本文主要在產生具圓柱向量偏振的雷射與研究其非線性動態行為，總共有兩部分的研究。第一部分用雙折射晶體Nd:GdVO4與Cr4+:YAG，經由共振腔設計產生被動式Q開關的方位角偏振脈衝雷射。提高泵源功率，系統會經由倍週期路徑進入混沌。在週期二，空間中的脈衝序列會隨著光束的方位角改變。在混沌範圍，脈衝序列具有時間與空間的混沌，而此時依然維持方位角偏振。第二部分的研究為產生雙波長的圓柱向量光束。使用擴散接合的Nd:YVO4/Nd:GdVO4晶體產生雙波長，且藉由共振腔設計產生方位角偏振。兩個雷射波長為1064.04 nm與1066.41 nm，分別由Nd:YVO4與Nd:GdVO4產生。

In this thesis, we generate the laser with cylindrical vector polarization and study the nonlinear dynamics. There are two experiments. In the first part, the passively Q-switched laser with azimuthally polarized is generated. When the pump power is increased, a period-doubling route to chaos is observed. At a period of two, the pulse trains are varied with azimuthal angles. The spatiotemporal chaos is observed under the invariant distribution of polarization. In the second part, a dual-wavelength laser with azimuthal polarization is achieved by using the diffusion-bonded Nd:YVO4/Nd:GdVO4 crystal. The lasing wavelengths are 1064.04 nm and 1066.41 nm which are generated by Nd:YVO4 and Nd:GdVO4, respectively.

[1] Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1-57 (2009).
[2] K. Venkatakrishnan, and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16, 2603-2607 (2006).
[3] M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A. 86, 329-334 (2007).
[4] Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12, 337-3382 (2004).
[5] L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal Field Modes Probed by Single Molecules,” Phys. Rev. Lett. 86, 5251-5254 (2001).
[6] S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2234-2239 (1990).
[7] E. G. Churin, J. Hoßfeld, and T. Tschudi, “Polarization configurations with singular point formed by computer generated holograms,” Opt. Commun. 99, 13-17 (1993).
[8] G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Efficient extracavity generation of radially and azimuthally polarized beams,” Opt. Lett. 32, 1468-1470 (2007).
[9] D. Pohl, “Operation of a Ruby laser in the purely transverse electric mode TE01,” Appl. Phys. Lett. 20, 266-267 (1972).
[10] J.-F. Bisson, J. Li, K. Ueda, and Yu. Senatsky, “Radially polarized ring and arc beams of a neodymium laser with an intra-cavity axicon,” Opt. Express 14, 3304-3311 (2006).
[11] K.-C. Chang, T. Lin, and M.-D. Wei, “Generation of azimuthally and radially polarized off-axis beams with an intracavity large-apex-angle axicon,” Opt. Express 21, 16035-16042 (2013).
[12] M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization inYb:YAG thin-disk lasers,” Opt. Lett. 32, 3272-3274 (2007).
[13] J.-l. Li, K.-i. Ueda, L.-x. Zhong, M. Musha, A. Shirakawa, and T. Sato, “Efficient excitations of radially and azimuthally polarized Nd3+: YAG ceramic microchip laser by use of subwavelength multilayer concentric gratings composed of Nb2O5/SiO2,” Opt. Express 16, 10841-10848 (2008).
[14] M. P. Thirugnanasambandam, Y. Senatsky, and K.-i. Ueda, “Generation of radially and azimuthally polarized beams in Yb:YAG laser with intra-cavity lens and birefringent crystal,” Opt. Express 19, 1905-1914 (2011).
[15] K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31, 2151-2153 (2006).
[16] J.-l. Li, K.-i. Ueda, M. Musha, L.-x. Zhong, and A. Shirakawa, “Radially polarized and pulsed output from passively Q-switched Nd:YAG ceramic microchip laser,” Opt. Lett. 33, 2686-2688 (2008).
