||Generations and nonlinear dynamic behaviors of off-axis modes in Nd-doped laser systems
||Department of Photonics
geometric ring mode
trigonometrical ray tracing
cylindrical vector beam
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 Nd-doped 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 three-mirror cavity configuration to generate the azimuthally polarized laser which is a kind of cylindrical vector beam. Through the birefringence of laser crystal, the o-ray-preferred region was generated at the edge of the stable region. Further combining the modulation system; the period-doubling 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 diffusion-bonded Nd:YVO4/Nd:GdVO4 to generate an azimuthally polarized laser with dual-wavelength.
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 off-axis modes in Nd-doped 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 Dual-wavelength with azimuthal polarization 30
2.3 Summary 36
Chapter 3. Nonlinear dynamic behaviors in off-axis 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
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, 182-184 (1964).
2. J. O'connor, "Unusual Crystal‐Field Energy Levels And Efficient Laser Properties Of Nd:YVO4," Applied physics letters 9, 407-409 (1966).
3. A. Zagumennyĭ, V. Ostroumov, I. A. Shcherbakov, T. Jensen, J. Meyen, and G. Huber, "The Nd: GdVO4 crystal: a new material for diode-pumped 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, 1794-1800 (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 Solid-State 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 Q-switched laser output of LD-end-pumped 1.06 μm c-cut Nd: LuVO4 laser," Optics express 15, 3206-3211 (2007).
7. H. Yu, H. Zhang, and J. Wang, "Growth and Characterization of Vanadate Laser Crystals," Acta Physica Polonica A 124, 301-304 (2013).
8. J. Sulc, H. Jelínková, J. K. Jabczynski, W. Zendzian, J. Kwiatkowski, K. Nejezchleb, and V. Skoda, "Comparison of diode-side-pumped triangular Nd: YAG and Nd: YAP laser," in Solid State Lasers XIV: Technology and Devices, (International Society for Optics and Photonics, 2005), 325-335.
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, 920-925 (2007).
10. A. Minassian, B. Thompson, G. Smith, and M. Damzen, "High-power scaling (> 100 W) of a diode-pumped TEM00 Nd: GdVO4 laser system," IEEE Journal of selected topics in quantum electronics 11, 621-625 (2005).
11. J. Tung, T. Wu, H. Liang, and Y. Chen, "Precise measurement of the thermo-optical coefficients of various Nd-doped vanadates with an intracavity self-mode-locked scheme," Laser Physics 24, 035804 (2014).
12. W. Koechner, "Thermal lensing in a Nd: YAG laser rod," Applied optics 9, 2548-2553 (1970).
13. Z. Cai, H. Xu, and G. Stéphan, "Bipolarization and multiwavelength diode-pumped Nd: YVO4 microchip laser," Optics communications 135, 295-299 (1997).
14. A. E. Siegman, Lasers (University Science Books, 1986).
15. D. Herriott, H. Kogelnik, and R. Kompfner, "Off-axis paths in spherical mirror interferometers," Applied Optics 3, 523-526 (1964).
16. I. Ramsay and J. Degnan, "A ray analysis of optical resonators formed by two spherical mirrors," Applied optics 9, 385-398 (1970).
17. B. Sterman, A. Gabay, S. Yatsiv, and E. Dagan, "Off-axis folded laser beam trajectories in a strip-line CO2 laser," Optics letters 14, 1309-1311 (1989).
18. J. Dingjan, M. van Exter, and J. Woerdman, "Geometric modes in a single-frequency Nd: YVO4 laser," Optics communications 188, 345-351 (2001).
19. C. Chen, P. Huang, and C. Kuo, "Geometric modes outside the multi-bouncing 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 ray-wave duality in solid-state lasers with off-axis 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, 1559-1566 (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 off-axis beams in an axially pumped solid-state laser," Optics Express 12, 3459-3464 (2004).
24. K. V. Volodchenko, M. S. Kurdoglyan, C.-M. Kim, and G. U. Kim, "Observation and investigation of off-axis modes in a high-power Nd: YAG laser," Applied optics 43, 4768-4773 (2004).
25. Q. Zhan, "Cylindrical vector beams: from mathematical concepts to applications," Advances in Optics and Photonics 1, 1-57 (2009).
26. S. Sato, Y. Harada, and Y. Waseda, "Optical trapping of microscopic metal particles," Optics letters 19, 1807-1809 (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, 1839-1841 (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, 329-334 (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, 2234-2239 (1990).
34. M. Bashkansky, D. Park, and F. K. Fatemi, "Azimuthally and radially polarized light with a nematic SLM," Optics express 18, 212-217 (2010).
35. M. R. Beversluis, L. Novotny, and S. J. Stranick, "Programmable vector point-spread function engineering," Optics express 14, 2650-2656 (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, 1468-1470 (2007).
37. D. Pohl, "Operation of a ruby laser in the purely transverse electric mode TE01," Applied Physics Letters 20, 266-267 (1972).
38. 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," Optics letters 31, 2151-2153 (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 c-cut 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, 3063-3065 (2005).
42. J.-F. Bisson, J. Li, K. Ueda, and Y. Senatsky, "Radially polarized ring and arc beams of a neodymium laser with an intra-cavity axicon," Optics Express 14, 3304-3311 (2006).
