無繞射光束(non-diffracting beams)早在1987年就被提出，但大多還是利用全像術(Hologram)和Spatial light modulation(SLM)的方式所產生。Mathieu-Gauss Beams(MGBs)被第一次從雷射共振腔產生是在2008年，但自雷射共振腔產生的MGB模態仍是不可預期的。
本篇論文的工作是，提出一種可於末端激發型固態雷射中選擇性激發MGBs的方法及共振腔設計，並模擬驗證其可行性。本論文所提出的MGBs激發方式，經過簡單的調控就可以改變激發出來的MGBs模態，這樣對往後研究無繞射光束的空間傳播特性和在應用上會有更大的便利性。
在末端激發固態雷射控制MGBs的方法分成兩個部分，第一部分是「控制增益位置和大小」，第二部分是「控制共振腔對稱性」，控制增益位置和大小可以控制MGBs的階數，而改變共振腔的對稱性則可控制MGBs的特徵參數q。

Non-diffracting beams was proposed in 1987, and most of them were generated by Hologram and Spatial light modulation (SLM) . Mathieu-Gauss Beams (MGBs) was first generated from the laser cavity in 2008; however, the resulting MGBs are unpredictable.
This thesis proposes a cavity design and a method to the selective generation of MGBs from end-pumped solid-state lasers. This thesis also performs numerical simulation to verify if the proposed method is practicable. With the proposed method, we can easily control the lasing MGBs form end-pumped solid-state lasers. The results this thesis proposed will be useful to the future research on characteristics of propagation of non-diffracted beams, and the application of non-diffracted beams.
The method to the selective MGB-excitation form end-pumped solid-state lasers contains two parts. The first part is "controlling of the location and the size of the cavity gain", and the second part is "controlling the cavity asymmetry". Controlling cavity gain location and size can decide the order of lasing MGBs. Changing the symmetry of the cavity can tune the characteristic parameters q of lasing MGBs.

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