
系統識別號 
U00260408201815535500 
論文名稱(中文) 
掺釹雷射系統中離軸光束的產生與非線性動態行為 
論文名稱(英文) 
Generations and nonlinear dynamic behaviors of offaxis modes in Nddoped laser systems 
校院名稱 
成功大學 
系所名稱(中) 
光電科學與工程學系 
系所名稱(英) 
Department of Photonics 
學年度 
106 
學期 
2 
出版年 
107 
研究生(中文) 
邱紀斌 
研究生(英文) 
ChiPin Chiu 
學號 
l78031083 
學位類別 
博士 
語文別 
英文 
論文頁數 
61頁 
口試委員 
口試委員蔡宗祐 口試委員黃勝廣 口試委員曾碩彥 口試委員羅仕守 口試委員林家弘 指導教授魏明達

中文關鍵字 
幾何環行光束
三角光線追跡法
圓柱向量光束
非線性動力學

英文關鍵字 
geometric ring mode
trigonometrical ray tracing
cylindrical vector beam
nonlinear dynamics

學科別分類 

中文摘要 
本論文主要在產生兩種不同之雷射，幾何環型光束與具圓柱向量偏振光束，並針對這兩種光束研究其非線性動態行為。首先，透過不同晶體長度之摻釹釩酸釔(Nd:YVO4)晶體配合四面鏡共振腔產生幾何環型光束，配合三角光線追跡法計算光線於腔內行經路徑，探討其成因。而幾何環形光束也可在三面鏡系統中發現。接著透過晶體本身之雙折射特性與幾何光學的ABCD矩陣設計共振腔，當共振腔靠近穩定邊緣時，只有尋常光可以在共振腔內來回增益放大，進而得到圓柱向量光束。建立於前述之光束，我們將藉由泵源調討論其非線性動態行為。當調製頻率靠近鬆弛震盪頻率時，觀察到雷射系統循倍週期路徑進入混沌。在週期二時，觀察到輸出的兩光點強度序列相反，這說明環形光束為兩個不同之模態。隨調製深度逐漸增加，將可發現極端事件的產生。類似的非性動態行為同樣的在圓柱向量偏振光束上觀察到。相較於幾何環型光束，圓柱向量偏振光束的動態行為與空間分佈是相關聯的。因此週期二的強度變化隨空間上不同角度而改變。當調製深度增加，極端事件伴隨的混沌的產生而被觀察到。

英文摘要 
In this dissertation, we generate two kinds of laser, the geometric ring mode and the cylindrical vector beam, and investigate the behavior of nonlinear dynamics. Using different lengths of Nddoped laser crystals with different cavity configurations to generate the geometric ring mode. Based on the trigonometrical ray tracing, the intracavity trace of cavity mode was analyzed and the numerical simulations were supported the experiment results. We used threemirror cavity configuration to generate the azimuthally polarized laser which is a kind of cylindrical vector beam. Through the birefringence of laser crystal, the oraypreferred region was generated at the edge of the stable region. Further combining the modulation system; the perioddoubling route to chaos were determined. At a period of two, the two spots of geometric ring mode had inverse period two evolutions. When modulation depth increased, extreme event was observed. The cylindrical vector beam has similar nonlinear dynamics behaviors to the geometric ring mode. Compared with the geometric ring mode, the nonlinear dynamics behaviors in the cylindrical vector beam is spatially dependent. At a period of two, the intensity evolution gradually varied with the azimuthal angle. When the modulation depth increased the spatiotemporal extreme events occurred with the generation of the chaos.
At similar cavity configuration which is used in the previous experiment for cylindrical vector beam, we change the laser crystal to the diffusionbonded Nd:YVO4/Nd:GdVO4 to generate an azimuthally polarized laser with dualwavelength.

論文目次 
摘要 I
Abstract II
誌謝 IV
Table of Contents V
List of Figures VII
List of Table IX
Chapter 1. Introduction 1
1.1 Off axis mode 3
1.2 Cylindrical vector beam 5
1.3 The background of nonlinear dynamics 8
Chapter 2. Generations of offaxis modes in Nddoped laser systems 10
2.1 Geometric ring mode 11
2.1.1 Experimental setup 11
2.1.2 Trigonometrical ray tracing in optical system 12
2.1.3 Results and discussion 16
2.2 Cylindrical Vector beams 24
2.2.1 Experimental setup 24
2.2.2 Theory 25
2.2.3 Experimental results of azimuthally polarized laser 27
2.2.4 Dualwavelength with azimuthal polarization 30
2.3 Summary 36
Chapter 3. Nonlinear dynamic behaviors in offaxis mode 37
3.1 Nonlinear dynamic behaviors in geometric ring modes 37
3.2 Chaos and extreme events in an azimuthally polarized laser beam 45
3.3 Summary 51
Chapter 4. Conclusions and future works 52
4.1 . Conclusions 52
4.2 Future work 53
Reference 55

參考文獻 
1. J. Geusic, H. Marcos, and L. Van Uitert, "Laser oscillations in Nd‐doped yttrium aluminum, yttrium gallium and gadolinium garnets," Applied Physics Letters 4, 182184 (1964).
