本論文的研究目的是於末端光激發固態L 型數位雷射中產生以高斯光束和貝塞耳光束(Bessel beams)當作最小像素拼貼的任意結構光束。在成功架設端光激發L 型數位雷射後，會對兩類結構光束做討論，第一類是以不同腰寬ω0=100μm和ω0=200μm的高斯光束疊加的結構光束，第二類ω0=200μm零階貝塞耳光束疊加的結構光束。研究結果發現，以高斯光束疊加的結構光束無法形成指定的形狀，而以貝塞耳光束疊加的結構光束可形成與理論一致的場型，且帶有贋無繞射光束的特性。兩類結構光束的實驗結果都和模擬有相似的結果。

The purpose of this study is to set up the end-pumped solid-state L-shaped digital laser,and excites triangular and square structural laser beams by superposition of Gaussian-beams and Bessel-Gaussian beams. We experimentally set up the end-pumped L-shaped digital laser, and generate the structural beams. It is only necessary to control the phase diagram of the spatial light modulator (SLM) in the digital laser to achieve the output of any structure field. Here we show the triangular and square Gaussian and Bessel-Gaussian
structure beams, also compared the experimental results with simulation. It’s found that the structure beam superimposed by Bessel-Gaussian beams has the characteristics of non-diffracting beams, so that the structure beam can achieve good convergence in the resonant cavity, and the propagation fields have a long focal depth.

1. S. Ngcobo, I. Litvin, L. Burger and A. Forbes, "A digital laser for ondemand
laser modes ," Nat. Commun. 4, 2289 (2013).
2. K. F. Tsai and S. C. Chu, "Generating laser output with arbitrary lateral
shape by using multi-point beam superposition method in digital lasers, "
Laser Phys. 28 075801(2018).
3. K. F. Tsai and S. C. Chu, " Numerical study on the selective excitation of
Helmholtz–Gauss beams in end-pumped solid-state digital lasers with the
control of the laser gain transverse position provided by off-axis end
pumping, "Laser Phys. 28 035801(2018).
4. J. W. Goodman, Introduction to Fourier Optics(Roberts & Company
Publishers, 2004), Chap. 4.
5. J. Durnin, "Exact solutions for nondiffracting beams. I. The scalar theory,"
J. Opt. Soc. Am. A 4, 651-654 (1987).
6. F. Gori, G. Guattari, and C. Padovani,”Bessel-Gauss beams,”Opt.
Commun. 64(6), 491-495(1987).
7.. J. C. Gutiérrez-Vega and M. A. Bandres, "Helmholtz–Gauss waves," J.
Opt. Soc. Am. A 22, 289-298 (2005).
8. M. Endo, "Numerical simulation of an optical resonator for generation of a
doughnut-like laser beam," Opt. Express 12, 1958-1965 (2004)
9. S. C. Chu, K. Otsuka, "Numerical study for selective excitation of Ince-
Gaussian modes in end-pumped solid-state lasers," Opt. Express 15, 16506-
16519 (2007).
10. T. Ohtomo, S. C. Chu, and K. Otsuka, "Generation of vortex beams from
lasers with controlled Hermite- and Ince-Gaussian modes," Opt. Express 16,
5082-5094 (2008).
11. S. C. Chu, Y. T. Chen, K. F. Tsai, and K. Otsuka, "Generation of highorder
Hermite-Gaussian modes in end-pumped solid-state lasers for square
vortex array laser beam generation," Opt. Express 20, 7128-7141 (2002).
12. National Institutes of Health, "ImageJ", Retrieved July 22, 2018, from
https://imagej.nih.gov/ij/
13. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, K.
Dholakia, "Creation and manipulation of three-dimensional optically trapped
structures," Science 296 1101-1103 (2012)
14. V. Gâté, G. Bernaud, C. Veillas, A. Cazier, F. Vocanson, Y. Jourlin, M.
Langlet, "Fast dynamic interferometric lithography for large submicrometric
period diffraction gratings production," Opt. Eng. 52 091712(2013)
15. N. J. Jenness, K. D. Wulff, M. S. Johannes, M. J. Padgett, D. G. Cole, and
R. L. Clark, "Three-dimensional parallel holographic micropatterning using a
spatial light modulator," Opt. Express 16, 15942-15948 (2008)