Wide-angle spectral filter for energy-saving windows designed using quantum annealing-enhanced active learning

Abstract

Multi-band spectral filters that can transmit visible light but block ultraviolet and infrared light can be used for energy-saving windows to address global warming. However, such filters typically only consider normal incident light. The present disclosure describes PML structures that allows selective solar spectrum transmission in wide angles using a quantum computing-enhanced active learning scheme, which includes machine learning, quantum annealing, and wave-optics simulation in an iterative loop. The optical characteristics of the PML structure disclosed herein may be capable of reducing the temperature rise in an enclosure space when combined with a thermal radiation layer (e.g., reduction of 5.4 – 7.2°C and an annual energy saving of ~97.5 MJ / m2). The structure disclosed herein may be incorporated into new and existing windows (e.g., in buildings or automobiles) to reduce energy consumption (e.g., relating to cooling), and the active learning scheme can be applied to design other materials with complex properties.

Description

135404.ND24-017-040900WIDE-ANGLE SPECTRAL FILTERFOR ENERGY-SAVING WINDOWS DESIGNED USING QUANTUM ANNEALING-ENHANCED ACTIVE LEARNINGCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 614,703 filed on December 26, 2023, entitled “WIDE-ANGLE SPECTRAL FILTER FOR ENERGYSAVING WINDOWS DESIGNED USING QUANTUM ANNEALING-ENHANCED ACTIVE LEARNING”, which is herein incorporated by reference in its entirety.FIELD OF THE DISCLOSURE

[0002] The present description relates generally to energy savings and more particularly to a wide-angle spectral filter.BACKGROUND

[0003] Windows are typically fixed vertically in buildings, thus the angle between direct sunlight and the normal vector of windows varies throughout the daytime. For example, around noon, when ambient temperature is high, the solar incident angle to vertically placed windows is high. Existing spectral filters for thermal management have been designed considering only normally incident sunlight. Such filters have poor spectral selectivity at high incident angles, resulting in reduced visibility, which is suboptimal for practical applications.BRIEF DESCRIPTION OF THE DRAWINGS

[0004] FIG. 1 is an example wide-angle spectral filter for energy-saving windows in accordance with embodiments of the present disclosure.

[0005] FIG. 2 depicts an example user device that may implement the subject methods and systems, in accordance with one or more implementations

[0006] FIG. 3 is a flow chart of an example quantum annealing (QA)-enhanced active learning process in accordance with embodiments of the present disclosure.

[0007] FIG. 4 is a flow chart of an example process for making a wide-angle spectral filter in accordance with embodiments of the present disclosure.

[0008] FIG. 5A is a benchmark calculation for PML with Ni = 6 in accordance with embodiments of the present disclosure.

[0009] FIG. 5B is a graph of minimum FOM associated with only s-polarized light (FOMS) as a function of optimization cycles in accordance with embodiments of the present disclosure.- 1 - ACTIVE 704306223v1135404.ND24-017-040900

[0010] FIG. 6A is a graph of minimum FOMSas a function of optimization cycles with different Ni in accordance with embodiments of the present disclosure.

[0011] FIG. 6B is a set of graphs of transmitted irradiance through the optimally designed photonic structure, TRC, and silver-coated (low-E) glass under s-polarized light with different incident angles in accordance with embodiments of the present disclosure.

[0012] FIG. 6C is a graph comparing FOMSof the optimally designed photonic structure with other glasses that can be used as energy-saving windows in accordance with embodiments of the present disclosure.

[0013] FIG. 7 is a graph of a performance comparison of the designed photonic structure at the incident angle of 70° with the needle optimization and a QA-enhanced active learning in accordance with embodiments of the present disclosure.

[0014] FIGS. 8A-8D are graphs of minimum FOMSas a function of optimization cycles for (A) 6, (B) 8, and (C) 12-layered spectral filters under normal incident light, and (D) is a graph of minimum FOMSas a function of optimization cycles for the 12-layered spectral filter at an incident angle of 30°.

[0015] FIG. 9A is a six-layer photonic structure in accordance with embodiments of the present disclosure.

[0016] FIG. 9B is a graph of the transmission efficiency through the photonic structure of FIG. 9A.

[0017] FIG. 9C is a graph of the transmitted irradiance through the photonic structure of FIG. 9A under s-polarized light with different incident angles.

[0018] FIG. 10A is a 20-layer photonic structure in accordance with embodiments of the present disclosure.

[0019] FIG. 10B is a graph of the transmission efficiency through the photonic structure of FIG. 10A.

[0020] FIG. 11A is an optimally designed photonic structure with a FOMSof 0.8159 in accordance with embodiments of the present disclosure.

[0021] FIGS. 11B-11E are photonic structures with one layer changed from the optimal structure of FIG. 11 A and corresponding FOMS.

[0022] FIG. 12 is a diagrammatic view of an example embodiment of a computing environment in accordance with embodiments of the present disclosure.

[0023] The drawings accompanying and forming part of this specification are included to depict certain aspects of the disclosure. A clearer conception of the disclosure, and of the- 2 - ACTIVE 704306223v1135404.ND24-017-040900components and operation of systems provided with the disclosure, will become more readily apparent by referring to the exemplary, and therefore non-limiting, embodiments illustrated in the drawings, wherein like reference numbers (if they occur in more than one view) designate the same elements. The disclosure may be better understood by reference to one or more of these drawings in combination with the description presented herein.DETAILED DESCRIPTION

[0024] Optical spectral filters that can offer spectral selectivity in desired wavelength regimes may be applied to various fields such as photovoltaics, light-emitting diodes, and sensors. Planar multilayered (PML) photonic structures (also referred to herein as “PML structures” or “photonic structures”), which are stacked optical thin-film layers with distinctive refractive indices, provide a platform for designing spectral filters by allowing selective transmission or reflection of light depending on the wavelength of the light. Accordingly, an optical spectral filter made of PML structures can be designed to effectively reduce optical heating by selectively reflecting light, such as ultraviolet (UV) and near-infrared (NIR) photons, from sunlight while maintaining visible transparency.

[0025] The optical spectral filter can be placed (e.g., coated) on windows (e.g., in buildings or cars) for passive thermal management to reduce energy consumed for cooling (e.g., by air conditioning systems). Additionally, in some embodiments, a polymer (e.g., poly dimethylsiloxane (PDMS)) layer (e.g., a micrometer-thick) can be capped (e.g., coated) on top of the spectral filter surface so the PML structure emits thermal radiation through the atmospheric window (AW) (e.g., 8-13 pm) to realize radiative cooling. Such an integration of radiative cooling with the spectral filter may further increase energy saving for cooling.