2. J. O'connor, "Unusual Crystal‐Field Energy Levels And Efficient Laser Properties Of Nd:YVO4," Applied physics letters 9, 407409 (1966).
3. A. Zagumennyĭ, V. Ostroumov, I. A. Shcherbakov, T. Jensen, J. Meyen, and G. Huber, "The Nd: GdVO4 crystal: a new material for diodepumped lasers," Soviet journal of quantum electronics 22, 1071 (1992).
4. C. Maunier, J. Doualan, R. Moncorgé, A. Speghini, M. Bettinelli, and E. Cavalli, "Growth, spectroscopic characterization, and laser performance of Nd: LuVO4 a new infrared laser material that is suitable for diode pumping," JOSA B 19, 17941800 (2002).
5. T. Ogawa, Y. Urata, S. Wada, T. Shimizu, M. Higuchi, J. Takahashi, J. Morikawa, and T. Hashimoto, "Optical properties and thermal characteristics of the floating zone grown Nd: LuVO4 crystals," in Advanced SolidState Photonics, (Optical Society of America, 2005), 36.
6. H. Yu, H. Zhang, Z. Wang, J. Wang, Z. Shao, M. Jiang, and X. Zhang, "CW and Qswitched laser output of LDendpumped 1.06 μm ccut Nd: LuVO4 laser," Optics express 15, 32063211 (2007).
7. H. Yu, H. Zhang, and J. Wang, "Growth and Characterization of Vanadate Laser Crystals," Acta Physica Polonica A 124, 301304 (2013).
8. J. Sulc, H. Jelínková, J. K. Jabczynski, W. Zendzian, J. Kwiatkowski, K. Nejezchleb, and V. Skoda, "Comparison of diodesidepumped triangular Nd: YAG and Nd: YAP laser," in Solid State Lasers XIV: Technology and Devices, (International Society for Optics and Photonics, 2005), 325335.
9. D. Ran, H. Xia, S. Sun, F. Liu, Z. Ling, W. Ge, H. Zhang, and J. Wang, "Thermal properties of a Nd: LuVO4 crystal," Crystal Research and Technology: Journal of Experimental and Industrial Crystallography 42, 920925 (2007).
10. A. Minassian, B. Thompson, G. Smith, and M. Damzen, "Highpower scaling (> 100 W) of a diodepumped TEM00 Nd: GdVO4 laser system," IEEE Journal of selected topics in quantum electronics 11, 621625 (2005).
11. J. Tung, T. Wu, H. Liang, and Y. Chen, "Precise measurement of the thermooptical coefficients of various Nddoped vanadates with an intracavity selfmodelocked scheme," Laser Physics 24, 035804 (2014).
12. W. Koechner, "Thermal lensing in a Nd: YAG laser rod," Applied optics 9, 25482553 (1970).
13. Z. Cai, H. Xu, and G. Stéphan, "Bipolarization and multiwavelength diodepumped Nd: YVO4 microchip laser," Optics communications 135, 295299 (1997).
14. A. E. Siegman, Lasers (University Science Books, 1986).
15. D. Herriott, H. Kogelnik, and R. Kompfner, "Offaxis paths in spherical mirror interferometers," Applied Optics 3, 523526 (1964).
16. I. Ramsay and J. Degnan, "A ray analysis of optical resonators formed by two spherical mirrors," Applied optics 9, 385398 (1970).
17. B. Sterman, A. Gabay, S. Yatsiv, and E. Dagan, "Offaxis folded laser beam trajectories in a stripline CO2 laser," Optics letters 14, 13091311 (1989).
18. J. Dingjan, M. van Exter, and J. Woerdman, "Geometric modes in a singlefrequency Nd: YVO4 laser," Optics communications 188, 345351 (2001).
19. C. Chen, P. Huang, and C. Kuo, "Geometric modes outside the multibouncing fundamental Gaussian beam model," Journal of Optics 12, 015708 (2009).
