臺灣博碩士論文加值系統

本論文中有興趣的是分子離子HeH+的紅外光譜，HeH+是一個由兩個電子、兩個原子核組成的四體系統，因為結構單純，故可由量子力學出發解得高準確度的能階，其振動轉動頻率目前理論計算準確度可達30 MHz，實驗結果準確度為30~60 MHz。我們希望量測它的躍遷譜線至1 MHz的準確度。另外，在宇宙中大部份的組成為電漿，而分子離子HeH+是由兩個宇宙中含量最量豐富且最輕的元素組成，很多科學家推論宇宙中的星雲或星球可能有它的蹤跡。
拜近幾年來固態雷射與非線性晶體蓬勃發展之賜，及在近紅外與綠光頻率標準的確認，我們建立了一套窄線寬的中紅外可調雷射光源，功率約1.3~1.5 毫瓦，且具有非常高的頻率準確度(~1 MHz)。此紅外光的產生是結合1.2瓦、波長1064 nm的摻銣釔鋁石榴石(Nd:YAG) 雷射與大於1.5瓦、波長780~870 nm的鈦藍寶石 (Ti:Sapphire)雷射光經過非線性晶體-準相位匹配週期反轉鈮酸鋰晶體 (QPM PPLN: quasi-phase match periodically-poled LiNbO3)，而產生兩入射雷射的頻率差(DFG-Difference Frequency Generation )的中紅外光，其波長涵蓋2.92~4.77 μm)。藉由雷射頻率鎖在碘分子的超精細結構 (hyperfine structure)上及差頻(Offset)鎖頻線路，我們可以準確改變與得知中紅外光的頻率。
建立此中紅外雷射光源後，我們測量甲烷(CH4)分子在3.39 μm飽和吸收的二次微分訊號，以測試系統頻率的準確度。甲烷分子在 P(7) F2(2) band 3.39 μm的飽和吸收是國際上採用的長度標準，其頻率為88376181.60018(27) MHz 。我們的測量結果為88376182.694(40) MHz，約比標準值大1.1 MHz。真正的誤差來源還不清楚，但我們可以確定此中紅外雷射光源具有1.1 MHz的準確度。同時，我們也測量甲烷在這波長附近的另二條飽和吸收譜線的頻率P(7) band: A2及E。
接著，利用此雷射光源我們量測HeH+於電子基態的五條躍遷譜線R(0)-R(4)(v=1-0)。光譜測量的靈敏度約 10^-8 cm-1/Hz^0.5 ，頻率的準確度約7~15 MHz。同時，也探討了HeH+離子於放電管中的飄移速度(drift velocity)與溫度等物理性質。
我們期望不久的將來，利用此雷射光源加上共振腔量測HeH+的飽和吸收訊號，以提高要遷頻率測量的準確度。另外，我們還希望測量H3+及HD的吸收訊號，它們與HeH+一樣在理論計算及天文上扮演非常重要的角色。

In this dissertation, we are interested in molecular ion HeH+. Second only to H2+, the helium hydride HeH+, hydrogen deuterium HD and their isotopes are the simplest heternuclear molecules. They are the good theoretical testing ground and also play important roles in the astrophysics. It is composed of the two most abundant elements in the universe. Hence it has been suggested presenting in the astronomical objects. At present, the accuracy in theoretical and experimental results is about 30 MHz. We have achieved an improved accuracy to a few MHz.
A stable and narrow linewidth DFG (Difference Frequency Generation) source in mid-IR was set up with power 1.3~1.5 mW and the accuracy of about 1 MHz. The DFG source was based on a Nd:YAG laser of power 1.2 W at 1064 nm, and a Ti:Sapphire laser with power >1.5 W at 780-870 nm. A multi-channel periodically poled LiNbO3 (PPLN) was used to generate the difference frequency within the tuning range 2.92~4.77 μm. The method which we used to get the frequency of the DFG source was to know the individual frequency of Ti:Sapphire and two YAG lasers, with the aid of hyperfine transitions of iodine molecule.
Before measuring the transition frequency of HeH+, we have tested the accuracy of system by measuring the second derivative saturation absorption of methane F2(2), P(7) line of the band at 3.39 μm. It is one of the recommended frequencies. Our measured result was 88376182.694(40) MHz and it is 1.1 MHz larger than the recommended value 88376181.60018(27) MHz. At present, we do not know the origin of the discrepancy. However, we can conclude that the frequency accuracy of our DFG source is ~1MHz. In addition to F2(2) P(7) line of the band, we have also measured the frequencies of E and A2 transitions of the P(7) line .
Five spectra, R(0) to R(4), in fundamental band of HeH+ in the electronic ground state were measured by the concentration modulation. The sensitivity in the present experimental setup was about 10^-8 cm-1/Hz^0.5 . Meanwhile, we have also investigated some physical properties of HeH+ in the discharge tube.
In the future, we expect to improve the accuracy of the transition frequency of HeH+ to ~1 MHz by observing the saturation spectroscopy with cavity enhancement technique. We plan to remeasure the transition frequencies of other simple molecules such as HD and H3+. Both HD and H3+ play import roles in the quantum mechanics calculation and in the astrophysics.

List of Figures
List of Tables
Ch 1 Introduction
1.1 Motivation-----------------------------------------1
1.2 Review of HeH+ Spectroscopy------------------------3
1.3 Overview of this Dissertation----------------------5
References------------------------------------------9
Ch 2 Theoretical Calculation of HeH+ and Its Spectrum
2.1 Schrödinger Equation and Solution---------------11
2.2 Spectroscopy------------------------------------18
2.3 High Accurate Theoretical Result of HeH+--------22
References------------------------------------------29
Ch 3 Background Knowledge of Our DFG Source
3.1 Nonlinear Optics--------------------------------31
3.2 Saturation Spectroscopy-------------------------35
3.3 Wavelength Modulation and Frequency Modulation--38
3.4 Hyperfine Structures of Iodine Molecule---------43
References------------------------------------------56
Ch 4 Tunable Mid-IR Difference Frequency Generation Source
4.1 Tunable Mid-IR Difference Frequency Generation Source-58
4.2 Frequency Stabilization of Nd:YAG Laser---------------61
4.3 Frequency Stabilization of Ti:Sapphire Laser----------64
4.4 Frequency Control by Off-set Lock Loop----------------66
4.5 Accuracy Test of DFG source------------------------------68
References------------------------------------------------86
Ch5 Precision Spectroscopy of HeH+
5.1 Observation of HeH+-----------------------------------88
5.2 Results and Discussions-------------------------------91
5.3 Summary----------------------------------------------101
References-----------------------------------------------115
Ch6 Summary and Future Work
6.1 Summary----------------------------------------------117
6.2 Future Works-----------------------------------------118
References-----------------------------------------------120
Appendix I
The properties of the electronic state of diatomic molecules121
Appendix II
The specifications of lasers in our experiment--------------122
Appendix III
The servo loop for the frequency stabilization of 450 mW Nd:YAG laser------------------------------------------------124
Appendix IV
The servo loop for the frequency stabilization of Ti:Sapphire laser-------------------------------------------------------125
Appendix V
The offset lock loop-------------------------------------------------------------------------------------------------------126

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