[0026] Windows are typically affixed to buildings, and thus the angle between direct sunlight and the normal vector of windows varies throughout the day. For instance, around noon, when the ambient temperature is high, the solar incident angle to vertically placed windows is high. Designing spectral filters for thermal management considering only normally incident sunlight results in worse spectral selectivity at high incident angles and in reduced visibility, which is less practical than ordinary windows. Accordingly, to efficiently manage the temperature of enclosed spaces over the day while maintaining visibility, the design of spectral filters may consider the variation of solar incident angles. Additionally, it may be beneficial to have higher spectral selectivity by selectively reflecting light (e.g., UV / NIR photons) as much as possible when the ambient temperature is at its highest (e.g., around noon time) to reduce solar heating of interior spaces defined in part by the windows.- 3 - ACTIVE 704306223v1135404.ND24-017-040900

[0027] Achieving band-selective optical characteristics (e.g., visible light transmission and UV / NIR light reflection) across a wide-angle range is challenging due to increased optimization complexity and constraints. Optimization schemes, such as genetic algorithms, needle optimization, and adjoint methods, may be employed to design PML structures under such constraints. However, the properties of PML structures are sensitive to the change in structural parameters. Hence, classical computer-based schemes may encounter challenges in finding optimal structures when dealing with non-linear and non-convex optimization problems attributed to complex target properties. Furthermore, classical optimization strategies that rely on gradient-based methods may face difficulties in finding optimal structures due to the risk of getting trapped in local optima in discretized and large design spaces.

[0028] Quantum computing-assisted active learning schemes may be efficient in solving combinatorial optimization problems, especially when designing problems involving discrete variables and large numbers of possible combinations. In these schemes, a supervised machine learning model may formulate a Hamiltonian as an objective function, describing the relationship between structures and the corresponding figures of merit (FOMs). Quantum annealing (QA), based on superconductor qubits, may then employed to find the ground state of the Hamiltonian. The quantum computing-assisted active learning scheme can be adaptive to different optimization problems.

[0029] The present disclosure describes a high-performance wide-angle spectral filter using a QA-enhanced active learning scheme, which may then be used to develop practical and energy-saving windows. The spectral filter may include a PML structure on a substrate. The active learning scheme may find the optimal PML configuration in a large design space, which results in multi-band spectral selectivity in wide incident angles. A thin polydimethylsiloxane (PDMS) layer on a PML surface may be a radiative cooling layer that emits thermal radiation through the AW. The resulting PML structure has improved spectral selectivity in a wider range of incident angles and thus also has improved cooling performance (e.g., temperature reduction of 5.4°C-7.2°C and annual cooling energy saving of -97.5 MJ / m2, compared with glass that does not include the spectral filter). Although the wide-angle spectral filter of the present disclosure is described with respect to windows for reducing cooling energy consumption, it is contemplated that the QA-enhanced active learning scheme may be generalized for the design of other complex materials with complicated properties.

[0030] FIG. 1 is an example wide-angle spectral filter for energy-saving windows 102 in accordance with embodiments of the present disclosure.- 4 - ACTIVE 704306223v1135404.ND24-017-040900

[0031] Spectral filters, such as PML structures 106, may be designed on a silica substrate 104 using one or more of four dielectric materials with distinct refractive indices. The dielectric materials may form the PML structure 106, and varying the configurations of the PML structure 106 may result in different optical properties, including transmission and reflection. The PML structure 106 may include Ni layers, each with a thickness of approximately 100 nm, resulting in a total thickness of approximately IOOX nm. In some embodiments, one or more layers may have a different thickness than the other layers.

[0032] Each layer may be made of one of the four dielectric materials, which may be assigned two-digit binary labels: silicon dioxide (SiCL) = ‘00’, silicon nitride (SisN^ = ‘01’, aluminum oxide (AI2O3) = ‘ 10’ , and titanium dioxide (TiCb) = ‘11’. Therefore, a PML structure 106 can be represented by a binary vector (e.g., 2V / -long) by concatenating binary labels, effectively transforming a quaternary optimization problem into a binary optimization problem. For example, a six-layer PML structure 106 of six layers [SiCh, TiCh, AI2O3, Si3N4, AI2O3, TiCL] can be expressed (e.g., encoded) as a binary vector [00, 11, 10, 01, 10, 11].

[0033] Representing the dielectric materials with binary labels enables problem solving (e.g., optimization) using a quantum annealer (e.g., D-Wave Advantage System 4.1). An ideal spectral filter may exhibit unity (e.g., 100% or near 100%) transmission efficiency in the visible spectrum while maintaining zero (e.g., 0% or near 0%) transmission efficiency in the UV and NIR ranges for the angles of interest (e.g., angles of the sun during the day, 30° to 70°). In addition, achieving high emission efficiency in the long-wavelength infrared (LWIR) range may be achieved for the radiative cooling effect, a feature achievable by applying a thin PDMS layer 108 atop of the spectral filter.

[0034] FIG. 2 depicts an example computing system that may implement the subject methods and systems in accordance with one or more embodiments. Not all of the depicted components may be used in all implementations, however, and one or more implementations may include additional or different components than those shown in FIG. 2. Variations in the arrangement and type of the components may be made without departing from the spirit or scope of the claims as set forth herein. Additional components, different components, or fewer components may be provided.

[0035] The computing system 202 may be an electronic device including one or more of a host processor 204, a memory 210, an input / output ( I / O ) interface 206, and / or a communication interface 208. The host processor 204 may include suitable logic, circuitry, and / or code that enable processing data and / or controlling operations of the computing system 202. In this- 5 - ACTIVE 704306223v1135404.ND24-017-040900regard, the host processor 204 may be enabled to provide control signals to various other components of the computing system 202. The host processor 204 may also control transfers of data between various portions of the computing system 202. The host processor 204 may further implement an operating system or may otherwise execute code to manage operations of the computing system 202.

[0036] The memory 210 may include suitable logic, circuitry, and / or code that enable storage of various types of information such as received data, generated data, code, and / or configuration information. The memory 210 may include volatile memory (e.g., random access memory (RAM)) and / or non-volatile memory (e.g., read-only memory (ROM), flash, and / or magnetic storage). The memory 210 may include a TMM module 212 to perform and / or store the results of a transfer matrix method (e.g., to calculate FOMs). The memory 210 may also include an FM module 214 to train an FM model and / or perform and / or store inference with the FM model (e.g., to generate a predicted FOM, a Hamiltonian, etc.). The memory 210 may also include a training dataset 216 for training the FM model. As disclosed in further detail below with respect to FIG. 4, the training dataset 216 may initially be randomly generated and then populated with additional data from each iteration of the process disclosed with respect to FIG. 4.

[0037] The I / O interface 206 may include one or more input devices and / or output devices. The input devices may include, for example, a mouse and a keyboard. The input devices allow the user to provide data to the computing system 202 for use by the computing system 202 in carrying out the processes disclosed herein. The output devices may include, for example, a display. The output devices allow the computing system 202 to provide data to the user, such as an optimal PML structure.