20. Y. Chen, J. Tung, P. Chiang, H. Liang, and K. Huang, "Exploring the effect of fractional degeneracy and the emergence of raywave duality in solidstate lasers with offaxis pumping," Physical Review A 88, 013827 (2013).
21. J. Visser, N. J. Zelders, and G. Nienhuis, "Wave description of geometric modes of a resonator," JOSA A
22, 15591566 (2005).
22. A. A. Malyutin, "Modes of a plano–spherical laser resonator with the Gaussian gain distribution of the active medium," Quantum Electronics 37, 299 (2007).
23. H.H. Wu, "Formation of offaxis beams in an axially pumped solidstate laser," Optics Express 12, 34593464 (2004).
24. K. V. Volodchenko, M. S. Kurdoglyan, C.M. Kim, and G. U. Kim, "Observation and investigation of offaxis modes in a highpower Nd: YAG laser," Applied optics 43, 47684773 (2004).
25. Q. Zhan, "Cylindrical vector beams: from mathematical concepts to applications," Advances in Optics and Photonics 1, 157 (2009).
26. S. Sato, Y. Harada, and Y. Waseda, "Optical trapping of microscopic metal particles," Optics letters 19, 18071809 (1994).
27. H. Kawauchi, K. Yonezawa, Y. Kozawa, and S. Sato, "Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam," Optics letters 32, 18391841 (2007).
28. L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, "Longitudinal field modes probed by single molecules," Physical Review Letters 86, 5251 (2001).
29. K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, "STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis," Nature 440, 935 (2006).
30. M. Meier, V. Romano, and T. Feurer, "Material processing with pulsed radially and azimuthally polarized laser radiation," Applied Physics A 86, 329334 (2007).
31. V. Niziev and A. Nesterov, "Influence of beam polarization on laser cutting efficiency," Journal of Physics D: Applied Physics 32, 1455 (1999).
32. R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Physical review letters 91, 233901 (2003).
33. S. C. Tidwell, D. H. Ford, and W. D. Kimura, "Generating radially polarized beams interferometrically," Applied Optics 29, 22342239 (1990).
34. M. Bashkansky, D. Park, and F. K. Fatemi, "Azimuthally and radially polarized light with a nematic SLM," Optics express 18, 212217 (2010).
35. M. R. Beversluis, L. Novotny, and S. J. Stranick, "Programmable vector pointspread function engineering," Optics express 14, 26502656 (2006).
36. G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, "Efficient extracavity generation of radially and azimuthally polarized beams," Optics letters 32, 14681470 (2007).
37. D. Pohl, "Operation of a ruby laser in the purely transverse electric mode TE01," Applied Physics Letters 20, 266267 (1972).
38. K. Yonezawa, Y. Kozawa, and S. Sato, "Generation of a radially polarized laser beam by use of the birefringence of a ccut Nd: YVO4 crystal," Optics letters 31, 21512153 (2006).
39. K. Yonezawa, Y. Kozawa, and S. Sato, "Compact laser with radial polarization using birefringent laser medium," Japanese Journal of Applied Physics 46, 5160 (2007).
40. Y. Kozawa, K. Yonezawa, and S. Sato, "Radially polarized laser beam from a Nd: YAG laser cavity with a ccut YVO4 crystal," Applied Physics B 88, 43 (2007).
41. Y. Kozawa and S. Sato, "Generation of a radially polarized laser beam by use of a conical Brewster prism," Optics Letters 30, 30633065 (2005).
42. J.F. Bisson, J. Li, K. Ueda, and Y. Senatsky, "Radially polarized ring and arc beams of a neodymium laser with an intracavity axicon," Optics Express 14, 33043311 (2006).
43. M. A. Ahmed, M. Haefner, M. Vogel, C. Pruss, A. Voss, W. Osten, and T. Graf, "Highpower radially polarized Yb: YAG thindisk laser with high efficiency," Optics express 19, 50935103 (2011).
44. A. Nesterov and V. Niziev, "Laser beams with axially symmetric polarization," Journal of Physics D: Applied Physics 33, 1817 (2000).
45. T. Moser, M. A. Ahmed, F. Pigeon, O. Parriaux, E. Wyss, and T. Graf, "Generation of radially polarized beams in Nd: YAG lasers with polarization selective mirrors," Laser Physics Letters 1, 234236 (2004).
46. M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, "Multilayer polarizing grating mirror used for the generation of radial polarization in Yb: YAG thindisk lasers," Optics letters 32, 32723274 (2007).
47. Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, "Cylindrical vector laser beam generated by the use of a photonic crystal mirror," Applied physics express 1, 022008 (2008).
