本研究由幾何模態出發，由以往平凹腔形式的離軸幾何模態的基本知識，架設出四面鏡系統的幾何模態雷射，產生正、反向軌跡模態，而此環形路徑會隨輸出偶合鏡的推移，正、反向光束路徑會漸漸的重和為Hermite-Gaussian mode輸出，探討四面鏡系統下幾何模態雷射基本輸出特性斜效率、發散角與腔內光束路徑。
本研究另一重點在探討調製泵源下的非線性動力學行為，探討幾模模態與Hermite-Gaussian mode在外加弦波調製，兩者都會去探討其週期路徑與混沌路徑，固定調製頻率，調變調製深度的情況下，去觀察混沌閥值的高低與端事件的發生。

In this thesis, we study the nonlinear dynamics of geometry-mode laser by pump modulation. The main researches include the geometry mode and laser system with pump modulation. Without using a plano - concave cavity, we construct a four-mirror Nd:YVO4 laser with a geometry path in cavity. In our experiments we have studied the efficiency of output power, off-axis path in laser cavity, divergence angle of geometric profile. On the other hand, we discuss the chaotic characteristics by pump modulation. Beside the ordinary bifurcation and Lyapunov analysis, we find a particular behavior occur in chaotic system what are extreme events.

[1]D. Herriott, H. Kogelnik, and R. Kompfner , “Off-Axis Paths in Spherical Mirror Interferometers”, Appl. Opt. 3(4) 523 (1964).
[2]I.-A. Ramsay, J.-J. Degnan, “A Ray Analysis of Optical Resonators Formed by Two Spherical Mirrors”, Appl. Opt. 9 385 (1970).
[3]C. Palma, “Complex dynamics of a beam in a Gaussian cavity”, Optics Comm. 129, 120-133. (1996).
[4]M.-D. Wei, W.-F. Hsieh, C.-C. Sung, “Dynamics of an optical resonator determined by its iterative map of beam parameters”, Optics Comm. 146, 201-207. (1998).
[5]A.-A. Hnilo, “Self-mode-locking Ti:sapphire laser description with an iterative map”, J. Opt. Soc. Am. B 12 718-725. (1995).
[6]L.-M. Sánchez, A.-A. Hnilo, “Optical cavities as iterative maps in the complex plane”, Optics Comm. 166, 229-238. (1999).
[7]J. Dingjan, M.-P. van Exter, J.-P. Woerdman, “Geometric modes in a single-frequency Nd:YVO4 laser”, Optics Comm. 188, 345-351. (2001).
[8]H.-H. Wu, “Formation of off-axis beams in an axially pumped solid-state laser”, Opt. Express 12, 3459-3464. (2004).
[9]E. Ott, et al., “Chaos in Dynamical Systems(2st ed)”, New York：Cambridge University Press, (2002).
[10]D. Gulick, et al., “Encounter with chaos”, New York：McGraw-Hill, (1992).
[11]E.-N. Lorenz, “Deterministic Nonperiodic Flow”, J. Atmos. SCi. 20 130. (1983).
[12]Y.-F. Chen, T.-M. Huang, K.-H. Lin, C.-F. Kao, C.-L. Wang, S.-C. Wang, “Analysis of the effect of pump position on transverse modes in fiber-coupled laser diode end pumped lasers”, Opt. Comm. 136, 399. (1997).
[13]H. Kogelnik,”On the propagation of Gaussian beams of light through lens-like media including those with a loss or gain variation,”Appl. Opt. 4,1562-1569 (1965).
[14]M.-D. Wei and W.-F. Hsieh, “Cavity-configuration-dependent nonlinear dynamics in Kerr-lens mode-locked lasers”, J. Opt. Soc. Am. B 17, 1335
-1342. (2000).
[15]C.-H. Chen, M.-D. Wei, and W.-F. Hsieh, “Beam-propagation-dominant instability in an axially pumped solid-state laser near degenerate resonator configurations”, J. Opt. Soc. Am. B 18, 1076-1083, (2001).
[16]C. Metayer, A. Serres, E.-J. Rosero, W. A. S. Barbosa, F. M. de Aguiar, J. R. Rios Leite, , and J. R. Tredicce, “Extreme events in chaotic lasers with modulated parameter”, Opt. Express 22, 19850-19859. (2014).
[17]U. F. de Pinho, P. C. Liu, and C. E. P. Ribeiro, “ Freak waves at Campos Basin, Brazil,” Geofizika 21, 53 (2004).
[18]R. Meucci, A. Poggi, F. T. Arecchi, and J. R. Tredicce, “Dissipativity of an optical chaotic system characterized via generalized multistability”, Opt. Comm. 65, 151–156 (1988).