我們在這本論文中，主要探討封閉躍遷路徑下與外加光場之相位相依雙Λ 電磁波引發透明系統之物理性質。雙Λ 電磁波引發透明系統不同於一般克爾效應(Kerr Effect) 下只與外加光場強度相關之系統結構，雙Λ 電磁波引發透明系統其物理性質還會受到外加光場之相位影響。為了深入理解穩態情況下其中的物理圖像，我們解由光學布拉赫方程式和馬克士威-薛丁格方程式組成的聯立微分方程組，因而得到穩態理論解析解公式。利用得到的穩態理論解析解公式，我們以雙Λ 電磁波引發透明系統為基礎提出達成門檻較低的系統參數達成最佳光頻率轉換效率，也提出低光學密度，低光強下，發展π 級全光學相位調製(π-order all-optical phase modulation)的條件。

In this thesis, we study a double-Λ electromagnetically induced transparency (EIT) system. The property of the double- Λ medium with a closed-loop configuration depends on the relative phase of the applied fields. The phase-dependent mechanism makes the double-Λ medium is different from the conventional Kerr-based nonlinear medium which only depends on the intensities of the applied fields. The steady-state analytical solutions of the phase-dependent system are obtained by solving the Maxwell-Schrödinger equations. Additionally ,we discuss an efficient all-optical phase modulation based the double- Λ EIT scheme.

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