43. M. A. Ahmed, M. Haefner, M. Vogel, C. Pruss, A. Voss, W. Osten, and T. Graf, "High-power radially polarized Yb: YAG thin-disk laser with high efficiency," Optics express 19, 5093-5103 (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, 234-236 (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 thin-disk lasers," Optics letters 32, 3272-3274 (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 higher-order transverse mode operation of a radially polarized Nd: YAG laser using an annularly reflectivity-modulated photonic crystal coupler," Optics letters 33, 2278-2280 (2008).
49. I. Moshe, S. Jackel, and A. Meir, "Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects," Optics letters 28, 807-809 (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, 2443-2445 (2013).
51. F. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, "Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser," Physical Review Letters 49, 1217 (1982).
52. D. Ivanov, Y. I. Khanin, I. Matorin, and A. Pikovsky, "Chaos in a solid-state laser with periodically modulated losses," Physics Letters A 89, 229-230 (1982).
53. N. V. Kravtsov and E. G. e. Lariontsev, "Lasing regimes in solid-state ring lasers with modulated parameters," Quantum Electronics 34, 487 (2004).
54. A. N. Pisarchik, R. Jaimes-Reátegui, R. Sevilla-Escoboza, G. Huerta-Cuellar, 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, 19850-19859 (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 all-solid-state laser with modulation of losses," Optics letters 41, 3010-3012 (2016).
57. J. Ahuja, D. B. Nalawade, J. Zamora-Munt, R. Vilaseca, and C. Masoller, "Rogue waves in injected semiconductor lasers with current modulation: role of the modulation phase," Optics express 22, 28377-28382 (2014).
58. S. Perrone, R. Vilaseca, J. Zamora-Munt, 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, 1057-1060 (2014).
63. A. Montina, U. Bortolozzo, S. Residori, and F. Arecchi, "Non-Gaussian 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. Zamora-Munt, 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. Zamora-Munt, 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 normal-dispersion fiber laser," Optics letters 40, 1366-1369 (2015).
69. D. V. Churkin, O. A. Gorbunov, and S. V. Smirnov, "Extreme value statistics in Raman fiber lasers," Optics letters 36, 3617-3619 (2011).
70. S. Randoux and P. Suret, "Experimental evidence of extreme value statistics in Raman fiber lasers," Optics letters 37, 500-502 (2012).
71. C. Lecaplain, P. Grelu, J. Soto-Crespo, and N. Akhmediev, "Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser," Physical review letters 108, 233901 (2012).
72. J. Soto-Crespo, P. Grelu, and N. Akhmediev, "Dissipative rogue waves: extreme pulses generated by passively mode-locked 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 Kerr-lens mode-locked 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, 4449-4451 (2011).
75. 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," 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 all-solid-state 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 solid-state laser with a periodically modulated pump," Optics letters 9, 561-563 (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, 423-426 (2017).
80. K. Lünstedt, N. Pavel, K. Petermann, and G. Huber, "Continuous-wave simultaneous dual-wavelength operation at 912 nm and 1063 nm in Nd: GdVO4," Applied Physics B 86, 65-70 (2007).
81. Y.-F. Chen, "cw dual-wavelength operation of a diode-end-pumped Nd: YVO4 laser," Applied Physics B 70, 475-478 (2000).
82. B. Wu, P. Jiang, D. Yang, T. Chen, J. Kong, and Y. Shen, "Compact dual-wavelength Nd: GdVO4 laser working at 1063 and 1065 nm," Optics express 17, 6004-6009 (2009).
83. Y. Lü, J. Xia, H. Liu, and X. Pu, "Simultaneous triple 914 nm, 1084 nm, and 1086 nm operation of a diode-pumped 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 high-power terahertz beating in a dual-wavelength synchronously mode-locked laser with dual gain media," Optics letters 39, 1477-1480 (2014).
85. Y. Huang, H. Cho, Y. Tzeng, H. Liang, K. Su, and Y. Chen, "Efficient dual-wavelength diode-end-pumped laser with a diffusion-bonded Nd: YVO 4/Nd: GdVO 4 crystal," Optical Materials Express 5, 2136-2141 (2015).
86. Y.-J. Huang, Y.-S. Tzeng, C.-Y. Tang, and Y.-F. Chen, "Efficient dual-wavelength synchronously mode-locked 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, 56-62 (2015).
87. Y. Huang, H. Cho, Y. Tzeng, H. Liang, K. Su, and Y. Chen, "Efficient dual-wavelength diode-end-pumped laser with a diffusion-bonded Nd: YVO4/Nd: GdVO4 crystal," Optical Materials Express 5, 2136-2141 (2015).
88. Y. Huang, H. Cho, K. Su, and Y. Chen, "Dual-Wavelength Intracavity OPO With a Diffusion-Bonded Nd: YVO4/Nd: GdVO4 Crystal," IEEE Photonics Technology Letters 28, 1123-1126 (2016).
89. P. Kjeldsen, "A sudden disaster-in Extreme Waves," Rogue Waves 2000, 19-35 (2001).
90. S. Aberg and G. Lindgren, "Height distribution of stochastic Lagrange ocean waves," Probabilistic Engineering Mechanics 23, 359-363 (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, 413-435 (1999).
92. S.-Y. Tsai, C.-P. Chiu, K.-C. Chang, and M.-D. Wei, "Periodic and chaotic dynamics in a passively Q-switched Nd:YVO4 laser with azimuthal polarization," Optics letters 41, 1054-1057 (2016).