應用電光探測技術於向量電場之量測

Abstract

在本論文中，首先對電光探測（Electro-Optic Probing）技術的基本原理及各種系統架構作一完整的介紹。利用此技術，我們完成一個電光探測的及時量測系統，並成功展示其量測1GHz訊號的能力；接著，我們提出將電光探測技術應用於二維及三維向量電場量測的理論及方法。在二維向量電場量測方面，我們提出以鉭酸鋰晶體（LiTaO3）作成的電光探測頭，結合一種新的電光調變技術及傳統的調變技術來解析出二維向量電場兩個分量，此一新的電光調變技術是利用電光晶體因外加電場產生的主軸旋轉效應，不同於傳統的折射率橢圓球因外加電場產生的伸縮形變效應。我們對此一新的電光調變效應有詳細的理論推導並建立一實驗系統驗證其可行性，實驗結果與商用電場模擬軟體 Ansoft Maxwell 3-D Field Simulator 的計算結果相當吻合。此一實驗量測系統對平面二維電場的靈敏度為76 mV/cm/(Hz)^1/2及0.8 V/cm/(Hz)^1/2，向量電場方向角度誤差的均方根值為1.5度。 為量測三維向量電場，我們進一步提出一種利用三束雷射光在電光探測頭中三種不同的傳遞路徑的方法，因為每束光的延遲量（Retardation）會受到三個電場分量不同的影響，因此只要校正每束光的延遲量會受到三個電場分量影響係數，結合三束光延遲量即可解析出三維向量電場的每個分量。我們分析磷酸二氫鉀[KH2PO4 (KDP)]及氧化矽鉍[Bi12SiO20 (BSO)]兩種晶體對此一方法的適合性，結果發現氧化矽鉍較磷酸二氫鉀適合此一方法。因此，我們建立一個用氧化矽鉍晶體為電光探測頭的實驗系統，並利用三組模擬結果做為校正的數據，經校正後量測的數據與其他模擬結果相當吻合。此一實驗量測系統三個電場分量的靈敏度皆為0.6 V/cm/(Hz)^1/2。

In the dissertation, the fundamental and various configurations for electro-optic probing are carefully introduced first. Using this technique, the waveform measurements up to 1 GHz signals were successfully demonstrated. Then, an electro-optic probing tip made of a LiTaO3 crystal to do a tangentially two-dimensional electric-field vector measurement is presented. A new electro-optic modulation technique and a conventional one are combined to resolve the two electric-field components. Instead of conventional compressed/stretched deformation of the index ellipsoid, the new modulation effect on the optical probing beam is caused by the principal axis rotation of the index ellipsoid, which is also proportional to the applied electric-field strength. Since there is no free charge involved in the axis rotation, the axis-rotation modulation can be as fast as the conventional type. The principles are derived and an experimental system is constructed to perform the measurement of two-dimensional electric-field vectors on a test pattern. The results are in good agreement with those obtained by the commercial "Ansoft Maxwell 3-D Field Simulator'' software for electromagnetic simulation. The sensitivities for two tangential electric-field component are 76 mV/cm/(Hz)1/2 and 0.8 V/cm/(Hz)1/2. The root-mean-square error of electric-field direction measurement is 1.5°. In order to perform three-dimensional electric-field vector measurement, another new technique of using three laser beams with different propagation paths in an electro-optic crystal was proposed. The retardation of each beam is differently affected by each one of three electric-field components. Therefore, once individual effect of three electric-field components on each beam can be characterized, for given retardation of three beams, all components of three-dimensional electric-field vector can be resolved. Two kinds of similar crystals with the simple electro-optic tensor form, KH2PO4 (KDP) and Bi12SiO20 (BSO), were analyzed to find which one is more suitable for this technique. The result showed that BSO was the better one. An experimental system using a probe tip made of BSO crystal was constructed. Three sets of data from simulation results obtained by the same software mentioned above were used for calibration purpose. After the calibration process, the measurement results were in good agreement with all the simulation results. In this experimental system, a sensitivity of 0.6 V/cm/(Hz)1/2 was achieved. 2. Principle of the Electro-Optic Effect 2.1 Propogation Behavior of a Plane-Wave in Anisotropic Materials 2.2 The INdex Ellipsoid and Eigenwaves 2.3 The Linear Electro-Optic Effect 2.4 Eignwaves in an Electro-Optic Crystal with Electric-Field Bias 3. The Electro-Optic Probing Technique 3.1 Electro-Optic Amplitude Modulation 3.1.1 Longitutinal Electro-Optic Modulation 3.1.2 Transverse Electro-Optic Modulation 3.2 Electro-Optic Probing System 3.2.1 Probing Geometries 3.2.2 Electro-Optic Probing System Arrangements 3.3 Bandwidth 3.4 Sensitivity 3.5 Spatial Resolution 3.6 Invasiveness 4. Two-Dimensional Electric-Field Vector Measurement Tecnhique 4.1 Principle 4.1.1 Electro-Optic Analysis of a HR Probe Tip 4.1.2 Electro-Optic Analysis of a TIR Probe Tip 4.1.3 Numerical Comparison of Electric-Field Response for Two Probe Tips 4.2 Two-Dimensional Electric-Field Vector Measurement 4.3 System Set-Up 4.4 Experiments and Measuremnent Results 5. Three-Dimensional Electric-Field Vector Measurement Technique 5.1 Principle 5.1.1 Electro-Optic Analysis of a KDP Crystal 5.1.2 Electro-Optic Analysis of a BSO Crystal 5.1.3 Three-Dimensional Electric-Field Vector Measurement Using BSO Crystal 5.2 Experimental System Set-Up 5.3 Measurement and Simulation Results 5.3.1 Structure of Devices Under Test 5.3.2 Measurement Results without Calibration 5.3.3 Measurement Results with Electric-Field Strength Calibration by Simulation Data 6. Conclusions