高功率雷射在放大過程中，容易產生高頻空間訊號，造成雷射光斑有缺陷。因此，我們需要設計一個光學空間濾波器改善實驗系統中高功率窄頻Nd:YAG雷射光斑。根據透鏡的傅立葉轉換特性，光束在焦平面上會產生傅立葉頻譜，空間頻率越高會分布在越外緣，利用適當大小的孔洞可以過濾高頻空間雜訊，使雷射光斑獲得改善。我們使用圓錐狀的孔洞，與傳統圓形孔洞相比較，此圓錐狀設計可以增加孔洞材料承受雷射能量的面積，增加孔洞的壽命。孔洞固定在玻璃真空管中以降低空氣中電漿的產生與孔洞的損害。我們使用尺寸最小的孔徑為380微米，材料為不銹鋼。實驗結果顯示雷射光斑品質已明顯改善，且孔洞可承受雷射強度16.9 TW/cm2。另外，我們應用此空間濾波器在相位量測系統與雷射加工上，也明顯提高干涉條紋在空間上的穩定與加工的品質。

In amplification of high-power laser, the high-spatial-frequency components are generated usually, causing the defect in laser beam profile. Therefore, we design an optical spatial filter to improve the beam profile of narrow-band Nd:YAG laser in our experimental system. According Fourier optics, Fourier power spectrum is produced in the focal plane of lens. The higher spatial-frequency components are located at the position far from optical axis. Thus, an aperture with proper size can be used to remove high-spatial-frequency noise so that the beam profile is improved. We apply an aperture with conical shape. This design can increase the interaction area of incident beam and material surface lead to longer lifetime for aperture. In order to reduce the air plasma and damage of aperture, we fix the aperture in a glass vacuum tube. The minimum aperture size is 380 μm and material is stainless steel. Experimental results show the beam profile is improved obviously and the aperture can tolerate intensity 16.9 TW/cm2. Besides, we apply this spatial filter to the phase measurement system and laser processing. The spatial stability of interference pattern and the quality of laser processing are better than before.

[1] Joseph W. Goodman, “Introduction of Fourier Optics”, Third Edition, Colorado, Roberts & Company Publichers, 2005.
[2] HoganW J, Moses E I, Warner B E, Sorem M S and Soures J M, “The national ignition facility”, Nucl. Fusion, Vol.41, No.5, pp.567-573, 2001.
[3] Waxer L J et al, “High-energy petawatt capability for the omega laser”, Opt. Photonics News, Vol.16, Issue 7, pp.30–36, 2005.
[4] Dunne M, “A high-power laser fusion facility for Europe”, Nat. Phys., Vol. 2, pp. 2–5, 2006.
[5] Glaze J A, “High energy glass lasers”, Opt. Eng., Vol. 15, pp. 136–142, 1975.
[6] J. A, Fleck, J. R. Morris, and E. S. Bliss, “Small-Scale Self-Focusing Effects in a High Power Glass Laser Amplifier”, IEEE JOURNAL OF QUANTUM ELECTRONICS, Vol. QE-14, No. 5, pp. 353-363, 1978.
[7] Zhijun Ye, Jianlin Zhao, Tao Peng, Dong Li, “Evolution of the hot image effect in high-power laser system with cascaded kerr medium”, Optics and Lasers in Engineering, Vol. 47, pp. 1199-1204, 2009.
[8] Hunt J T, Renard P A, Simmons W W. “Improved performance of fusion lasers using the imaging properties of multiple spatial filters”, Appl Opt, Vol. 16, Issue 4, pp. 779–782, 1977.
[9] Hunt J T, Glaze J A, Simmons W W, et al. “Suppression of self-focusing through low-pass spatial filtering and relay imaging”, Appl Opt, Vol. 17, Issue 13, pp. 2053–2057, 1978.
[10] N. A. Kumit, S. A. Letzring arid R. P. Johnson, “A high-damage threshold pinhole for glass fusion laser applications”, Proc. SPIE, Vol. 3492, pp. 896-900, 1999.
[11] Korniski R J, Edward E R, Miller J L., ”Spatial filter lens design for the main laser of the National Ignition Facility”, Proc SPIE, Vol. 3482, pp. 737–747, 1998.
[12] Peter M. Celliers, Kent G. Estabrook, Russell J. Wallace, James E. Murray, Luiz B. Da Silva,
Brian J. MacGowan, Bruno M. Van Wonterghem, and Kenneth R. Manes, “Spatial filter
64
pinhole for high-energy pulsed lasers”, APPLIED OPTICS, Vol. 37, No. 12, pp. 2371-2378, 1998.
[13] James E. Murray, David Milam, Charles D. Boley, Kent G. Estabrook, and John A. Caird, “Spatial filter pinhole development for the National Ignition Facility”, APPLIED OPTICS, Vol. 39, No. 9, pp. 1405-1420, 2000.
[14] Potemkin A K, Barmashova T V, Kirsanov A V, Martyanov M A, Khazanov E A and Shaykin A A, “Spatial filters for high-peak-power multistage laser amplifiers”, APPLIED OPTICS, Vol. 46, No. 20, pp. 4423-4430, 2007.
[15] Garanin S G, Epatko I V, L’vov L V, Serov R V and Sukharev S A, “Self-focusing suppression in a system of two nonlinear media and a spatial filter”, Quantum Electron., Vol. 37, No. 12, pp. 1159–1165, 2007.
