光固子在一維光子能隙結構中均勻地摻有兩能階共振原子的傳播

Abstract

在這本論文中,我們的數值研究包含了布拉格光固子的傳播在沒有摻雜物的能隙結構，自感應透明光固子的傳播及autosoliton的傳播在有摻雜物的能隙結構。我們使用Maxwell-Bloch方程式來研究超短脈衝的布拉格光固子不在低光強的理論限制下的傳播行為與其特性。在此同時地，我們使用了NLCME-Bloch方程式來研究自感應透明光固子在有摻雜物的能隙結構的傳播特性。這脈衝傳播意指著自感應透明光固子與布拉格光固子的共存狀態，稱作SIT-gap光固子。雖然這SIT-gap光固子已經被理論預測在能隙結構旁可以存在的，而我們的研究在更展示了SIT-gap光固子在深入能隙結構也可以存在。我們也使用Maxwell-Bloch方程式模擬關於在光波在勻均地摻有共振原子的產生的高階共振現象，這高階共振是因為光與共振原子的交互作用時被布拉格共振所散射，這個現象展示使得Bloch-NLCMEs中的基本假設的正確性被確認。在此同時地，我們展示了autosoliton在能隙結構中的光放大介質。這是一個在數值理論中發現的新類型的光固子，我們稱它為布拉格autosoliton。我們對布拉格autosoliton在增益飽和及非增益包和作用下所表現截然不同的特性也作了研究。

In this dissertation, we numerically study the pulse propagation of Bragg soliton in undoped photonic band gap (PBG) structure, self-induced transparency (SIT) soliton and autosoliton in uniformly doped PBG. The propagation and characteristics of the ultrashort Bragg soliton, which is beyond the low intensity limit, in an undoped PBG is shown by simulating Maxwell-Bloch equations. Meanwhile, the propagation of the SIT soliton in a uniformly doped PBG is investigated by simulating the Bloch equations and the nonlinear coupled-mode equations (Bloch-NLCMEs). The propagation indicates the coexistence of the SIT soliton and Gap soliton, which is called SIT-gap soliton. Although SIT-gap soliton near the PBG edge has been theoretically predicted, we numerically show that such a solitary wave still exist even if its central frequency is located deeply inside the PBG. The phenomena argument of the high-order harmonics, resulting from the light-atom interaction diffracted by Bragg resonance, is shown by directly simulated the Maxwell-Bloch equation. The high-order harmonic associated with the validity of the basic assumption for the Bloch-NLCMEs is verified. Meanwhile, the autosoliton in PBG with amplifier is found as the new solitary wave, which is called Bragg autosoliton. The distinguishing characteristics of the Bragg autosoliton with gain saturation and unsaturation effect are investigated.