本研究旨在設計具有寬頻且結構短小的積體光路（Photonic Integrated Circuit, PIC）元件，利用絕熱理論設計基於鈮酸鋰薄膜波導（Thin Film Lithium Niobate, TFLN）平台的 800nm 與 488nm 波長之分波多工器（Wavelength Division Multiplexer, WDM）。此元件將在全光調製器中的輸入端將泵浦端（Pump）的 488nm TE 入射光與信號端（Signal）的 800nm TE 入射光結合；在輸出端將 Pump 與 Signal+idler 分開，以此產生參量頻率轉換（Parametric Frequency Conversion）及參量放大（Parametric Amplification）。為滿足使用需求，需要設計一個在 800nm 具有寬頻（750-850nm）及 488nm 具有穩定低損耗的分波器。過去文獻大多使用傳統光學元件進行，故本文設計此元件以期將全光調製器完全積體化，並將整體損耗目標訂為小於 -1.5dB。
此篇研究分別利用模態耦合 (Mode Coupling) 與模態演化 (Mode Evolution) 針對波長 800nm 入射光設計絕熱耦合器,並藉由絕熱捷徑 (Shortcut to adiabacity, STA) 縮短元件尺寸，使波長 488nm 入射光來不及耦合至第二根波導進而達成寬頻分波的功能。其原理為短波長的光源在相同波導中相較於長波長光源之侷限性 (Confinment) 更佳，即光場被侷限在光波導之中，進而導致短波長會需要更長的耦合距離。我們藉由設計針對 800nm 光源的耦合器，並利用絕熱捷徑縮短耦合區長度，使得 800nm 的長波長光源可以順利耦合；而 488nm 的短波長光源則來不及耦合並保留在原始波導，進而達成寬頻分波的效果。設計理論參照量子物理，利用波導模態演化過程與二階量子系統的相似性，帶入絕熱理論進行優化，並找出模態最佳演化路徑，進而縮短元件尺寸並提升頻寬與製程容忍度。
本文提出兩種 STA 優化方式，分別為 Lewis-Riesenfeld不變協定與逆向工程 (Lewis-Riesenfeld Invariant-based Inverse Engineering, LRIIE) ，及快速準絕熱動態 (Fast Quasiadiabatic Dynamics, FAQUAD)。使用 FAQUAD 設計的結果在 800nm 皆有損耗為 -0.17dB 的輸出；488nm 則有損耗小於 -1.15dB，整體結構長度(包含S-bend) 114um。LRIIE 設計分別為 -0.74dB 及 -2.07dB，長度 150um；先進行 LRIIE 再 FAQUAD 的結果則為 -0.23dB 及 -1.20dB，長度為um。考慮頻寬與製程容忍度後最佳的結果為進行 FAQUAD。成功實現具備寬頻的低損耗分光結構。各結構與光場分布如圖2。經模擬驗證後可有效分光，同時除模態展開法驗證外，我們也使用 FDTD 再次複查，其結果也與模態展開法近似。

In this thesis, we propose and demonstrate a broadband, compact photonic integrated circuit (PIC) device utilizing adiabatic theory. A wavelength division multiplexer (WDM) based on the thin-film lithium niobate (TFLN) waveguide platform is designed to efficiently multiplex and demultiplex optical signals at wavelengths of 800 nm and 488 nm. This component serves as the input coupler of an all-optical modulator, combining the 488 nm pump and 800 nm signal beams at the input port. At the output, it separates the pump from the signal and idler, thereby facilitating parametric frequency conversion and amplification. For practical integration, the WDM should exhibit broadband performance across the 800 nm band (750–850 nm) and maintain consistently low insertion loss at 488 nm. The losses target is set as below -1.5 dB.

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