[16] Yan-Qi Gao, Bao-Qiang Zhu, Dai-Zhong Liu, and Zun-Qi Lin, “Propagation of flat-topped multi-Gaussian beams through an apertured ABCD optical system”, J. Opt. Soc. Am. A, Vol. 26, No. 10, pp. 2139-2146, 2009.
[17] Yanqi Gao, Baoqiang Zhu, Daizhong Liu, and Zunqi Lin, “Propagation of flat-topped multi-Gaussian beams through a double-lens system with apertures”, OPTICS EXPRESS, Vol. 17, No. 15, pp. 12753-12766, 2009.
[18] Yan-Qi Gao, Bao-Qiang Zhu, Dai-Zhong Liu and Zun-Qi Lin, “Influences of the alignment and misalignment spatial filters on the beam quality in high power laser systems”, J. Opt. Vol. 12, No. 9, 2010.
[19] J. P. Levesque, K. D. Litzner, M. E. Mauel, D. A. Maurer, G. A. Navratil, and T. S. Pedersen, “A high-power spatial filter for Thomson scattering stray light reduction”, Rev. Sci. Instrum. Vol. 82, Issue 3, pp. 033501-1-033501-5, 2011
[20] Zhang Xin, Zhao Junpu, Zhou Wei, Deng Wu, Zhang Kun, Dai Wanjun, Hu Dongxia, Jiang Xuejun, “Optimum design of spatial filter pinhole in high power solid laser system”, Photonics
65
and Optoelectronics (SOPO), 2011, pp. 16-18. [21] H. –Z. Wang, “Controlling the waveform of sub-femtosecond pulse train by synthesized fundamental and harmonics of a Q-switched”, M.S. thesis, National Tsing Hua University, Taiwan, 2011. [22] W. –J. Chen, H. –Z. Wang, R. –Y. Lin, C. –K. Lee, and C. –L. Pan, “Attosecond pulse synthesis and arbitrary waveform generation with cascaded harmonics of an injection-seeded high-power Q-switched Nd:YAG laser,” Laser Phys. Lett., Vol. 9, No. 3, pp. 212-218, 2012.
[23] Han-Sung Chan, Zhi-Ming Hsieh, Wei-Hong Liang, A. H. Kung, Chao-Kuei Lee, Chien-Jen Lai, Ru-Pin Pan, Lung-Han Peng, “Synthesis and Measurement of Ultrafast Waveforms from Five Discrete Optical Harmonics,” Science, Vol. 331, No. 6021, pp. 1165-1168, 2011.
[24] Vasily Lednev, Sergey M. Pershin and Alexey F. Bunkin, “Laser beam profile influence on LIBS analytical capabilities: single vs. multimode beam”, J. Anal. At. Spectrom., Vol. 25, Issue 11, pp. 1745–1757, 2010.
[25] K. Venkatakrishnan*, B. Tan, L.H.K. Koh, B.K.A. Ngoi, “Femtosecond pulsed laser ablation with spatial Filtering”, Optics and Lasers in Engineering, Vol. 38, Issue 6, pp. 425–432, 2002.
[26] V. Strelkov, A. Zaïr, O. Tcherbakoff, R. López-Martens, E. Cormier, E. Mével and E. Constani, “ Generation of attosecond pulse with ellipticity- modulated fundamental “, App. Phys. B: laser and optics, Vol. 78, No. 7-8, pp. 879-884, 2004.
[27] Jay S. Pearlman and John P. Anthes, “Closure of pinholes under intense laser radiation”, APPLIED OPTICS, Vol. 16, No. 8, pp. 2328-2331, 1977.
[28] J. M. Auerbach, N. C. Holmes, J. T. Hunt, and G. J. Linford, “Closure phenomena in pinholes irradiated by Nd laser pulses”, APPLIED OPTICS, Vol. 18, No. 14, pp. 2495-2499, 1979.
[29] R. G. Bikmatov, C. D. Boley, I. N. Burdonski, V. M Chemyak, A. V. Fedorov, A. Y. Goltsov, V. N. Kondrashov, S. N. Koptyaev, N. G. Kovalsky, V. N. Kuznetsov, D. Milam, J. Murray, M. I. Pergament, V. M. Petryakov, R. V. Smirnov, V. I. Sokolov, and E. V. Zhuzhukalo,
66
“Pinhole closure in spatial filters of large-scale ICF laser systems”, Proc. SPIE, Vol. 3492, pp. 510–523, 1998.
[30] F. Krausz and M. Ivanov” Attosecond physics”Rev. Mod. Phys. Vol. 81, pp. 163-234, 2009.
Alfano, R. R., and S. L. Shapiro, “Emission in the Region 4000 to 7000 Å Via Four-Photon Coupling in Glass”, Phys. Rev. Lett. Vol. 24, Issue 11, pp. 584-587, 1970.
[31] Eugene Hecht, “Optics”, Fourth Edition, United States, Addison Wesley, 2002.
[32] Haidan Mao and Daomu Zhao, “Different models for a hard-aperture function and corresponding approximate analytical propagation equations of a Gaussian beam through an apertured optical system”, J.Opt. Soc. Am. A, Vol.22, No.4, pp. 647-653, 2005.
[33] Jeffrey P. Koplow, Dahv A. V. Kliner, Lew Goldberg, “Single-mode operation of a coiled multimode fiber amplifier”, OPTICS LETTERS, Vol. 25, No. 7, pp. 442-444, 2000.
[34] D. M. Kane and V. G. Ta’eed, “Spatial beam profiles from a laser-diode system with optical feedback: the importance of interference”, APPlIED OPTICS, Vol. 40, No. 24, pp. 4316-4321, 2001.