[0038] The communication interface 208 may include suitable logic, circuitry, and / or code that enables wired or wireless communication, such as between the computing system 202 and the QA 218. The communication interface 208 may include, for example, one or more of a Bluetooth communication interface, an NFC interface, an Ethernet communication interface, a WLAN communication interface, a USB communication interface, a cellular interface, or generally any communication interface. The communication interface 208 may be configured to send a Hamiltonian to the QA 218 to optimize (e.g., determine an optimal binary vector of the Hamiltonian), which may then be received by the communication interface 208. The QA 218 may be a quantum computer, such as a quantum annealer.- 6 - ACTIVE 704306223v1135404.ND24-017-040900

[0039] In one or more implementations, one or more of the host processor 204, the memory 210, the I / O interface 206, the communication interface 208, and / or one or more portions thereof may be implemented in software (e.g., subroutines and code), may be implemented in hardware (e.g., an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), a Programmable Logic Device (PLD), a controller, a state machine, gated logic, discrete hardware components, or any other suitable devices) and / or a combination of both.

[0040] FIG. 3 is a flow chart of an example QA-enhanced active learning process 300 in accordance with embodiments of the present disclosure. For explanatory purposes, the process 300 may be performed by the computing system disclosed below with respect to FIG. 12, and thus the process 300 may be computer-implemented. Additionally, for explanatory purposes, the operations of the process 300 are disclosed herein as occurring sequentially or linearly. However, multiple operations of the process 300 may occur in parallel. The operations of the process 300 need not be performed in the order shown, and one or more operations of the process 300 need not be performed or can be replaced by other operations.

[0041] At operation 302, a computing system may generate an initial set of random PML structures (also referred to as the “initial dataset”). The initial dataset includes a set of randomly generated PML structures (e.g., PML configurations), which may include numerical (e.g., binary) representations of the possible arrangements of the respective layers in each PML structure. For example, a six-layer PML structure may be represented by binary vectors like [00, 11, 10, 01, 10, 11], where each binary pair corresponds to a specific material in the layer. The initial set of random PML structures may be used to create a training dataset for training a machine learning model, such as a factorization machine (FM) model.

[0042] The random PML structures of the initial dataset may be generated in a manner that enables diversity in the dataset, covering a wide range of possible designs without relying on pre-existing knowledge about optimal structures. Accordingly, the initial dataset is not limited to six-layer PML structures but may also or instead include one-, two-, three-, . . ., twentylayer, etc., PML structures or combinations thereof. The QA-enhanced active learning process 300 may be particularly effective for exploring large design spaces. In some embodiments, PML structures with up to 20 layers (Ni < 20) may be designed, encompassing a design space of approximately LlxlO12possible configurations.

[0043] At operation 304, the computing system may evaluate each configuration in the initial dataset using a computational method, such as a physical simulation (e.g., the transfer matrix method (TMM)), to calculate its corresponding FOM. For instance, one configuration- 7 - ACTIVE 704306223v1135404.ND24-017-040900might result in a high FOM value, indicating poor optical performance, while another might yield a low FOM, indicating better performance. These computed FOM values may then be paired with their respective configurations in the initial dataset to form the training data for the FM.

[0044] The design process for spectral filters may target near-ideal performance across a wide range of light incident angles. To guide optimization, FOMs may be defined to measure the deviation of the performance of a candidate PML structure (e.g., a spectral filter with a PDMS layer) from the ideal performance. A lower FOM value may correspond to optical characteristics (e.g., transmission or reflectance efficiency) of the candidate structure approaching those of the ideal design.

[0045] To calculate FOM, optical characteristics (e.g., transmitted irradiance TI (A)) of the designed PML structure under solar illumination S (A) may be evaluated using TMM. For the TMM, it may be assumed that the plane wave (e.g., electromagnetic wave, such as light) travels from the top PDMS layer through the PML layers to the bottom substrate (e.g., UV-fused silica). The FOM may be calculated under s-polarized (FOMS), p-polarized (FOMP), or unpolarized light (FOMulipoiarized), where the latter may be the average of FOMSand FOMP. The process is based on the following equations.TISor p (A) = T’s or p (A) x 5(A) (1)10C P W -TIidealW ) dA\ FOMs or p(0) = -V- x weights(O) (2)C w2 dX / F0Ms or p= Average[FOMs or p(0)] (3)

[0046] In equation 1, S(T) represents the solar spectral irradiance (e.g., air mass 1.5 global), Ts or p(A) represents the transmission efficiency of the PML structure for s- or p-polarized light, and TIs or p(A) represents the transmitted irradiance through the PML structure for s- or p-polarized light.

[0047] In equation 2,(A) represents the transmitted irradiance of the ideal PML structure (e.g., S(A) Tideal(A)). The solar incident angle changes (30°-70°) during the daytime, and so the weighting factor for incident angle 9 may be used to prioritize better performance at higher angles, reflecting conditions when ambient temperatures are typically at their peak. The incident angles (30°-70°) may be assigned weights (e.g., weighting factor) derived from solar - 8 - ACTIVE 704306223v1135404.ND24-017-040900intensity as a function of angle (e.g., with specific values of 0.6077, 0.8434, 1.0443, 1.2285, and 1.3115 for 30°, 40°, 50°, 60°, and 70°, respectively). The weights may place greater emphasis on performance during peak solar intensity periods. The final FOM for optimization may be obtained by averaging the weighted FOMSfor all angles.

[0048] In equation 3, the final FOM for optimization may be obtained by averaging the weighted FOMS. While the weight assignments are based on current solar intensity data, the active learning algorithm used in the optimization approach disclosed herein can adapt to different weighting schemes, maintaining its applicability across varied optimization criteria.

[0049] In some embodiments, to save computational costs of TMM calculations, s-polarized light (FOMS) may be utilized for optimization, although sunlight is unpolarized, because the optimized structure considering unpolarized light is shown to have similar performance as the optimized structure considering only s-polarized light.

[0050] At operation 306, the relationship between the PML structures and their FOMs may be modeled using a machine learning surrogate model, such as an FM model (e.g., xLearn). The surrogate model enables optimization of PML structures via a QA-enhanced active learning scheme.

[0051] The FM model may be trained (e.g., by the computing system) using supervised learning, where a training goal may be to minimize the error between the predicted FOM values (e.g., generated by the FM model) and the actual FOM values (e.g., obtained from simulations or experimentation). The FM model may leverage its ability to model interactions between features, which may be particularly useful in the context of multilayer photonic structures. For example, the optical properties of a PML structure may not be solely determined by individual layer materials but also by the interactions between adjacent layers. The FM model may capture these interdependencies by representing the feature interactions in a low-dimensional latent space, which enables it to generalize well even with limited training data.

