在許多科學應用上，不同波段的雷射都有其重要的應用，但雷射光波長由於產生機制的特性，其頻率特定。利用倍頻晶體可以將可用雷射光頻率增多，但由於不同晶體適用的雷射源不同，為了能讓各種波段的雷射源都能倍頻，就需要各式各樣的非線性光學晶體。所以對於這些晶體影響非線性光學現象之發生機制等等的徹底瞭解，可以幫助我們找尋或是合成更多的非線性光學晶體。其中氧化物非線性光學晶體由於其損傷門檻高，所以成為一類重要的非線性光學晶體。

對於影響氧化物晶體其非線性光學發生機制的相關研究，之前的研究工作已指出一些明顯的方向，例如像是硼酸鹽晶體中，陰離子基團對於倍頻效應機制具有重大的影響。在本工作中，我們利用新的分析技術，從電荷密度的角度來分析氧化物非線性光學晶體，使我們得知影響氧化物非線性光學晶體的主要因素為何。

利用我們之前研究工作的另一項技術『能帶解析χ(2)』，能使我們得知分子中，對於對倍頻係數最重要的分子軌域為何。本工作的重點則是將此技術應用在固體中，並將晶體中對倍頻係數最重要的軌域以權重方式去加總各個電荷密度。透過此技術『SHG-Density 分析方法』，將空間中對倍頻現象有貢獻的電子雲密度呈現出來，可使我們清楚知道產生倍頻的機制。並且發現了對於氧化物非線性光學晶體其孤立電子對效應為影響非線性光學機制的主因。

為了進一步證實我們看到的是孤立電子對，於是發展了『孤立電子對判定方法』這項技術，並以具有孤立電子對的簡單分子結構來做各項測試，確定程式的可用性及正確性後再將其應用至我們想進行分析的結構之上。結果果真證實了先前的預測即---孤立電子對在非線性光學氧化物中是一個對其倍頻效應機制的重要來源。而這也使我們對非線性光學材料有了更深一層的認識。

最後，對於幾種鄰近於 VIA 族的非線性光學氮化物及鹵化物，我們以相同的技術去分析，並就結果作初步的探討，以期能更加深入和廣泛的理解各種非線性光學材料的性質。

Laser sources of different wavelengths have their own important use in industrial applications as well as fundamental researches, but since light is emitted as a result of transition between electronic states, the available wavelengths is limited in the entire EM wave spectrum. Frequency conversion techniques using Non-linear optical crystals allow the production of laser beam at different wavelengths, and are therefore very desirable. For example, harmonic generation can be used to produce laser beam at shorter wavelength which is essential for the next generation lithography, optical storage and fiber communication. Since each NLO crystal works at certain frequency range and has their own characteristics, it is also desirable to search for wider variety of them. A systematic study of the mechanism of NLO properties of these crystals will be beneficial.

In UV/Visible range, oxide crystals are one of the most important types, which usually have high damage threshold, making them durable under high laser power operation. There has already some progress in the past on understanding the mechanism of NLO properties of oxides. Borate, for example, was found to have largely due to their anion group. In this work, we have proposed a new analysis scheme, which reveals the main factor of optical non-linearity from the picture of electron density.

Using one of our analyzing tools "band-resolved of second order susceptibility", one can identify which several orbitals or bands contribute most in a molecule. This work extends the idea further and makes it
applied on solids even more easily. This is achieved by summing each orbital density based on the SHG weight. Through this "SHG-density plots" we can visualize the electron densities that have with significant contribution to the optical nonlinearity and reveal the SHG mechanism. Using this method that we found that lone-pair electrons play the major role in non-linear optics mechanism of oxide family NLO crystals.

In order to identify lone-pair electrons, the technique of “Lone-pair identification scheme” is developed. After testing this scheme on a few simple molecules known to have lone-pair, the reliability of the scheme is confirmed. This method is then applied to the structures which we are interested in, and it dose prove our claim — lone-pair is one of the significant source leads to the non-linear optical properties of oxide. This leads to a further understanding on the mechanism of non-linear optical materials.

Further more, non-linear optical Nitride and Halide crystals which are next to VIA group are also analyzed by this technique. Some preliminary results were obtained which might be useful toward a general understanding on the properties of various non-linear optical materials.

目錄	
第一章：晶體中的光學非線性          	1
非線性光學現象研究之開端               	1
雷射光倍頻的應用                    	1
氧化物非線性光學晶體的重要性          	2
第一原理計算輔助材料設計              	4
非線性光學係數χ(2) 計算             	5
能帶解析與SHG-density分析方法          	6
能帶解析                            	6
SHG-density分析                          	8
之前的文獻回顧及理論研究現況             	9
本論文後續各章的概述                   	9
參考文獻                            	11
	
第二章：孤立電子對的理論判定方法    	14
孤立電子對的定義與其在化學上的重要性	14
路易斯（Lewes）符號裡的孤立電子對   	14
孤立電子對                          	15
孤立電子對在電子結構計算中要如何界定	17
系統化判定孤立電子對的公式          	19
在晶體結構內判定孤立電子對所遇到的問題	20
在公式中加入chi2值                          21
門檻的選取                            	22
LPDOS                                	22
Error function                       	23
關於孤立電子對的結論                	26
參考文獻                              	27
	
第三章：氧化物晶體中之孤立電子對以及其它重要的SHG-density 28
參數設定                             	30
χ(2) 計算                              	31
能帶解析χ(2) 及孤立電子對權重          	32
各結構廣義的能帶解析圖              	33
主要SHG-density群組 (HOMO/LUMO群組) 與LP-density	35
主要的SHG-density群組               	35
LP-density                          	38
其他佔據態與未佔據態群組的SHG-density	40
高能區空band收斂性測試                	40
VE未佔據態低能量群組                  	45
VE未佔據態高能量群組                	48
VH佔據態高能量群組                   	51
VH佔據態低能量群組                   	54
實空間波函數切割                    	56
SrBe3O4 的配位數問題                	58
本章結論                            	60
對於 SHG-density 的結論              	60
對氧化物的結論                       	60
為什麼氧化物如此重要                	61
參考文獻                             	61
	
第四章：氮化物與鹵化物的孤立電子對探討	62
結構NH3、NH4＋                        	62
結構BN、GaN、MgGeN2                 	63
參數設定                            	65
BN、GaN、MgGeN2結構廣義的能帶解析圖  	66
SHG-density與LP-density             	67
結構 CsGeCl3、CsGeBr3、CsGeI3           	70
參數設定                             	72
CsGeCl3、CsGeBr3、CsGeI3的廣義的能帶解析圖	73
SHG-density與LP-density             	75
結構 Si3N4、Si2CN4、SiC2N4、C3N4      	78
參數設定                            	80
Si3N4、Si2CN4、SiC2N4、C3N4的廣義能帶解析圖	81
SHG-density與LP-density             	82
第四章總結討論                      	86
參考文獻                            	87

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