[17] Z. Fang, K. Xia, Y. Yao, and J. Li, “Radially polarized and passively Q-switched Nd:YAG laser under annular-shaped pumping,” IEEE J. Sel. Top. Quantum Electron. 21, 1600406 (2015).
[18] K.-C. Chang, D.-L. Li, and M.-D. Wei, “Self-sustaining azimuthal polarization in a passively Q-switched Nd:GdVO4 laser with a Cr4+:YAG saturable absorber,” J. Opt. Soc. Am. B 31, 382-386 (2014).
[19] 劉秉正, 非線性動力學與混沌基礎 (徐氏基金會, 1998)。
[20] E. N. Lorenz, “Deterministic non-periodic flow,” J. Atoms. Sci. 20, 130-141 (1963).
[21] M. Tachikawa, F.-L. Hong, K. Tanii, and T. Shimizu, “Deterministic chaos in passive Q-switching pulsation of a CO2 laser with saturable absorber,” Phys. Rev. Lett. 60, 2266-2268 (1988).
[22] J. J. Zayhowski, and C. Dill, “Diode-pumped passively Q-switched picosecond microchip lasers,” Opt. Lett. 19, 1427-1429 (1994).
[23] D. Y. Tang, S. P. Ng, L. J. Qin, and X. L. Meng,“Deterministic chaos in a diode-pumped Nd:YAG laser passively Q switched by a Cr4+:YAG crystal,” Opt. Lett. 28, 325-327 (2003).
[24] S. P. Ng, D. Y. Tang, L. J. Qin, X. L. Meng, and Z. J. Xiong, “Period-doubling route to chaos in diode-pumped passively Q-switched Nd:GdVO4 and Nd:YVO4 lasers,” Int. J. Bifur. Chaos 16, 2689-2696 (2006).
[25] M. Kovalsky, and A. Hnilo, “Chaos in the pulse spacing of passive Q-switched all-solid-state lasers,” Opt. Lett. 35, 3498-3500 (2010).
[26] D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054-1057 (2007).
[27] J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. Rios Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: origin, predictability, and suppression,” Phys. Rev. A 87, 035802 (2013).
[28] N. M. Granese, A. Lacapmesure, M. B. Agüero, M. G. Kovalsky, A. A. Hnilo, and J. R. Tredicce, “Extreme events and crises observed in an all-solid-state laser with modulation of losses,” Opt. Lett. 41, 3010-3012 (2016).
[29] C. Bonazzola, A. Hnilo, M. Kovalsky, and J. R. Tredicce,“Optical rogue waves in an all-solid-state laser with a saturable absorber: importance of the spatial effects,”J. Opt. 15, 064004 (2013).
[30] C. R. Bonazzola, A. A. Hnilo, M. G. Kovalsky, and J. R. Tredicce, “Features of the extreme events observed in all-solid-state laser with a saturable absorber,” Phys. Rev. A 92, 053816 (2015).
[31] K. Lünstedt, N. Pavel, K. Petermann, and G. Huber, “Continuous-wave simultaneous dual-wavelength operation at 912 and 1063 nm in Nd:GdVO4,” Appl. Phys. B 86, 65-70 (2007).
[32] Y. F. Chen, “CW dual-wavelength operation of a diode-end-pumped Nd:YVO4 laser,” Appl. Phys. B 70, 475-478 (2000).
[33] Y. F. Chen, M. L. Ku, and K. W. Su, “High-power efficient tunable Nd:GdVO4 laser at 1083 nm,” Opt. Lett. 30, 2107-2109 (2005).
[34] Y. J. Huang, Y. S. Tzeng, C. Y. Tang, S. Y. Chiang, H. C. Liang, and Y. F. Chen, “Efficient high-power terahertz beating in a dual-wavelength synchronously mode-locked laser with dual gain media,” Opt. Lett. 39, 1477-1480 (2014).
[35] Y. J. Huang, Y. S. Tzeng, C. Y. Tang, and Y. F. Chen, “Efficient dual-wavelength synchronously mode-locked picosecond laser operating on the 4F3/2-4F11/2 Transition with compactly combined dual gain media,” IEEE J. Sel. Top. Quantum Electron. 21, 56-62 (2015).