[0052] During training, the parameters of the FM model, including the weights for individual features and the latent factors representing feature interactions, may be iteratively adjusted to minimize a loss function, such as the mean squared error (MSE) between the predicted and actual FOM values. For instance, if the FM predicts a FOM of 2.0 for a given configuration, but the actual FOM is 1.8, the parameters are updated to reduce this error in subsequent predictions. Techniques like stochastic gradient descent (SGD) or its variants may be used for this optimization.- 9 - ACTIVE 704306223v1135404.ND24-017-040900

[0053] As training progresses, the FM model may leam to associate specific patterns in the input configurations with corresponding FOM outcomes. For example, the FM model might learn that configurations with alternating high- and low-refractive-index materials tend to have lower FOM values, reflecting better optical performance.

[0054] Once trained, the FM model may predict the FOM for new configurations without requiring the computationally expensive TMM simulation, making it a powerful surrogate model for guiding optimization. Particularly, the trained FM model can describe the relationship between PML structures (x, binary vectors) and corresponding FOMs (y, outputs) with the following equation;where w0, w,, vtf, and k are respectively bias, linear strength, quadratic coefficient, and size of latent space (e.g., 8).

[0055] At operation 308, the computing system, using the FM model, may formulate a Hamiltonian as an objective function. The Hamiltonian may represent the relationship between PML structures and the corresponding FOMs. The Hamiltonian may be in the form of a quadratic unconstrained binary optimization (QUBO) problem (Q). The Hamiltonian can be directly mapped into a QA domain with the following equation:y = XTQXxe{o,i}n

[0056] At operation 310, the computing system may use QA to efficiently evaluate all possible PML structures (e.g., binary vectors) of the given Hamiltonian and identify the ground state (e.g., global minimum), which corresponds to the predicted optimal binary vector (xpo) (representing the predicted optimal PML structure) that has the lowest FOM (FOMPO,QA) (representing the lowest energy state of the QUBO).

[0057] In the early stages of optimization, the predicted optimal PML structure may not be a true optimal structure in a global design space because the FM model trained on a limited number of training data may not be universally accurate. However, the predicted optimal PML structure may generally perform better than a random PML structure.

[0058] In the latter stages of optimization, the predicted optimal PML structure may already exist in the dataset. In which case, the computing system may continue to utilize the optimal PML structure in the rest of this iteration if convergence is going to be reached.- 10 - ACTIVE 704306223v1135404.ND24-017-040900

[0059] In some embodiments, to give the dataset more diversity, the computing system may select a random structure (xrandom) instead of the repeated optimal PML structure.

[0060] At operation 312, the computing system may generate (e.g., calculate) the FOM (FOMPO,TMM) (e.g., an optimal FOM) for the predicted optimal PML structure (in a manner similar to operation 304). Because the QA-predicted FOM (FOMPO,QA) may be inaccurate (e.g., due to limited training data), the computing system may utilize TMM to calculate the FOM (FOMPO,TMM) for the predicted optimal PML structure.

[0061] At operation 314, the computing system may update the training dataset to include the calculated FOM (FOMPO,TMM) and the predicted optimal PML structure (xpo) and then retrain the FM model to incorporate the new information. Iterations of this process (also referred to as “optimization cycles”) may refine the training dataset and improve the accuracy of the FM model in predicting the FOMs, enabling the FM model to progressively identify betterperforming PML structures. An optimal PML structure can be found within tens to several thousands of iterations depending on the design space size (determined by Ni).

[0062] In some embodiments, if the number of data (n) in a training dataset accumulates more than a threshold amount (e.g., 200 data points), then the computing system may randomly select 200+(n-200) / 2 data points to build a new training dataset for improving optimization efficiency. The new training dataset may be split into a training set (0.8) and validation set (0.2).

[0063] In some embodiments, two thresholds may be set to stop optimization to save computational cost if an optimal structure seems to be identified. The first threshold may be that of the last 100 iterations, 90 xrandom may be generated, which means QA selects the repeated structure because convergence has already been reached. The second may be when the number of optimization cycles meets or exceeds a particular number, such as 8000.

[0064] In summary, the QA-enhanced active learning scheme enables the design of high-performance wide-angle spectral filters, which may be used for energy-saving window applications. The spectral filter demonstrates exceptional multi-band spectral selectivity, allowing high transmission of visible light while reflecting UV and NIR light across a wide range of incident angles (e.g., the angle of the sun during the day). These optical characteristics effectively mitigate solar-induced optical heating, a factor in reducing cooling energy demands.

[0065] The optical and radiative cooling properties of the PML structure, which may include a top thermal radiation layer, were experimentally validated in field tests. Notably, the PML structure is estimated to reduce cooling energy consumption by up to 97.5 MJ / m2,- 11 - ACTIVE 704306223v1135404.ND24-017-040900underscoring its energy-saving potential. Its planar design and scalability, combined with robust wide-angle spectral selectivity, make the structure highly suitable for practical deployment in real-world applications, such as windows.

[0066] Beyond this specific design of spectral filter, the QA-enhanced active learning approach has broader implications. Its adaptability and efficiency indicate that it may be widely applicable to the optimization of other complex material systems with intricate performance criteria, offering a powerful tool for advancing material science and engineering.

[0067] FIG. 4 is a flow chart of an example process 400 for making a wide-angle spectral filter in accordance with embodiments of the present disclosure. For explanatory purposes, the process 400 may be performed by the computing system disclosed below with respect to FIG.12, and thus the process 400 may be computer-implemented. Additionally, for explanatory purposes, the operations of the process 400 are disclosed herein as occurring sequentially or linearly. However, multiple operations of the process 400 may occur in parallel. The operations of the process 400 need not be performed in the order shown, and one or more operations of the process 400 need not be performed or can be replaced by other operations.

[0068] At operation 402, a computing system may obtain (e.g., access, receive) a sequence of layers for a PML structure of a wide-angle spectral filter. The sequence of layers may be determined by QA with active learning, as disclosed above with respect to process 300.

[0069] At operation 404, a plurality of layers of a plurality of dielectric materials may be deposited on at least one side of a substrate, such as ultraviolet-fused silica substrate (e.g., SiO2) or glass. The deposition may be according to the layer sequence from operation 402 to form the PML structure.

[0070] Of the dielectric materials, silicon dioxide (SK ) and silicon nitride (SiaNa) may be deposited by plasma-enhanced chemical vapor deposition (PECVD). In this process, a substrate may be placed in a reaction chamber (e.g., with PleasmaTherm 790 Series, Unaxis), and gaseous precursors may be introduced. A plasma may be generated using radiofrequency (RF) or microwave energy, which excites the gas molecules, causing a chemical reaction that deposits the desired material onto the substrate in a thin, uniform layer.

[0071] Of the dielectric materials, aluminum oxide (AI2O3) and titanium dioxide (TiO2) may be deposited using atomic layer deposition (ALD). The process may alternate between introducing a precursor gas and a reactant gas into the chamber (e.g., FlexAL system, Oxford Instruments), with purging steps in between to remove excess material. Each cycle may deposit- 12 - ACTIVE 704306223v1135404.ND24-017-040900a single atomic (e.g., molecular) layer for uniformity. In some embodiments, the deposition can be conducted with e-beam evaporation and / or physical vapor deposition.

