Freeform Matrix Fourier Optics―Inside Back Cover of Advanced Optical Materials

Our research has been spotlighted on the inside back cover of Advanced Optical Materials, Volume 13, Issue 24, dated August 25, 2025.

About the Cover: The first topology-optimized freeform metasurface is designed and fabricated to realize matrix Fourier optics, enabling diffraction of multiple polarization states into distinct far-field orders. By combining forward design with gradient-based inverse optimization, high polarization contrast of up to 98.7% is achieved. This work paves the way for compact, polarization-selective optical components.

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關於封面：我們設計並製作了首個透過拓樸優化的自由形狀超穎介面，用以實現矩陣傅立葉光學，能夠將多種偏振態繞射至不同的遠場繞射階次。透過將前向設計與基於梯度的反向優化相結合，實驗上達成高達 98.7% 的偏振對比度。本研究為實現微小化、偏振選擇性的光學元件奠定了基礎。

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Abstract: In this research, a forward design approach is combined with inverse design topology optimization to realize matrix Fourier optics, creating a single-layered metasurface that diffracts incident light of various polarizations to specific positions in the far field, fabricated via atomic layer deposition. It is aimed to optimize diffraction efficiency for each polarization using the adjoint method and gradient descent-based topology optimization, achieving significant improvements in simulations and experiments. The freeform metasurface successfully processed six mixed polarizations, aligning with the matrix Fourier optics concept, demonstrating a polarization contrast of up to 94.4% in numerical and 98.7% in experimental results. Future applications of such polarization-selective gratings can enhance polarization analysis while reducing component size and improving convenience.

摘要：本研究結合正向設計與反向設計中的拓樸優化方法，實現矩陣傅立葉光學，打造出單層超穎介面元件，能將不同偏振態的入射光繞射至遠場特定位置。該元件以原子層沉積技術製作，並透過伴隨場法與基於梯度下降的拓樸優化來提升各偏振態的繞射效率，在模擬與實驗中皆展現顯著改善。此自由形狀超穎介面成功處理六種混合偏振態，符合矩陣傅立葉光學的設計理念，並達成高達 94.4%（模擬）與 98.7%（實驗）的偏振對比度。未來此類具偏振選擇性的光柵結構，將有助於提升偏振分析的效能，同時降低光學元件體積、提升整合便利性。