光波導技術是近眼顯示與空間運算領域的核心基石。然而，單層均勻光柵波導系統在大範圍傳輸時，其出光強度會隨著與光柵交互作用次數的增加而迅速衰減。如何同時有效擴大視場角並優化畫面之照度均勻度，仍是當前AR光學顯示技術面臨的重要物理挑戰。本研究專注於 AR 光波導結構的微觀波動建模與巨觀光學性能之優化，建立了一套由微觀波動光學至巨觀的幾何光學之跨尺度模擬架構。首先，利用FDTD針對亞波長光柵結構進行單元晶格波動建模，並透過次波長模型（Lumerical Sub-Wavelength Model, LSWM）封裝為高維度數據檔案。隨後導入幾何光學追跡軟體Zemax的非序列光學模式（Non-Sequential Component Mode, NSC）中，建構包含入耦合光柵、高折射率玻璃基板（n = 1.8）、出耦合光柵之 AR 眼鏡系統級光學模型。在光柵設計上，入耦合端引入傾斜光柵以破壞空間對稱性，使能量集中於+1階繞射光傳導；出耦合端採六角陣列排列之橢圓柱二維光柵結構。本研究透過倒晶格動量空間（k-space）之二維向量閉環方程，計算出滿足RGB三色光動量匹配之基本週期，包含入射光柵週期 392 nm 以及二維出射光柵X與Y方向週期為 785 nm 與 1359.66 nm，在消除色散的同時實現微幅出瞳擴展。為尋求微觀結構之最佳化參數配置，本研究引入粒子群優化演算法（Particle Swarm Optimization, PSO）進行多變數優化。優化後之傾斜式入耦合光柵+1階耦合效率為紅光 53.76%、綠光 55.24%、藍光 48.64%，二維出耦合光柵出光效率紅光 8.03%、綠光 5.85%、藍光 5.55%，總出光效率為 4.32%、 3.23%以及 2.7%。

This study aims to expand the field of view (FOV) and optimize illuminance uniformity in augmented reality (AR) near-eye displays by overcoming light attenuation in single-layer uniform grating waveguides. A cross-scale simulation framework was developed, integrating microscopic wave optics with macroscopic geometrical optics. The finite-difference time-domain (FDTD) method and Lumerical Sub-Wavelength Model (LSWM) were utilized to model unit cells and extract diffraction matrices, which were subsequently imported into a non-sequential ray-tracing model. The system features a slanted in-coupling grating for directional energy concentration into the +1 transmission order, and a hexagonal 2D elliptical out-coupling grating. Reciprocal lattice momentum space (k-space) equations determined the fundamental periods for RGB momentum matching. Finally, Particle Swarm Optimization (PSO) was applied to optimize microscopic structural parameters. Results indicate the optimized slanted grating achieved +1 order coupling efficiencies of 53.76% (red), 55.24% (green), and 48.64% (blue). The 2D out-coupling grating yielded forward extraction efficiencies of 8.03%, 5.85%, and 5.55%, resulting in total optical efficiencies of 4.32%, 3.23%, and 2.7%, respectively. In conclusion, the proposed cross-scale design and PSO-driven parameter configuration successfully eliminate dispersion, enable pupil expansion, and efficiently regulate RGB light propagation, offering a robust structural solution for advanced AR waveguide performance.

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