[0072] For example, the UV-fused silica substrate may be loaded into a PECVD or ALD chamber, depending on the layer to be applied. Layers of dielectric materials may be deposited sequentially, with each layer carefully monitored to achieve the desired thickness e.g., substantially 100 nanometers (nm) thick). After the multilayers are applied, a final capping layer or additional film (e.g., PDMS for radiative cooling) may be spin-coated on top.

[0073] In some embodiments, the computing system may direct one or more devices (e.g., reaction chambers) to perform operation 404.

[0074] At operation 406, the PML structure may be coated with a radiative cooling layer. The radiative cooling layer may be polydimethylsiloxane (PDMS), which may also act as an anti-reflection layer leading to higher transmission efficiency in the visible wavelength range. The radiative cooling layer may be spin-coated (e.g., 1,500 rpm for 1 min) on the PML surface. The spin-coating may be performed by a spin-coater, which is a machine equipped with a motorized stage that spins the substrate at high speeds causing the PDMS to spread evenly across the surface with centrifugal force (e.g., to approximately 41 micrometers (pm) thick).

[0075] In some embodiments, the radiative cooling layer may be applied by dip-coating. The PML substrate may be dipped into a PDMS solution and withdrawn at a controlled rate. The thickness of the PDMS layer may be determined by the withdrawal speed and solution viscosity.

[0076] In some embodiments, the radiative cooling layer may be applied by spray-coating. A spray gun or automated spray system may be used to deposit PDMS in a fine mist onto the PML structure.

[0077] In some embodiments, the radiative cooling layer may be applied by bar-coating. A blade or bar is used to spread the PDMS solution evenly across the PML substrate.

[0078] In some embodiments, the computing system may direct one or more devices (e.g., reaction chambers) to perform operation 406.

[0079] At operation 408, the PDMS layer may be cured at an elevated temperature (e.g., 60-200°C for 10-60 minutes) in an oven or on a hot plate to solidify the layer.

[0080] Before curing, the PDMS solution may be prepared by mixing a silicone base with a curing agent (e.g., a platinum-catalyzed cross-linker), and then the mixture may be degassed under vacuum to remove trapped air bubbles. After curing, a secondary curing step (e.g., at a higher temperature) may be performed to enhance thermal and / or mechanical stability.- 13 - ACTIVE 704306223v1135404.ND24-017-040900

[0081] In some embodiments, the process 400 or the product of process 400 may be applied to a pane of glass to make a window with a wide-angle spectral filter. The pane of glass may be pre-installed onto a structure, such as a building.

[0082] In some embodiments, the computing system may direct one or more devices (e.g., reaction chambers) to perform operation 408.

[0083] FIG. 5A is a benchmark calculation for PML with Ni = 6 in accordance with embodiments of the present disclosure. The total number of all possible configurations is 4,096. Results shown in FIG. 5A indicate that most PML structures exhibit high FOMunpoiarized values (>2.4), while the optimal structure, represented by the binary vector [10, 11, 00, 10, 11, 10], achieves the lowest FOMunpoiarized of 1.8163.

[0084] FIG. 5B demonstrates that optimizing for unpolarized light (the average of s- and p-polarized components) yields the same optimal structure ([10, 11, 00, 10, 11, 10]) as optimizing solely for s-polarized light. The converged FOM for both cases is 1.1598, suggesting that s-polarized light predominantly determines the spectral filter’s performance. Based on this observation, s-polarization (FOMS) may be utilized as a proxy for unpolarized light (e.g., sunlight) to reduce computational demands.

[0085] The efficiency of the QA -enhanced approach is highlighted by its ability to identify the optimal structure within a few hundred optimization cycles, significantly faster than exhaustive enumeration. The optimization process consistently succeeds regardless of the initial training dataset, although the time to convergence may vary from 0.5 to 4.6 hours.

[0086] FIG. 6A is a graph of minimum FOMSas a function of optimization cycles with different Ni in accordance with embodiments of the present disclosure. Particularly, the optimization results for PML structures with Ni = 6 to Ni = 20 are shown. Generally, as the number of layers increases, the optimal structures achieve lower FOMS, with the Ni = 20 configuration exhibiting the lowest FOMSvalue of 0.8159. This optimal structure demonstrates wide-angle spectral selectivity, and the transmitted irradiance of this optimal structure closely aligns with that of the ideal structure across different incident angles, showing high transmission in the visible range and minimal transmission in the UV and NIR ranges, as shown in graph 602 of FIG. 6B.

[0087] While transparent radiative coolers (TRCs) and metal-coated glasses can be used in energy-saving windows to reflect NIR photons, they are typically designed for normal incident light, which limits their performance at higher angles. For instance, as shown in graph 604 of FIG. 6B, a TRC may perform optimally under normal incidence but exhibits degraded spectral- 14 - ACTIVE 704306223v1135404.ND24-017-040900selectivity at higher angles, resulting in a high FOMSof 2.9133. Similarly, silver-coated glass, a commercially available low-emissivity (low-E) coating material, also demonstrates a high FOMSof 2.7033, as shown in graph 606 of FIG. 6B.

[0088] In contrast, the PML structures developed according to embodiments of the present disclosure outperform their peers by achieving the lowest FOMSfor similar functionalities, as shown in FIG. 6C. This demonstrates their superiority in maintaining spectral selectivity across a wide range of incident angles, making them well-suited for applications like energy-saving windows that demand consistent optical performance under varying light conditions.

[0089] FIG. 7 is a graph of a performance comparison of the designed PML structure at the incident angle of 70° with the needle optimization and with the QA-enhanced active learning in accordance with embodiments of the present disclosure. To further highlight the effectiveness of the QA-enhanced active learning scheme, PML structures were optimized using the needle optimization method, a robust technique for multilayer design. Both approaches were applied to optimize structures at a fixed incident angle of 70° for various layer counts. The needle optimization approach finds a location to add a layer in the PML structure, and then grows the added layer thickness to solve the following equation:Find (n, t): M(n, t) -» minwhere M(n, t) is an objective function (e.g., FOM), refractive index n — {n1(n2, ... , n , layer thickness t = {tq, t2, ... , tj, and i represents zthlayer in the PML.

[0090] As shown in FIG. 7, the QA-enhanced active learning scheme of the present disclosure consistently identified structures with lower FOMScompared to those found using the needle optimization method. The QA-enhanced active learning scheme excels in achieving this goal by efficiently pinpointing the global ground state. By leveraging the quantum annealer, embodiments of the present disclosure rapidly navigate the complex design space to uncover the optimal structure, providing a clear advantage over other optimization approaches like needle optimization.

[0091] FIGS. 8A-8D are graphs of minimum FOMSas a function of optimization cycles for (A) 6-, (B) 8-, and (C) 12-layered spectral filters under normal incident light, and (D) is a graph of minimum FOMSas a function of optimization cycles for the 12-layered spectral filter at an incident angle of 30°.

