本論文系統性研究雙Λ型電磁誘發透明（Electromagnetically Induced Transparency， EIT）系統在多層無鏡式共振腔結構下之增益、反射與輸出動態行為。本研究以 Maxwell–Bloch方程描述原子與光場之耦合動力學，並進一步引入非同調泵浦雷射以形成增益腔體結構。研究顯示，在引入泵浦雷射後，單Λ型EIT系統可展現出增益行為，並出現快光與慢光切換現象。進一步地，雙Λ型EIT系統在兩束對向耦合雷射（Coupling）作用下，可形成等效的「EIT 鏡子」結構，並以此建構完全無需實體鏡面的共振腔。當我們在原子腔體中引入非同調泵浦雷射後，使介質內探測雷射（Probe）在傳播過程中逐步放大，形成類共振腔的增益。本論文深入分析去同調率 γ 對共振腔增益之影響。數值模擬顯示探測雷射成長率隨 γ 增加而上升，呈現反直覺行為。透過對原子極化項建立近似解析模型，其特徵解成功重現數值結果趨勢，驗證 γ 在腔體增益機制中同時扮演抑制與促進的雙重角色。 進一步分析顯示，我們提出的無鏡式共振腔可呈現三種輸出模式：脈衝、穩態以及振盪。振盪行為源自增益區與耗散區之空間交替配置，並受光學密度、泵浦強度與去同調率控制。此結果顯示無需傳統物理鏡面即可實現增益及自振盪行為。本研究建立了一套完整之雙Λ型 EIT 共振腔理論與數值框架，釐清原子極化項在增益系統中的角色，並替未來發展基於全光學的量子光學元件與新型增益裝置提供理論基礎。;This thesis systematically investigates the gain， reflection， and output dynamics of a double-Λ electromagnetically induced transparency (EIT) system in a multilayer mirrorless resonator. The atom–light coupled dynamics are described by the Maxwell–Bloch equations， and an incoherent pumping laser is further introduced to form a gain-assisted cavity structure. The results show that， with incoherent pumping， a single-Λ EIT system exhibits optical gain together with a switching behavior between slow and fast light. In the double-Λ configuration， two counter-propagating coupling fields create an effective “EIT mirror，” enabling a resonator without any physical mirrors. When incoherent pumping is applied， the probe field is gradually amplified during propagation through the atomic medium， leading to cavity-like gain behavior. This work further analyzes the influence of the decoherence rate γ on the cavity gain. Numerical simulations reveal a counterintuitive trend in which the growth rate of the probe field increases with γ. An approximate analytical model based on the atomic polarization term successfully reproduces this behavior， confirming the dual role of γ in both suppressing and enhancing cavity gain. In addition， the proposed mirrorless resonator exhibits three output regimes: pulsed， steady-state， and oscillatory. The oscillatory behavior originates from the spatial alternation of gain and decay regions， and is governed by the optical density， pumping strength， and decoherence rate. These results demonstrate that gain and self-oscillation can be achieved without conventional mirrors. Overall， this study establishes a theoretical and numerical framework for double-Λ EIT mirrorless resonators and provides a foundation for future all-optical quantum devices and novel gain media.
