摘要
我們用775nm高斯光束打入單晶週期性極化KTP非線性晶體，經自發輻射的方式生成通訊波段1550nm的光源。此晶體兩邊鍍上對1550nm的高反射鍍膜，使得晶體有如空腔般的特性，讓1550nm光源得以在晶體內共振。此方法除了可以使得輸出光源為單一頻率，也大幅降低了輸出光源的頻寬至3MHz。除此之外，晶體的輸出端也鍍上了對pump波長的高反射膜，使得pump光會依原光路返回而使得轉換效率增加，並且使得晶體內更難有其他頻率模態產生。
在確認古典光—光學參量震盪器—的各種性質後，我們降低pump光強度低過其閥值約3mW，希望使得一定的短時間內只會輸出一對經SPDC產生的雙光子signal與idler。接著用單光子偵測器去討論此雙光子在時域上的二次強度關聯函數，藉此得到雙光子的波函數在時域上寬度長達200ns-300ns。時域較寬的波函數得以在實際應用上附加訊號在上面或是用現有儀器在時間上做操控。
我們並計算波函數在頻域上的頻寬約為2.5MHz，其與古典光測量結果相近。我們測量到並運算出雙光子產生率為3800/(s*mW)，而在考慮所有光纖、濾波片以及偵測器等等損失的效率後，計算出實際雙光子產生率至少為194000/(s*mW)。接著應用雙重反關聯參數的方法分析二次強度關聯函數去討論雜訊的影響。
藉由Hanbury-Brown and Twiss實驗測量出我們的系統在pump為400µW以下可以成為一個好的單光子源。並且嘗試用電光調製器調製pump光訊號，試圖間接調製產生的單光子波函數，進而影響二次強度關聯函數。

Abstract
We use 775nm gaussian beam to pump monolithic periodically poled KTP crystal(PPKTP) to generate 1550nm light source via spontaneous parametric down conversion(SPDC) process. The 1550nm light source is able to oscillate in the crystal because we deposit high-reflection coatings on both sides of the crystal at 1550nm so that our specifically designed crystal performs just like optical cavity; therefore, the bandwidth of output 1550nm light is reduced significantly to 3MHz. In addition, we also deposit high-reflection coating at 775 nm on the end face of the crystal so that the pump will doubly pass the crystal, which will increase the conversion efficiency of SPDC process and suppress the generation of other frequency modes.
After investigating various properties of classical light (optical parametric oscillation, OPO), we reduce pump power to 3mW below threshold. By doing this, only a pair of bi-photon can be generated through SPDC process in a short time. Then, we apply single photon detection module(SPDM) to get second-order intensity correlation function in time domain . As a result, we find that the width of bi-photon wavefunction in time domain is up to 200ns-300ns in our system. In practical application, the photon with broad wavefunction in time domain can be attached information easily or even be manipulated by equipment.
By analyzing function, the bandwidth of wavefunction in frequency domain is about 2.5MHz that is really closed to the result of what we get in OPO. Our detected bi-photon generation rate is 3800/(s*mW). In consideration of all the loss such as fibers, filters and the low detection efficiency of 1550nm SPDM, bi-photon generation rate is calculated to be at least 194000/(s*mW). Then, using two-fold anti-correlation parameter to analyze second-order intensity correlation function to discuss the effect of the noise.
Via Hanbury-Brown and Twiss experiment, it can be assured that our system can serve as a nice single photon source when pump power is under 400µW. After that, we use electro-optical modulator to manipulate our pump to endeavor to tune the wavefunction of single photon indirectly. By this way, we expect it may further affect the second-order intensity correlation function.

第一章 實驗目的與動機 1
第二章 基本原理介紹
2.1 極化現象(Polarization phenomenon) 3
2.2 波動方程式
2.2.1 馬克士威波動方程組(Maxwell Equation) 4
2.2.2 非線性效應(Non-Linear Effect) 6
2.3 相位匹配與準相位匹配
2.3.1 相位匹配(Phase Matching Condition) 9
2.3.2 準相位匹配(Quasi-phase Matching Condition) 12
2.4 耦合波動方程式與二階強度關聯函數
2.4.1 耦合波動方程式 13
2.4.2 二階強度關聯函數 16
(Second-order Intensity Correlation Function)
2.5 反關聯參數(Anti-correlation Parameter)
2.5.1 前言 17
2.5.2 雙重反關聯參數 19
(Two-fold Anticorrelation Parameter)
2.5.3 三重反關聯參數 22
(Three-fold Anticorrelation Parameter)
2.6 光學參量震盪器簡述 25
(Optical Parametric Oscillation,OPO)
第三章 光學元件、儀器與非線性晶體
3.1 本章概要 25
3.2 外腔雷射系統 25
3.3 設計非線性晶體(PPKTP) 27
3.4 單光子偵測器 30
3.5 時間分析器(MSC6) 30
3.6 電光調製器(Electro-Optical Modulator,EOM) 33
第四章 實驗架設及儀器優化步驟和測量方法
4.1 製備1550nm 光源實驗架設圖 35
4.2 外腔雷射系統設定與調整 39
4.3 伽利略透鏡組 40
4.4 光波長計與回饋鎖頻 42
4.5 PPKTP 晶體與光學參量震盪器
4.5.1 PPKTP 晶體對光方法 45
4.5.2 Sellmier’s 方程式和光學參量震盪器的關聯特性 46
4.5.3 聲光調製pump 訊號 49
4.6 時間分析器(MSC6) 50
4.7 Hanbury-Brown and Twiss 實驗 51
4.8 電光調製Pump 光與MSC6 2D-Plot 功能 52
第五章 結果與討論
5.1 古典光頻寬 54
5.2 量子光特性
5.2.1 二階強度關聯函數圖形分析 56
5.2.2 Pump 強度分別和與雙光子產生率以及訊噪比的關係 57
5.2.3 單光子數目對Pump 關係 61
5.3 雙重反關聯參數 62
5.4 三重反關聯參數 HBT 實驗 63
5.5 調製pump 時間上波形對測量的影響
5.5.1 一般常用測量二階強度關聯函數的方法 66
5.5.2 MCS6 的2D-Plot 功能測量二階強度關聯函數的方法 67
第六章 總結與未來發展 71
第七章 參考資料 73

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