[0092] To determine the optimal thickness for each layer, spectral filters with 6 (FIG. 8A), 8 (FIG. 8B), and 12 (FIG. 8C) layers were optimized by varying layer thicknesses between 50 and 200 nm. In the analysis shown in FIGS. 8A-8D, the FOMSwere not weighted. Results - 15 - ACTIVE 704306223v1135404.ND24-017-040900indicated that spectral filters achieved their optimal performance, with consistently low FOMS, when each layer was approximately 100 nm thick. Based on these findings, a uniform thickness of approximately 100 nm per layer may be chosen for designing the wide-angle spectral filters disclosed herein. This standardization simplifies the design process while maintaining optimal optical performance.

[0093] FIG. 9A is a six-layer PML structure. For benchmarking, a six-layer PML (Ni = 6) may be selected, a scenario where all possible configurations (4,096 in total) could be exhaustively evaluated using the TMM, completing in approximately 160 hours. In some embodiments, a six-layer PML structure may include [AI2O3, TiC , SiC , AI2O3, TiC , AI2O3] from top layer to bottom layer and the corresponding binary vector may be [10, 11 , 00, 10, 11, 10],

[0094] FIG. 9B is a graph of the transmission efficiency through the PML structure of FIG.9A. The line 902 may represent the transmission efficiency of the ideal PML structure.

[0095] FIG. 9C is a graph of the transmitted irradiance through the PML structure of FIG.9A under s-polarized light with different incident angles. The shaded area 904 may represent the solar irradiance.

[0096] While the optimal six-layer structure demonstrates notable spectral selectivity, its performance can be further enhanced by increasing Ni (e.g., as shown in FIGS. 10A-10B), leveraging the larger design space for improved results. This validates the scalability and robustness of the QA-enhanced active learning scheme for optimizing complex PML structures.

[0097] FIG. 10A is a 20-layer PML structure. To improve the FOMSas compared to the six-layer PML structure, more layers may be added to the PML structure. An example 20-layer PML structure may be optimized as [AI2O3, TiO , AI2O3, AI2O3, TiO2, Si3N4, TiOz, AI2O3, AI2O3, TiO2, S13N4, TiO2, AI2O3, SiO2, AI2O3, TiO2, AI2O3, AI2O3, TiCL, AI2O3] from top to bottom layer, and the corresponding binary vector may be [10, 11, 10, 10, 11, 01, 11, 10, 10, 11, 01, IL 10, 00, 10, 11, 10, 10, 11, 10].

[0098] FIG. 10B is a graph of the transmission efficiency through the PML structure of FIG.10A. The line 1002 may represent the transmission efficiency of the ideal PML structure.

[0099] Plasma-enhanced chemical vapor deposition (PECVD) and atomic layer deposition (ALD) techniques may be used to construct the PML on a UV-fused silica substrate, followed by spin-coating to deposit the PDMS layer. The structure, optimized for wide-angle spectral filtering, may have excellent transparency in the visible spectrum, even at high incident angles.- 16 - ACTIVE 704306223v1135404.ND24-017-040900Furthermore, the PDMS layer enhances LWIR emission efficiency, supporting the radiative cooling effect.

[0100] A graph of the transmitted irradiance through the PML structure of FIG. 10A under s-polarized light with different incident angles is provided as graph 602 of FIG. 6B.

[0101] FIGS. 11A is an optimally designed PML structure with a FOMs of 0.8159 in accordance with embodiments of the present disclosure. The PML structure of FIG. 11A includes 20 layers on top of an S1O2 substrate with a PDMS layer. The corresponding FOMSof this PML structure is 0.8159.

[0102] FIGS. 11B-11E are PML structures with one layer changed from the optimal structure of FIG. HA and corresponding FOMs. These PML structures demonstrate that FOMSis sensitive to layer configurations. The ninth layer of the structure of FIG. 11B results in an increased FOMSof 1.1289. The fifth layer of the structure of FIG. 11C results in an increased FOMs of 0.9094. The fifteenth layer of the structure of FIG. 1 ID results in an increased FOMSof 2.0040. The sixteenth layer of the structure of FIG. 1 IE results in an increased FOMSof 0.8514.

[0103] FIG. 12 is a diagrammatic view of an example computing system 1200 with which aspects of the present disclosure may be implemented. A computing system 1200 may be, and / or may be part of, any electronic device for executing the features and processes disclosed in reference to FIGS. 1-11, including but not limited to a desktop computer, laptop computer, smartphone, tablet, or any other electronic device having the ability to execute instructions, such as those stored within a non-transitory computer-readable medium. Furthermore, while disclosed and illustrated in the context of a single computing system 1200, those of ordinary skill in the art will also appreciate that the various tasks disclosed hereinafter may be practiced in a distributed environment having multiple computing systems 1200 linked via a local or wide-area network in which the executable instructions may be associated with and / or executed by one or more of multiple computing systems 1200. In some embodiments, the computing system 1200 is a quantum computer, such as a quantum annealer.

[0104] In its most basic configuration, the computing system 1200 may include at least one processing unit 1202 and at least one memory 1204, which may be linked via a bus 1206. Depending on the exact configuration and type of computing system environment, memory 1204 may be volatile (such as RAM 1210), non-volatile (such as ROM 1208, flash memory, etc.) or some combination of the two. In some embodiments, the processing unit 1202 is a quantum processing unit (QPU).- 17 - ACTIVE 704306223v1135404.ND24-017-040900

[0105] Computing system 1200 may have additional features and / or functionality. For example, computing system 1200 may also include additional storage (removable and / or nonremovable) including, but not limited to, magnetic or optical disks, tape drives and / or flash drives. Such additional memory devices may be made accessible to the computing system 1200 by means of, for example, a hard disk drive interface 1212, a magnetic disk drive interface 1214, and / or an optical disk drive interface 1216. As will be understood, these devices, which would be linked to the system bus 1206, respectively, allow for reading from and writing to a hard drive 1218, reading from or writing to a removable magnetic disk 1220, and / or for reading from or writing to a removable optical disk 1222, such as a CD / DVD ROM or other optical media. The drive interfaces and their associated computer-readable media allow for the nonvolatile storage of computer-readable instructions, data structures, program modules and other data for the computing system 1200. Those of ordinary skill in the art will further appreciate that other types of computer-readable media that can store data may be used for this same purpose. Examples of such media devices include, but are not limited to, magnetic cassettes, flash memory cards, digital videodisks, Bernoulli cartridges, random access memories, nanodrives, memory sticks, other read / write and / or read-only memories and / or any other method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. Any such computer storage media may be part of computing system 1200.

