本論文旨在突破元件微縮與非絕熱損耗之間的物理瓶頸，成功將量子控制領域之反絕熱協定（Counterdiabatic Protocol）引入波導元件設計中，並深入探討其與波導軸向幾何彎曲（AxisBending）在物理機制上的等效性。
本研究推導出反絕熱輔助算符與共動座標系下幾何曲率微擾，在消除非對角哈 密頓量元素時的等價關係。在具體元件實現上，本研究成功開發出總長度50𝜇m的 反絕熱耦合器與彎曲耦合器。其中，反絕熱耦合器透過波導間距𝐷(𝑧)與寬度微擾𝛿𝑤(𝑧) 的動態非線性交錯，主動補償非絕熱損耗；彎曲耦合器則透過建構區域絕熱參 數𝐶(𝑧) 地圖，精確擷取使非絕熱躍遷極小化的最佳幾何彎曲軌跡𝑥0(𝑧)。
在嚴格限制元件核心長度為50𝜇m的條件下，兩款新型耦合器皆成功抑制了傳統短距結構常見的劇烈拉比震盪，分別達到99.51%與99.36%的極高目標模態轉換效率。此外，經由全面的頻寬分析與製程容忍度評估發現，兩者在各項分析中皆展現出高度一致的光強衰減與波動特徵，印證了反絕熱驅動與波導幾何彎曲在物理本質上的等價性。

This thesis aims to overcome the physical bottleneck between device miniaturization and non-adiabatic loss in silicon photonic integrated circuits by introducing the counterdiabatic protocol into waveguide design and investigating its physical equivalence with waveguide axis bending.
This research derives the equivalence between the counterdiabatic auxiliary operator and geometric curvature perturbation in eliminating off diagonal Hamiltonian elements. Experimentally, 50𝜇m counterdiabatic and bent couplers were successfully developed: the former compensates for non-adiabatic losses via dynamic waveguide gap 𝐷(𝑧) and width 𝛿𝑤(𝑧) variations, while the latter utilizes an adiabatic parameter 𝐶(𝑧) map to extract the optimal bending trajectory 𝑥0(𝑧).
Full-wave simulations show that both 50𝜇m couplers suppress Rabi oscillations and achieve high mode conversion efficiencies of 99.51% and 99.36%, respectively. Comprehensive evaluations further confirm their consistent bandwidth and fabrication tolerance characteristics, corroborating the physical equivalence between counterdiabatic driving and waveguide bending while demonstrating their strong potential for miniaturized, robust silicon photonic circuits.

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