[36] Y. J. Huang, H. H. Cho, Y. S. Tzeng, H. C. Liang, K. W. Su, and Y. F. Chen, “Efficient dual-wavelength diode-end-pumped laser with a diffusion-bonded Nd:YVO4/Nd:GdVO4 crystal,”Opt. Mater. Express 5, 2136-2141 (2015).
[37] Y. J. Huang, H. H. Cho, K. W. Su, and Y. F. Chen, “Dual-wavelength intracavity OPO with a diffusion-bonded Nd:YVO4/Nd:GdVO4 crystal,” IEEE Photon. Technol. Lett. 28, 1123-1126 (2016).
[38] P. Zhao, S. Ragam, Y. J. Ding, and I. B. Zotova, “Compact and portable terahertz source by mixing two frequencies generated simultaneously by a single solid-state laser,” Opt. Lett. 35, 3979-3981 (2010).
[39] J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications－explosives, weapons and drugs,” Semicond. Sci. Technol. 20, S266-S280 (2005).
[40] C. B. Reid, E. Pickwell-MacPherson, J. G. Laufer, A. P. Gibson, J. C. Hebden, and V. P. Wallace,“Accuracy and resolution of THz reflection spectroscopy for medical imaging,” Phys. Med. Biol. 55, 4825-4838 (2010).
[41] D. E. Zelmon, J. M. Northridge, J. J. Lee, K. M. Currin, and D. Perlov, “Optical properties of Nd-doped rare-earth vanadates,” Appl. Opt. 49, 4973-4978 (2010).
[42] A. E. Siegman, Lasers (University Science, Mill Valley, CA., 1986).
[43] J. T. Verdeyen, Laser Electronics (Prentice Hall, 1995).
[44] K. Spariosu, A. V. Shestakov, W. Chen, R. Stultz, and M. Birnbaum, “Dual Q switching and laser action at 1.06 and 1.44 μm in a Nd3+:YAG–Cr4+:YAG oscillator at 300 K,” Opt. Lett. 18, 814-816 (1993).
[45] A. Szabo, and R. A. Stein, “Theory of laser giant pulsing by a saturable absorber,” J. Appl. Phys. 36, 1562-1566 (1965).
[46] Y. Bai, N. Wu, J. Zhang, J. Li, S. Li, J. Xu, and P. Deng, “Passively Q-switched Nd:YVO4 laser with a Cr4+:YAG crystal saturable absorber,” Appl. Opt. 36, 2468-2472 (1997).
[47] C. Li, J. Song, D. Shen, N. S. Kim, J. Lu, K. Ueda, “Diode-pumped passively Q-switched Nd:GdVO4 lasers operating at 1.06 μm wavelength,” Appl. Phys. B 70, 471-474 (2000).
[48] Y.-F. Chen and S. W. Tsai, “Simultaneous Q-switching and mode-locking in a diode-pumped Nd:YVO4-Cr4+:YAG laser,” IEEE J. Quantum Electron. 37, 580-586 (2001).
[49] M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Phys. Rev. A 45, 3403-3411 (1992).
[50] J. C. Sprott, and G. Rowlands, Chaos Data Analyzer: The Professional Version (Physics Academic Software, 1998).
[51] M. Tsunekane, N. Taguchi, and H. Inaba, “High power operation of diode-end-pumped Nd:YVO4 laser using composite rod with undoped end,” Electron. Lett. 32, 40-42 (1996).
[52] M. Tsunekane, N. Taguchi, T. Kasamatsu, and H. Inaba, “Analytical and experimental studies on the characteristics of composite solid-state laser rods in diode-end-pumped geometry,” IEEE J. Sel. Top. Quantum Electron. 3, 9-18 (1997).
[53] R. Feldman, Y. Shimony, and Z. Burshtein, “Passive Q-switching in Nd:YAG/Cr4+:YAG monolithic microchip laser,” Opt. Mater. 24, 393-399 (2003).