[0106] A number of program modules may be stored in one or more of the memory / media devices. For example, a basic input / output system (BIOS 1224), containing the basic routines that help to transfer information between elements within the computing system 1200, such as during start-up, may be stored in ROM 1208. Similarly, RAM 1210, hard drive 1218, and / or peripheral memory devices may be used to store computer-executable instructions comprising an operating system 1226, one or more applications programs 1228, other program modules 1230, and / or program data 1232. Still further, computer-executable instructions may be downloaded to the computing system 1200 as needed, for example, via a network connection. The applications programs 1228 may include, for example, machine-readable instructions for performing quantum annealing with active learning (disclosed above with respect to process 300) and machine-readable instructions for making a wide-angle spectral filter (disclosed above with respect to process 400).

[0107] An end-user may enter commands and information into the computing system 1200 through input devices such as a keyboard 1234 and / or a pointing device 1236. While not- 18 - ACTIVE 704306223v1135404.ND24-017-040900illustrated, other input devices may include a microphone, a joystick, a game pad, a scanner, etc. These and other input devices would typically be connected to the processing unit 1202 by means of a peripheral interface 1238 which, in turn, would be coupled to bus 1206. Input devices may be directly or indirectly connected to processing unit 1202 via interfaces such as, for example, a parallel port, game port, firewire, or a universal serial bus (USB). To view information from the computing system 1200, a monitor 1240 or other type of display device may also be connected to bus 1206 via an interface, such as via video adapter 1242. In addition to the monitor 1240, the computing system 1200 may also include other peripheral output devices, not shown, such as speakers and printers.

[0108] The computing system 1200 may also utilize logical connections to one or more computing system environments. Communications between the computing system 1200 and the remote computing system environment may be exchanged via a further processing device, such as a network router 1248, that is responsible for network routing. Communications with the network router 1248 may be performed via a network interface component 1244. Thus, within such a networked environment, e.g., the Internet, wide area network (WAN), local area network (LAN), or other like type of wired or wireless network, it will be appreciated that program modules depicted relative to the computing system 1200, or portions thereof, may be stored in the memory storage device(s) of the computing system 1200.

[0109] The computing system 1200 may also include localization hardware 1246 for determining a location of the computing system 1200. In embodiments, the localization hardware 1246 may include, for example only, a GPS antenna, an RFID chip or reader, a WiFi antenna, or other computing hardware that may be used to capture or transmit signals that may be used to determine the location of the computing system 1200.

[0110] While this disclosure has described certain embodiments, it is understood that the claims are not intended to be limited to these embodiments except as explicitly recited in the claims. On the contrary, the instant disclosure is intended to cover alternatives, modifications and equivalents, which may be included within the spirit and scope of the disclosure. Furthermore, in the detailed description of the present disclosure, numerous specific details are set forth in order to provide a thorough understanding of the disclosed embodiments. However, the subject technology is not limited to the specific details set forth herein and can be practiced using one or more other embodiments. In other instances, well known methods, procedures, components, and circuits have not been described in detail as not to unnecessarily obscure various aspects of the present disclosure. Additionally, in one or more embodiments, structures- 19 - ACTIVE 704306223v1135404.ND24-017-040900and components are shown in block diagram form to avoid obscuring the concepts of the subject technology.

[0111] Some portions of the detailed descriptions of this disclosure have been presented in terms of procedures, logic blocks, processing, and other symbolic representations of operations on data bits within a computer or digital system memory. These descriptions and representations are the means used by those or ordinary skill in the data processing arts to most effectively convey the substance of their work to others of ordinary skill in the art. A procedure, logic block, process, etc., is herein, and generally, conceived to be a self-consistent sequence of steps or instructions leading to a desired result. The steps are those requiring physical manipulations of physical quantities. Usually, though not necessarily, these physical manipulations take the form of electrical or magnetic data capable of being stored, transferred, combined, compared, and otherwise manipulated in a computer system or similar electronic computing device. For reasons of convenience, and with reference to common usage, such data is referred to as bits, values, elements, symbols, characters, terms, numbers, or the like, with reference to various presently disclosed embodiments. It is understood, however, that these terms are to be interpreted as referencing physical manipulations and quantities and are merely convenient labels that should be interpreted further in view of terms commonly used in the art.

[0112] Unless specifically stated otherwise, as apparent from the discussion herein, it is understood that throughout discussions of the present embodiment, discussions utilizing terms such as “determining,” “outputting,” “transmitting,” “recording,” “locating,” “storing,” “displaying,” “receiving,” “recognizing,” “utilizing,” “generating,” “providing,” “accessing,” “checking,” “notifying,” “delivering,” or the like, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data. The data is represented as physical (electronic) quantities within the computer system’s registers and memories and is transformed into other data similarly represented as physical quantities within the computer system memories or registers, or other such information storage, transmission, or display devices as described herein or otherwise understood to one of ordinary skill in the art.

[0113] It is understood that any specific order or hierarchy of blocks in the processes disclosed is an illustration of example approaches. Based upon design preferences, it is understood that the specific order or hierarchy of blocks in the processes may be rearranged, or that all illustrated blocks be performed. Any of the blocks may be performed simultaneously. In one or more implementations, multitasking and parallel processing may be advantageous.- 20 - ACTIVE 704306223v1135404.ND24-017-040900Moreover, the separation of various system components in the implementations disclosed above should not be understood as requiring such separation in all implementations, and it should be understood that the disclosed program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0114] As used herein, the phrase “at least one of” preceding a series of items, with the term “and” or “or” to separate any of the items, modifies the list as a whole, rather than each member of the list (i.e., each item). The phrase “at least one of’ does not require selection of at least one of each item listed; rather, the phrase allows a meaning that includes at least one of any one of the items, and / or at least one of any combination of the items, and / or at least one of each of the items. By way of example, the phrases “at least one of A, B, and C” or “at least one of A, B, or C” each refers to only A, only B, or only C; any combination of A, B, and C; and / or at least one of any of A, B, and C.

[0115] The predicate words “configured to,” “operable to,” and “programmed to” do not imply any particular tangible or intangible modification of a subject, but, rather, are intended to be used interchangeably. In one or more implementations, a processor configured to monitor and control an operation or component may also mean the processor being programmed to monitor and control the operation or the processor being operable to monitor and control the operation. Likewise, a processor configured to execute code can be construed as a processor programmed to execute code or operable to execute code.

[0116] Phrases such as an aspect, the aspect, another aspect, some aspects, one or more aspects, an implementation, the implementation, another implementation, one or more implementations, one or more implementations, an embodiment, the embodiment, another embodiment, one or more implementations, one or more implementations, a configuration, the configuration, another configuration, some configurations, one or more configurations, the subject technology, the disclosure, the present disclosure, other variations thereof and alike are for convenience and do not imply that a disclosure relating to such phrase(s) is essential to the subject technology or that such disclosure applies to all configurations of the subject technology. A disclosure relating to such phrase(s) may apply to all configurations, or one or more configurations. A disclosure relating to such phrase(s) may provide one or more examples. A phrase such as an aspect or some aspects may refer to one or more aspects and vice versa, and this applies similarly to other foregoing phrases.

