論文題目：有限孔徑貝賽爾束二次諧波聲場
論文題目(外文)：Second harmonic generation inapertured Bessel beams
研究生：趙俞婷
論文摘要：
人們已在許多領域，如聲學、光學與物理相關學科，研究無繞射貝索(貝賽爾)束。已有的研究結果顯示，在孔徑為無限大的理想情況下，貝索聲束非線性二次諧波，像基波一樣，仍具有無繞射特性。波束寬度則為基波的二分之一，不像一般聲源多為1/ 。
本文主要目的是在實際情況下，研究貝索聲束的基波與二次諧波聲場，也就是說我們在實際研究過程中，考慮了波束孔徑的有限性及媒質聲衰減等因素對貝索聲場的影響。研究的出發點是根據KZK方程在微擾近似下的聲場積分解。為了簡化數值積分和降低計算量，我們應用高斯展開法來計算實際情況下貝索聲束基波與二次諧波聲場分佈。分析結果顯示，當孔徑比較大的情況下，貝索聲束仍保有理想情況下的主要特徵。
另外，我們還利用COMSOL這套軟體模擬了不同形狀活塞聲源輻射的聲場分佈，分析並討論其結果。而在模擬有限孔徑貝索聲束的聲場時，更發現模擬結果與高斯展開所得結果趨勢吻合很好。這顯示了COMSOL是很好的聲場分析工具。
The non-diffracting Bessel beam has been very widely studied in many fields of acoustics, optics and related physics. The existing investigation shows that for an ideal Bessel beam, the second harmonic generated nonlinearity is also almost radially non-diffracting and the beam width of the second harmonic is exactly equal to half times that of the fundamental, not as 2-1/2 times as the usual sound beams.
The present work studies the fundamental and second-harmonic sound field of the Bessel beam. In this study, the finite beam apertures and the attenuation of media are practically considered. This study is based on the integral solutions of the KZK nonlinear parabolic equation under the perturbation approximation. To simplify numerical integration and to reduce amount of calculation, we applied the efficient Gaussian expansion method to evaluate sound field distribution of the fundamental and the second harmonic in practical Bessel beams. The numerical result shows that for a practical Bessel beams with large apertures, it still has the basic properties of an ideal Bessel beam.
Furthermore, we have simulated the sound field radiated from the piston sources with various shapes by using finite element commercial software, COMSOL. Simulated results are analyzed and discussed. For the Bessel beam with finite aperture, simulation results agree well with those by the Gaussian expansion method. This indicates that COMSOL is a good tool for analysis of the sound radiation field.
目錄
第一章 緒論
1-1 研究背景和動機................................1
1-2 文獻回顧..........................................2
1-3 論文架構..........................................4
第二章 KZK方程之積分解
2-1 KZK方程研究背景..............................6
2-2 KZK方程積分解之推導........................7
第三章 高斯展開法
3-1 高斯展開法.......................................12
3-2 高斯展開法應用於二次諧波.................14
3-3 高斯展開之系數求法...........................15
3-4 高斯函數之完備性...............................18
第四章 貝索聲束基波與二次諧波
4-1 貝索高斯求解法...................................21
4-2 基次諧波理論......................................23
4-3 二次諧波理論......................................25
4-4 參數表格............................................27
第五章 模擬結果及分析
5-1 基波模擬分析.......................................32
5-2 二次諧波無聲衰減模擬分析....................41
5-3 二次諧波聲衰減模擬分析.......................51
第六章 COMSOL模擬及結果討論
6-1 活塞型聲束COMSOL模擬比較................66
6-2 貝索型聲束COMSOL模擬比較.................85
第七章 結論及未來展望
7-1 結論.......................................................90
7-2 未來展望.................................................91
參考文獻.......................................................93
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