBET-1032415).

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