Optical solar reflectors (OSRs) are widely used as radiative cooling coatings in spacecraft thermal control systems due to their low solar absorptivity and high infrared (IR) emissivity. With the continual increase in spacecraft power density, the demand for improved thermal dissipation capabilities in OSRs has grown. However, traditional OSRs exhibit intrinsically low emissivity in parts of the mid-to-far infrared range, primarily due to abrupt changes in the optical constants of surface materials such as quartz glass around 8.9 and 20.8 μm. This significantly limits their radiative cooling performance. To address this issue, we propose a novel surface microstructure design aimed at enhancing IR emissivity and improving thermal dissipation efficiency. Previous research on radiative property modulation through microstructured surfaces has mainly focused on optimizing dimensional parameters within predefined geometries. Such approaches are constrained by fixed geometric morphologies, thus limiting the ability to achieve true structural optimization. To overcome these limitations, we employ the material-field series-expansion (MFSE) topology optimization method, which enables simultaneous optimization of both geometric morphology and dimensional parameters. This approach allows the discovery of globally optimal structures beyond predefined shapes. In addition, the MFSE method substantially reduces the number of design variables while maintaining high optimization precision, thus lowering computational costs.

The effectiveness of topology optimization based on the pseudo-density method has been widely demonstrated. In this paper, it is applied to optimize OSR surface microstructures, aiming to maximize average emissivity over the 5?30 μm range to enhance thermal dissipation. A quartz glass OSR coated with aluminum is selected as an example. A surface layer of specified thickness is selected as the design domain, which is discretized into finite elements. The geometric center of each element serves as an observation point for constructing the material field. To avoid the formation of unmanufacturable suspended structures due to simultaneous optimization along both the x and y directions, different coherence lengths are assigned to each axis, restricting optimization to the x direction for structural feasibility. The material field is then expanded using eigenvalue decomposition and truncated based on a predefined threshold to achieve dimensionality reduction. The reduced-order material field model is integrated with material properties using an interpolation function to represent the OSR surface microstructure. Spectral emissivity is computed using the finite element method (FEM), and the sensitivity of the objective function with respect to the MFSE coefficients is evaluated. This sensitivity is fed into the method of moving asymptotes (MMA) for iterative optimization until convergence is reached, completing the topology optimization process.

MFSE-based topology optimization yields a surface grating microstructure for the OSR (Fig. 6). Unlike traditional methods that optimize size with a single periodic geometry, the proposed method generates multiple protrusions of varying widths, achieving simultaneous optimization of geometry and size. Under p-polarized incidence, the previously low emissivity in the infrared range is almost entirely eliminated. Improvements are also observed under s-polarized incidence (Fig. 7). To evaluate the overall thermal control performance, We calculate the Planck-averaged solar absorptivity, average infrared emissivity, and the solar absorption-emission ratio before and after optimization are calculated. The results indicate a significant increase in average emissivity across the 5?30 μm range, with minimal change in solar absorptivity in the 0.3?2.5 μm range (Table 1). Electric field distribution analysis of the optimized microstructure (Fig. 8) shows that surface phonon polariton (SPhP) modes are excited, resulting in multiple regions of high electric field intensity near the microstructure boundaries. These strong field areas enhance the power absorption density of the OSR (Fig. 9), thereby effectively improving its absorption characteristics in the infrared range.

To address the intrinsic low emissivity at 8.9 and 20.8 μm that limits the thermal dissipation performance of traditional OSRs, we employ the MFSE topology optimization method to design a novel surface microstructure for quartz glass aluminum-plated OSRs. The optimized structure significantly enhances infrared emissivity and improves thermal dissipation efficiency. Results demonstrate that the method surpasses conventional geometric constraints by enabling simultaneous optimization of shape and size, while greatly reducing the number of design variables and enhancing optimization efficiency. After optimization, the minimum emissivity under p-polarized incidence at 8.9 and 20.8 μm increases from 0.28 and 0.43 to 0.91 and 0.89, respectively. Under s-polarized incidence at 20.8 μm, emissivity rises from 0.43 to 0.81. Overall, the average emissivity in the 5?30 μm range increases from 0.839 to 0.941, while solar absorptivity in the 0.3?2.5 μm range remains unchanged. The solar absorption-emission ratio drops from 0.00739 to 0.00244, a 67% reduction, and thermal dissipation efficiency improves by 12.2%. These improvements are attributed to the excitation of SPhP modes and enhanced local electric fields. The proposed method offers a novel approach for optimizing thermal control coatings in spacecraft, with significant implications for performance improvement and lightweight design.