在量子光學實驗中，線寬窄、相干時間長、亮度高的糾纏光子光源是相當重要的工具，對於檢驗量子力學基本原理的實驗研究和發展量子通訊技術，以及製作量子電腦都具有重要的意義。本文主要通過理論計算和數值模擬對參量降頻轉換的單晶雙共振糾纏光子光源的模態做行為的分析。具體來說，從單模的緩慢變化波包近似方程出發，得到實驗上所需要的耦合方程，並從本來只有單模態的方程推廣成多模態的形式，並用數值模擬的方法分析了此類雙光子光源產生的光子的模態和實驗參數之間的關係，並把分析結果和實驗結果進行比較。

In the experiment of quantum optics, it is important to have a ultra-bright sources of temporally long, narrowband biphotons. it will be a useful tool in verifying fundamental principle in quantum mechanics, developing quantum communication technology or designing a quantum computer. In this article, I will analyze the behavior of monolithic doubly resonant biphoton source by theoretical computing and numerical simulation. More precisely, from the slow varying envelope equation of single-mode, we can get coupling equation of muti-mode. Numerical simulation can tell us the relation between the experiment parameter and the mode of photons. Finally, we compare the results of simulations and experiments.

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