48. Y. Kozawa and S. Sato, "Single higherorder transverse mode operation of a radially polarized Nd: YAG laser using an annularly reflectivitymodulated photonic crystal coupler," Optics letters 33, 22782280 (2008).
49. I. Moshe, S. Jackel, and A. Meir, "Production of radially or azimuthally polarized beams in solidstate lasers and the elimination of thermally induced birefringence effects," Optics letters 28, 807809 (2003).
50. M.D. Wei, Y.S. Lai, and K.C. Chang, "Generation of a radially polarized laser beam in a single microchip Nd: YVO4 laser," Optics letters 38, 24432445 (2013).
51. F. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, "Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Qswitched gas laser," Physical Review Letters 49, 1217 (1982).
52. D. Ivanov, Y. I. Khanin, I. Matorin, and A. Pikovsky, "Chaos in a solidstate laser with periodically modulated losses," Physics Letters A 89, 229230 (1982).
53. N. V. Kravtsov and E. G. e. Lariontsev, "Lasing regimes in solidstate ring lasers with modulated parameters," Quantum Electronics 34, 487 (2004).
54. A. N. Pisarchik, R. JaimesReátegui, R. SevillaEscoboza, G. HuertaCuellar, and M. Taki, "Rogue waves in a multistable system," Physical Review Letters 107, 274101 (2011).
55. C. Metayer, A. Serres, E. Rosero, W. Barbosa, F. de Aguiar, J. R. Leite, and J. Tredicce, "Extreme events in chaotic lasers with modulated parameter," Optics express 22, 1985019859 (2014).
56. 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 allsolidstate laser with modulation of losses," Optics letters 41, 30103012 (2016).
57. J. Ahuja, D. B. Nalawade, J. ZamoraMunt, R. Vilaseca, and C. Masoller, "Rogue waves in injected semiconductor lasers with current modulation: role of the modulation phase," Optics express 22, 2837728382 (2014).
58. S. Perrone, R. Vilaseca, J. ZamoraMunt, and C. Masoller, "Controlling the likelihood of rogue waves in an optically injected semiconductor laser via direct current modulation," Physical Review A 89, 033804 (2014).
59. E. Pelinovsky and C. Kharif, Extreme ocean waves (Springer, 2008).
60. D. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves," Nature 450, 1054 (2007).
61. S. Birkholz, E. T. Nibbering, C. Brée, S. Skupin, A. Demircan, G. Genty, and G. Steinmeyer, "Spatiotemporal rogue events in optical multiple filamentation," Physical review letters 111, 243903 (2013).
62. C. Liu, Z.Y. Yang, L.C. Zhao, G.G. Xin, and W.L. Yang, "Optical rogue waves generated on Gaussian background beam," Optics letters 39, 10571060 (2014).
63. A. Montina, U. Bortolozzo, S. Residori, and F. Arecchi, "NonGaussian statistics and extreme waves in a nonlinear optical cavity," Physical review letters 103, 173901 (2009).
64. C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. R. R. Leite, and J. R. Tredicce, "Deterministic optical rogue waves," Physical review letters 107, 053901 (2011).
65. J. ZamoraMunt, B. Garbin, S. Barland, M. Giudici, J. R. R. Leite, C. Masoller, and J. R. Tredicce, "Rogue waves in optically injected lasers: Origin, predictability, and suppression," Physical Review A 87, 035802 (2013).
66. F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, "Spatiotemporal chaos induces extreme events in an extended microcavity laser," Physical review letters 116, 013901 (2016).
67. J. A. Reinoso, J. ZamoraMunt, and C. Masoller, "Extreme intensity pulses in a semiconductor laser with a short external cavity," Physical Review E 87, 062913 (2013).
68. Z. Liu, S. Zhang, and F. W. Wise, "Rogue waves in a normaldispersion fiber laser," Optics letters 40, 13661369 (2015).
69. D. V. Churkin, O. A. Gorbunov, and S. V. Smirnov, "Extreme value statistics in Raman fiber lasers," Optics letters 36, 36173619 (2011).
70. S. Randoux and P. Suret, "Experimental evidence of extreme value statistics in Raman fiber lasers," Optics letters 37, 500502 (2012).
71. C. Lecaplain, P. Grelu, J. SotoCrespo, and N. Akhmediev, "Dissipative rogue waves generated by chaotic pulse bunching in a modelocked laser," Physical review letters 108, 233901 (2012).
72. J. SotoCrespo, P. Grelu, and N. Akhmediev, "Dissipative rogue waves: extreme pulses generated by passively modelocked lasers," Physical Review E 84, 016604 (2011).
