Freeform Matrix Fourier Optics with Topology Optimization

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.

We combine a forward design approach 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.

It is published in Advanced Optical Materials.

這是首個經拓撲優化設計並實作的自由形貌超穎介面成功實現矩陣傅立葉光學，可將多種偏振態的光繞射至不同的遠場繞射階次。

我們結合正向設計方法與拓撲優化的逆向設計，實現矩陣傅立葉光學，並打造出單層式超穎介面，能將各種偏振態的入射光繞射至遠場中指定的位置，並透過原子層沉積技術製作完成。此設計旨在利用伴隨法與基於梯度下降的拓撲優化，有效提升各偏振態的繞射效率，並在模擬與實驗中皆獲得顯著改善。該自由形貌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概念，並展現高達 94.4% 的數值偏振對比與 98.7% 的實驗偏振對比。此類偏振選擇性繞射元件未來有望應用於高效偏振分析，同時縮小光學元件尺寸並提升系統整合便利性。