在非即時自散焦材料中非相干回饋系統的調變不穩定現象及使用調變不穩定性產生慢光的研究

Modulation Instability in Noninstantaneous Self-defocusing Media with Incoherent Feedback and Slow Light Achieved by Modulation Instability in Noninstantaneous Self-focusing Media

周自翔(Chih-Shiang Chou)

指導教授 ： 石明豐

國立臺灣大學/理學院/物理研究所/博士(2010年)

https://doi.org/10.6342/NTU.2010.03324

摘要

許多非線性系統中都可見到調變不穩定（Modulation Instability，MI）的現象，此現象由載波中的振幅微小調變開始，隨著波的傳播，調幅因波與物質間的交互作用而得到增長，最後此載波變得不穩定，向某些位置集中。然而當波高度集中時，繞射或色散會變得更顯著，因此調幅並不能無限增長，最終這兩種互相對抗的作用會平衡，造成了MI。

在習慣上，MI的研究著重於非線性的機制，以及何種時間或空間中的形態會出現在MI之中，而鮮少討論非線性的反應時間如何影響MI。在本論文中，我們提出關於反應時間的問題，特別是在非線性光學系統中的現象。不僅如此，我們也研究空腔對於非即時性介質中MI的影響，並且研究在非即時介質中MI對於慢光的應用。第一章介紹了關於MI的詳細背景，並且介紹了數學工具以及隨後會使用到的數值模擬方法。

我們以理論與實驗研究了在非即時性自散焦介質中，MI自發條紋的產生。在這系統中，非線性介質被放置在超過循環光相干長度的空腔中，非線性的延遲反應增長了擁有特定的時間與空間頳率的雜訊。雖然沒有因不同循環的光造成干涉的共振條件，但此空腔依然如有共振般選出某特定頻率。若此頻率的條紋因非線性獲得的增益比空腔損失的多，則此條紋便會自發產生。

我們亦在理論上發現非即時性自聚焦介質中的MI可用來產生慢光。我們使用光束傳播法來模擬慢光，以及使用傅利葉分析分解光脤衝來預測在此介質中光的群速度。這種達成慢光的新方法可用於任何非即時反應的自聚焦介質中，並且提供了簡單的方法來調整光在介質中的群速度。在最後一章裡，我們做出結論以及建議未來可能的研究方向。

關鍵字

非線性光學 ； 調變不穩定性 ； 混沌 ； 自聚焦 ； 自散焦 ； 非相干性回饋 ； 非即時性 ； 慢光

並列摘要

Modulation Instability (MI) is a phenomenon that can occur in many different nonlinear systems. It usually starts from a small modulation of the amplitude of the carrier wave. As the wave propagates, the amplitude modulation grows larger by the interaction between the wave and the medium. As a result, the wave will be unstable and become more concentrated in certain locations. However the amplitude modulation cannot grow infinitely since the wave will diffract or disperse more when it is more concentrated. It is the balance between these two counter actions that define the end result of the MI.

Traditionally, the study of MI is focused on the mechanism of the nonlinearity as well as what patterns, either spatial or temporal, will emerge from the MI. Seldom is it discussed how the response time of the nonlinearity affects the MI. In this dissertation, we address on this issue, especially in a nonlinear optical system. More than that, we also study how MI in noninstantaneous medium is affected in a cavity and how can we use MI in noninstantaneous medium for slow light application. In Chapter 1, a detailed background of MI will be given. We also introduce the mathematical tool as well as the simulation method that is used for the later analysis.

We then study, theoretically and experimentally, the spontaneous pattern formation of modulation instability in a noninstantaneous self-defocusing medium, which is placed in a cavity longer than the coherence length of the circulating light. The delayed response of the nonlinearity can amplify the noise of certain spatial and temporal frequencies. Although it lacks the resonance condition resulted from the interference between different cycles, the cavity can still select one specific frequency. A pattern of this frequency can emerge spontaneously if its gain from the nonlinearity is larger than the total cavity loss.

We also find theoretically that modulation instability in a noninstantaneous medium could be used to achieve slow light. We use beam propagation method to simulate slow light and use Fourier decomposition of the light pulse to predict the reduced group velocity in such medium. This new method of achieving slow light can be used in any self-focusing medium with noninstantaneous nonlinear response. It also provides an easy way to adjust the group velocity of the light in the medium. In the last chapter, we will conclude the results and suggest possible research direction for the future.

並列關鍵字

nonlinear optics ； modulation instability ； chaos ； self-focusing ； self-defocusing ； incoherent feedback ； noninstantaneous ； slow light

參考文獻

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