73. A. A. Hnilo, M. G. Kovalsky, M. B. Agüero, and J. R. Tredicce, "Characteristics of the extreme events observed in the Kerrlens modelocked Ti: sapphire laser," Physical Review A 91, 013836 (2015).
74. M. G. Kovalsky, A. A. Hnilo, and J. R. Tredicce, "Extreme events in the Ti: sapphire laser," Optics letters 36, 44494451 (2011).
75. C. Bonazzola, A. Hnilo, M. Kovalsky, and J. R. Tredicce, "Optical rogue waves in an allsolidstate laser with a saturable absorber: importance of the spatial effects," Journal of Optics 15, 064004 (2013).
76. C. R. Bonazzola, A. A. Hnilo, M. G. Kovalsky, and J. R. Tredicce, "Features of the extreme events observed in an allsolidstate laser with a saturable absorber," Physical Review A 92, 053816 (2015).
77. R. Kingslake and R. B. Johnson, Lens design fundamentals (academic press, 2009).
78. W. Klische, H. Telle, and C. Weiss, "Chaos in a solidstate laser with a periodically modulated pump," Optics letters 9, 561563 (1984).
79. C.P. Chiu, X.W. Jiang, K.C. Chang, and M.D. Wei, "Chaos and extreme events in an azimuthally polarized Nd: GdVO4 laser with pump modulation," Optics letters 42, 423426 (2017).
80. K. Lünstedt, N. Pavel, K. Petermann, and G. Huber, "Continuouswave simultaneous dualwavelength operation at 912 nm and 1063 nm in Nd: GdVO4," Applied Physics B 86, 6570 (2007).
81. Y.F. Chen, "cw dualwavelength operation of a diodeendpumped Nd: YVO4 laser," Applied Physics B 70, 475478 (2000).
82. B. Wu, P. Jiang, D. Yang, T. Chen, J. Kong, and Y. Shen, "Compact dualwavelength Nd: GdVO4 laser working at 1063 and 1065 nm," Optics express 17, 60046009 (2009).
83. Y. Lü, J. Xia, H. Liu, and X. Pu, "Simultaneous triple 914 nm, 1084 nm, and 1086 nm operation of a diodepumped Nd: YVO4 laser," Journal of Applied Physics 116, 163107 (2014).
84. Y. Huang, Y. Tzeng, C. Tang, S. Chiang, H. Liang, and Y. Chen, "Efficient highpower terahertz beating in a dualwavelength synchronously modelocked laser with dual gain media," Optics letters 39, 14771480 (2014).
85. Y. Huang, H. Cho, Y. Tzeng, H. Liang, K. Su, and Y. Chen, "Efficient dualwavelength diodeendpumped laser with a diffusionbonded Nd: YVO 4/Nd: GdVO 4 crystal," Optical Materials Express 5, 21362141 (2015).
86. Y.J. Huang, Y.S. Tzeng, C.Y. Tang, and Y.F. Chen, "Efficient dualwavelength synchronously modelocked picosecond laser operating on the 4 F 3/2→ 4 I 11/2 transition with compactly combined dual gain media," IEEE Journal of Selected Topics in Quantum Electronics
21, 5662 (2015).
87. Y. Huang, H. Cho, Y. Tzeng, H. Liang, K. Su, and Y. Chen, "Efficient dualwavelength diodeendpumped laser with a diffusionbonded Nd: YVO4/Nd: GdVO4 crystal," Optical Materials Express 5, 21362141 (2015).
88. Y. Huang, H. Cho, K. Su, and Y. Chen, "DualWavelength Intracavity OPO With a DiffusionBonded Nd: YVO4/Nd: GdVO4 Crystal," IEEE Photonics Technology Letters 28, 11231126 (2016).
89. P. Kjeldsen, "A sudden disasterin Extreme Waves," Rogue Waves 2000, 1935 (2001).
90. S. Aberg and G. Lindgren, "Height distribution of stochastic Lagrange ocean waves," Probabilistic Engineering Mechanics 23, 359363 (2008).
91. R. Hegger, H. Kantz, and T. Schreiber, "Practical implementation of nonlinear time series methods: The TISEAN package," Chaos: An Interdisciplinary Journal of Nonlinear Science 9, 413435 (1999).
92. S.Y. Tsai, C.P. Chiu, K.C. Chang, and M.D. Wei, "Periodic and chaotic dynamics in a passively Qswitched Nd:YVO4 laser with azimuthal polarization," Optics letters 41, 10541057 (2016).

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