摘要
在這篇論文中,利用光傳播軸量測的方法在靠近氮化鎵帶溝的波段,對其非線性折射係數做了量測.實驗值的分佈和理論預測相符合.在波長為368 nm量測到的非線性折射係數為 -2.9±1.2’10-12, 和前人在532 nm所量到的正值 1’10-12 cm2/W有相同的等級.實驗結果顯示,氮化鎵是一個在紫外線波段擁有很大而且負值非線性折射係數的好材料.
如果光傳播軸量測使用了一個散光的雷射光源,所量測的訊號會受影響而變形.在這篇論文中,我們提出用狹縫代替圓孔來量測遠場的變化.這個方法提供了解決訊號變形的好方法.不僅可以精確量測非線性折射係數,而且可以同時量測到橢圓度和焦點的位置.

Abstract
In this thesis, nonlinear refractive index n2 of GaN was measured for below bandgap ultraviolet (UV) wavelength region using Z-scan techniques with femtosecond UV pulses. Nonlinear refractive indexes of -2.9±1.2’10-12, -1.2±0.5’10-12, -0.5±0.2’10-12 cm2/W were obtained for wavelengths of 368 nm, 371 nm, and 380 nm, respectively. The distribution of n2 versus wavelength is found to be consistent with a model described by the quadratic Stark effect, which is the dominant factor contributed to the nonlinear refractive index near the bandgap. Our experiments show that GaN is an excellent nonlinear material with large negative n2 in the UV region.
Z-scan measurement using an astigmatic Gaussian beam is also studied in this thesis. A slit instead of a circular aperture is used in the measurement. This technique provides a good solution to a distorted Z-scan trace induced by astigmatic Gaussian beam. The technique can accurately determine not only the nonlinear refractive index but also the ellipticity and beam waist positions of the astigmatic Gaussian beam.

Table of Contents
Acknowledgementi
Abstractii
Table of Contentsiv
List of Figuresvi
List of Tablesviii
Publication Listsix
Chapter 1 Nonlinear Refractive Index 1
1.1 Introduction 1
1.2 Third order susceptibility. 2
1.3 Self-focusing and self-defocusing 4
1.4 Self-phase modulation 8
Chapter 2 Nonlinear Refractive Index Measurement using Z-scan12
2.1 Techniques of nonlinear refractive index measurement12
2.2 Z-scan measurement technique 16
2.3Frequency dependent nonlinear refractive index30
Chapter 3 Z-scan measurement of GaN 40
3.1Experimental setup and sample characteristic 41
3.2Nonlinear refractive index of GaN 47
3.3Nonlinearities obtained from the fitting curve 56
3.4Discussion 66
Chapter 4 Z-scan measurement using an astigmatic Gaussian beam70
4.1Z-scan theory of astigmatic Gaussian beam 71
4.2Z-scan measurement with elliptical Gaussian beam74
4.3 Z-scan measurement with astigmatic Gaussian beam 80
Chapter 5 Summary 92

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