[0117] The word “exemplary” is used herein to mean “serving as an example, instance, or illustration.” Any implementation disclosed herein as “exemplary” or as an “example” is not- 21 - ACTIVE 704306223v1135404.ND24-017-040900necessarily to be construed as preferred or advantageous over other implementations. Furthermore, to the extent that the term “include,” “have,” or the like is used in the description or the claims, such term is intended to be inclusive in a manner similar to the term “comprise” as “comprise” is interpreted when employed as a transitional word in a claim.

[0118] The previous description is provided to enable any person of ordinary skill in the art to practice the various aspects disclosed herein. Various modifications to these aspects will be readily apparent to those or ordinary skill in the art, and the generic principles defined herein may be applied to other aspects. Thus, the claims are not intended to be limited to the aspects shown herein but are to be accorded the full scope consistent with the language claims, wherein reference to an element in the singular is not intended to mean “one and only one” unless specifically so stated, but rather “one or more.” Unless specifically stated otherwise, the term “some” refers to one or more. Headings and subheadings, if any, are used for convenience only and do not limit the subject disclosure.- 22 - ACTIVE 704306223v1

Claims

135404.ND24-017-040900CLAIMSWhat is claimed is:

1. A wide-angle spectral filter comprising:a silica substrate including a first side and a second side, wherein the second side is configured to be applied to a window;a planar multilayered (PML) structure including alternating layers of dielectric materials in a sequence determined by quantum annealing with active learning, wherein the PML structure is placed on the first side of the silica substrate; anda radiative cooling layer stacked on the PML structure.

2. The wide-angle spectral filter of claim 1, wherein the silica substrate is an ultraviolet-fused silica substrate.

3. The wide-angle spectral filter of claim 1, wherein each layer of the PML structure is substantially 100 nanometers thick.

4. The wide-angle spectral filter of claim 1, wherein the layers of the PML structure are each of a different thickness.

5. The wide-angle spectral filter of claim 1, wherein the dielectric materials include any one or more of silicon dioxide (SiCL), silicon nitride (SisN^, aluminum oxide (ALCh), and titanium dioxide (TiCh).

6. The wide-angle spectral filter of claim 1, wherein the radiative cooling layer is polydimethylsiloxane.

7. The wide-angle spectral filter of claim 1, wherein the radiative cooling layer is substantially 41 micrometers thick.

8. The wide-angle spectral filter of claim 1, wherein the quantum annealing with active learning comprises:- 23 - ACTIVE 704306223v1135404.ND24-017-040900generating an initial set of random PML structures, each random PML structure including a respective plurality of dielectric materials encoded as binary vectors;calculating, for the initial set of random PML structures, a set of figures of merit (FOMs) based on a transfer matrix method;training, based on the initial set of random PML structures labeled with the set of FOMs, a factorization machine (FM) model to generate a predicted FOM;generating a Hamiltonian with the trained FM model; anddetermining, with a quantum annealer, an optimal binary vector of the Hamiltonian, wherein the optimal binary vector has a lowest FOM of the Hamiltonian, and the optimal binary vector represents an optimal PML structure including a plurality of dielectric materials.

9. The wide-angle spectral filter of claim 8, further comprising:calculating, for the optimal PML structure, an optimal FOM based on the transfer matrix method; andre-training the FM model based on the optimal PML structure and the optimal FOM.

10. A method comprising:determining, by quantum annealing with active learning, a layer sequence for a planar multilayered (PML) structure of a wide-angle spectral filter;depositing a plurality of layers of a plurality of dielectric materials according to the layer sequence to form the PML structure on a first side of a silica substrate;coating the PML structure with a radiative cooling layer; andcuring the radiative cooling layer to form the wide-angle spectral filter.

11. The method of claim 10, wherein:the silica substrate is an ultraviolet-fused silica substrate;the plurality of dielectric materials include any one or more of silicon dioxide (SiCL) , silicon nitride (SisN^, aluminum oxide (AI2O3), and titanium dioxide ( Ti O2); andthe radiative cooling layer is polydimethylsiloxane.

12. The method of claim 10, wherein determining the layer sequence for the PML structure comprises:- 24 - ACTIVE 704306223v1135404.ND24-017-040900generating an initial set of random PML structures, each random PML structure including a respective plurality of dielectric materials encoded as binary vectors;calculating, for the initial set of random PML structures, a set of figures of merit (FOMs) based on a transfer matrix method;training, based on the initial set of random PML structures labeled with the set of FOMs, a factorization machine (FM) model to generate a predicted FOM;generating a Hamiltonian with the trained FM model; anddetermining, with a quantum annealer, an optimal binary vector of the Hamiltonian, wherein the optimal binary vector has a lowest FOM of the Hamiltonian, and the optimal binary vector represents an optimal PML structure including a plurality of dielectric materials.

13. The method of claim 12, wherein determining the layer sequence for the PML structure further comprises:calculating, for the optimal PML structure, an optimal FOM based on the transfer matrix method; andre-training the FM model based on the optimal PML structure and the optimal FOM.

14. The method of claim 10, wherein depositing the plurality of layers of the plurality of dielectric materials comprises plasma-enhanced chemical vapor deposition for silicon dioxide (SiO2) and silicon nitride (S i i N4 J layers.

15. The method of claim 10, wherein depositing the plurality of layers of the plurality of dielectric materials comprises atomic layer deposition for aluminum oxide (AI2O3) and titanium dioxide (TiCL).

16. The method of claim 10, wherein coating the PML structure comprises spin coating the radiative cooling layer onto the plurality of layers.

17. The method of claim 10, further comprising applying the wide-angle spectral filter onto a window.

18. The method of claim 17, wherein the window is pre-installed onto a structure.- 25 - ACTIVE 704306223v1135404.ND24-017-04090019. A window comprising:a pane of glass; anda wide-angle spectral filter applied to the pane of glass, wherein the wide-angle spectral filter comprises:a silica substrate including a first side and a second side, wherein the second side is configured to be applied to the window;a planar multilayered (PML) structure including alternating layers of dielectric materials in a sequence determined by quantum annealing with active learning, wherein the PML structure is placed on the first side of the silica substrate; and a radiative cooling layer stacked on the PML structure.

20. The window of claim 19, wherein the quantum annealing with active learning comprises:generating an initial set of random PML structures, each random PML structure including a respective plurality of dielectric materials encoded as binary vectors;calculating, for the initial set of random PML structures, a set of figures of merit (FOMs) based on a transfer matrix method;training, based on the initial set of random PML structures labeled with the set of FOMs, a factorization machine (FM) model to generate a predicted FOM;generating a Hamiltonian with the trained FM model; anddetermining, with a quantum annealer, an optimal binary vector of the Hamiltonian, wherein the optimal binary vector has a lowest FOM of the Hamiltonian, and the optimal binary vector represents an optimal PML structure including a plurality of dielectric materials.- 26 - ACTIVE 704306223v1

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