本研究設計一種應用於絕緣層覆矽（Silicon-on-Insulator, SOI）平台之寬頻彎曲式 2 × 2 3-dB 絕熱耦合器，並分別採用絕熱地圖（Adiabatic Map）與粒子群最佳化演算法（Particle Swarm Optimization, PSO）進行波導結構最佳化。絕熱地圖結合耦合局部模態理論（Coupled Local-Mode Theory, CLMT）與絕熱理論，藉由搜尋較低絕熱參數之演化路徑，決定彎曲波導的中心軌跡。而 PSO 逆向設計的核心為，基於移動材料邊界之擾動理論，將局部超模態間的耦合分解為各波導側壁位移所造成的貢獻，並固定耦合區長度，以波導局部傾斜角度作為粒子群最佳化演算法（PSO）的主要設計參數，根據元件的寬頻分光比與總傳輸功率進行最佳化。
結果顯示，透過絕熱地圖所設計元件之耦合區長度為 29.1 𝜇m，在 1475 -1578.8 nm 範圍內可維持 50 ± 2% 的分光比，操作頻寬為 103.8 nm；當波導寬度誤差為 ±20 nm 時，分光比仍可維持於約 50 ± 4% ，顯示其具有高製程容忍度。PSO 逆向設計所設計元件的耦合區長度為 30 𝜇m。當權重函數 𝜂1 = 0.3、𝜂2 = 0.7時，在 C、L、S band (1460 - 1625 nm) 內的最大分光比偏差約為 1.3%，以 50 ± 2% 為標準之操作頻寬可達 216 nm。當波導寬度誤差為 +10 nm 時，分光比仍可維持於約50 ± 5%。
研究實現了兼具寬頻、低損耗及製程容忍度之矽光子 3-dB 分光元件，並可作為光學開關、調製器與 Mach–Zehnder 干涉儀等積體光路之基礎元件。

This study presents a broadband bent-waveguide 2×2 3-dB adiabatic coupler designed on a silicon-on-insulator (SOI) platform. Two optimization approaches, namely an adiabatic map and particle swarm optimization (PSO), are employed to determine the geometry of the coupling waveguides. The adiabatic-map approach combines coupled local-mode theory (CLMT) with the adiabatic theorem to construct a two-dimensional distribution of the adiabaticity parameter. A waveguide center trajectory with relatively low nonadiabatic coupling is then selected from the map. In the PSO-based inverse-design approach, CLMT is combined with perturbation theory for shifting material boundaries to decompose the coupling between local supermodes into the contributions induced by the displacement of individual waveguide sidewalls. With the coupling-region length fixed, the local sidewalltilt angles are treated as the principal optimization variables, while the broadband splittingratio and total transmitted power are incorporated into the objective function.
The adiabatic-map-designed device has a coupling-region length of 29.1 μm and maintains a splitting ratio of 50±2% over the wavelength range from 1475 - 1578.8 nm, corresponding to an operating bandwidth of 103.8 nm. Under a waveguide-width deviation of ±20 nm, the splitting ratio remains approximately 50±4%, demonstrating good fabrication tolerance. The PSO-optimized device has a coupling-region length of 30 μm. Within the C, L, and S bands from 1460 to 1625 nm, the maximum splitting-ratio deviation is approximately 1.3%, while the bandwidth satisfying a 50±2% splitting-ratio criterion reaches 216 nm. Moreover, under a waveguide-width deviation of +10 nm, the splitting ratio remains withinapproximately 50±5%.
These results demonstrate a silicon photonic 3-dB power splitter that simultaneously provides broadband operation, low excess loss, and fabrication robustness. The proposed bent-waveguide adiabatic coupler is therefore suitable for use as a fundamental building block in photonic integrated circuits, including optical switches, modulators, and Mach– Zehnder interferometers.

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