隨著擴增實境(Augmented Reality, AR)顯示系統朝向輕薄化與全彩化發展，波導式顯示架構可利用透明基板傳遞影像光，具有縮小光學系統體積及整合至眼鏡型裝置之潛力。然而，紅、綠、藍三個波長通過相同光柵耦合器時，會因繞射條件不同而產生不同的傳播方向與效率分布，可能造成影像偏移、色彩分離及亮度不均等問題。因此，如何利用單一耦合結構同時控制多個可見光波長，為全彩波導顯示系統的重要設計課題。
本研究提出一種用於可見光消色差波導光學之二氧化鈦(TiO2)自由形狀超穎光柵，並採用基於伴隨法之拓樸最佳化方法，在單一週期內調整TiO2與空氣之材料分布。透過不同繞射階次的配置，使紅、綠、藍三個波長由空氣端入射後，皆可耦合至玻璃波導內接近相同的傳播方向。此外，最佳化過程中同時考慮結構邊界內縮、無偏移與邊界外擴等條件，以提升設計對製程尺寸偏差的容忍度，並針對局部細小特徵進行修正，使結構更符合實際製程需求。
完成設計後，本研究利用電子束微影與乾式蝕刻製程，將自由形狀TiO2製作於玻璃基板上，並進行單色光效率與全彩影像量測。實驗結果顯示，紅、綠、藍三色光皆可經由入耦合器導入玻璃波導，並由出耦合器重新導出。將實際樣品之材料折射率與結構厚度帶入模擬後，所得結果與實際量測趨勢較為接近，顯示材料光學參數及製程結構差異會明顯影響元件效率。全彩影像量測亦成功觀察到經波導系統傳輸後的色彩資訊與影像輪廓，驗證拓樸最佳化自由形狀超穎光柵應用於可見光多波長波導耦合及全彩影像傳輸之可行性。

As augmented reality (AR) displays continue to develop toward lighter, thinner, and full-color systems, waveguide architectures offer a promising approach for transmitting image light through a transparent substrate and integrating the optical system into AR glasses. However, red, green, and blue wavelengths experience different diffraction conditions when passing through the same grating coupler. The resulting variations in propagation direction and diffraction efficiency may cause image displacement, color separation, and brightness nonuniformity. Simultaneous control of multiple visible wavelengths using a single coupling structure is therefore a key design issue for full-color waveguide displays.
This study proposes a titanium dioxide (TiO2) freeform metagrating for achromatic visible-light waveguide optics. An adjoint-based topology optimization method is used to determine the distribution of TiO2 and air within one grating period. Different diffraction orders are assigned to the red, green, and blue wavelengths so that all three wavelengths are coupled into the glass waveguide at nearly the same propagation angle. The optimization also considers inward-shifted, unshifted, and outward-shifted structural boundaries to improve tolerance to dimensional variations introduced during fabrication. Small local features are subsequently modified to improve the manufacturability of the optimized structure.
The freeform TiO2 metagratings were fabricated on a glass substrate using electron-beam lithography and dry etching, and were subsequently characterized through monochromatic efficiency and full-color imaging measurements. The experimental results showed that red, green, and blue light could be coupled into the glass waveguide through the in-coupler and extracted through the out-coupler. Simulations based on the measured refractive indices and structural thickness showed wavelength-dependent trends more consistent with the experimental results, indicating that variations in material properties and fabricated dimensions strongly affect device efficiency. Full-color measurements further showed that color information and image contours could be transmitted through the waveguide system.
These results confirm the feasibility of using topology-optimized freeform metagratings for multiwavelength visible-light waveguide coupling and full-color image transmission.

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