本文在傳統雷射共振腔之中置入缺陷，製造出一個光波無法穿越的區域，進而造成雷射模態結構產生改變。實驗結果證實共振腔內的缺陷可以成為一個全新調整雷射模態的因素。

　　一維 Hermite-Gaussian (HG) 模態實驗結果證實操控金屬細線在共振腔內的位置可使HG模態轉換為落在幾何軌跡上的光束。利用該方式得到的雷射模態與透過離軸激發方式得到的結果有很好的對應。以HG模態作為基底進行數值分析，缺陷共振腔產生的模態也與HG簡併態的疊加結果有著良好的對應。

　　二維HG模態實驗結果亦顯示透過金屬細線形成的缺陷共振腔可操控雷射模態落在利薩如軌跡之上。更進一步發現共振腔缺陷所在的位置與相位有著密切的關係。藉由控制缺陷的位置可以有效的控制利薩如圖形的相位。

　　缺陷共振腔有別於以往盡可能降低腔內的干擾，以金屬細線影響雷射光在腔內的傳播，最後達到改變雷射模態結構的目的。實驗結果顯示了以金屬細線作為缺陷能有效操控雷射模態，成為一個重要的實驗參數。

In this research, we applied an additional mental wire into laser cavity served as an artificial defect to block the original light path. We’ve found this adjustment may interfere with output laser mode.

In the experiment of one-dimensional Hermite-Gaussian (HG) modes with an obstacle, the trajectory change matches the experimental results and numerical simulation of an off-axis laser perfectly.

Previous research suggests that if the ratio of L-mode and T-mode within a degenerate resonator is a rational number, than the superposition of each 2D HG modes will be localized on Lissajous parametric surfaces. However, an external obstruction may disturb the formation of Lissajous pattern. Thus, the position of the obstacle plays an important role in two-dimensional HG modes experiments, not only the Lissajous pattern matches with 2D off-axis laser, we also can control the phase of Lissajous pattern by fine tuning the opaque-wire.

Unlike traditional laser experiments, which usually try to reduce the number of defaces in laser cavity as much as possible, our newly developed technique becomes another useful method which also can manipulate laser modes.

參考文獻
[1] M. Nisoli, S. De Silvestri, O.Svelto, R. Szipocs,K. Ferencz, Ch.Spielmann, S. 　　　　　　　　　　　　　Sartania, and F.KrausZ, “Compression of high-energy laser pulses below 5 fs”
Opt. Lett. 22, 522(1997).
[2] Andrews, David L “Structured light and it’s applications: An introduction to phase-structured beams and nanoscale optical forces” Academic Press.
[3] S. J. van Enk ,G. Nienhuis “Eigenfunction description of laser beams and orbital
angular momentum of light,” Opt. Commun. 94, 147–158 (1992).
[4] A. Ashkin “Acceleration and trapping of particlas by radiation pressure” Phys.
Rev. Lett. 24, 156 (1970).
[5] A. Ashkin, J.M. Dziedzic, and T. Tamane, “Optical trapping and anipulation of
single cells using infrared laser beams” Nat. 330, 6150(1987).
[6] Steven M. Block, Lawrence S. B. Goldstein, Bruce J. Schnapp, ” Bead movement by single kinesin molecules studied with optical tweezers” Nat. 348, 348 - 352
(22 November 1990).
[7] G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital
angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[8] Eleonora Nagali, Fabio Sciarrino, Francesco De Martini, Lorenzo Marrucci, Bruno Piccirillo, Ebrahim Karimi, and Enrico Santamato, “Quantum Information Transfer from Spin to Orbital Angular Momentum of Photons” Phys. Rev. Lett. 103,
013601(2009).
[9] D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Effect of high-dimensional entanglement of Laguerre-Gaussian modes in parametric
downconversion,” J. Opt. Soc. Am. B 26(4), 797–804 (2009).
[10] J. Fu, Z. Si, S. Tang, and J. Deng “Classical simulation of quantum entanglement using optical transverse modes in multimode waveguides,” Phys. Rev. A 70(4),
042313 (2004).
[11] K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, “Entangling the spatial properties of laser beams”
Science 321(5888), 541–543 (2008).
[12] R. K. Bhaduri, Shuxi Li, K. Tanaka and J. C. Waddington, “ Quantum gaps and
classical orbits in a rotating two-dimensional harmonic oscillator,” J. Phys. A: Math. Gen. 27 L553 (1994).
[13] G. Nienhuis and L. Allen, “Paraxial wave optics and harmonic oscillators,” Phys.
Rev. A 48(1), 656–665 (1993).
[14] N.G. van Kampen, “The Expansion of the Master Equation” Adv. Chem. Phys.
34, 245 (1976)
[15] A. E. Kaplan, I. Marzoli, W. E. Lamb, Jr., and W. P. Schleich, “Multimode interference: Highly regular pattern formation in quantum wave-packet evolution,”
Phys. Rev. A 61(3), 032101 (2000).
[16] Shu-Chun Chu, Yun-Ting Chen, Ko-Fan Tsai , “Generation of high-order Hermite-Gaussian modes in end-pumped solid-state lasers for square vortex array
laser beam generation” Opt. Express 7128 (2012)
[17] A. Ramsay, J. J. Degnan, “A Ray Analysis of Optical Resonators Formed by
Two Spherical Mirrors” Appl. Opt. 385 (1970)
[18] http://www.solgel.com/articles/Sept00/Huignard.htm
[19] Xudong Li, Xin Yu, Fei Chen, Renpeng Yan, Junhua Yu, Deying Chen “Laser
properties of continuous-grownNd:GdVO4/GdVO4 and Nd:YVO4/YVO4 composite crystals under direct pumping” Opt. Express 12869
[20] 李季達,「我國DPSSSSL 雷射產業逐漸成形」光連：光電產業與技術情報, 25期,24-31(2000)
[21] 丁勝懋, 雷射工程導論(4th ed.) (2001)
[22] 國立中央大學晶體生長與分析實驗室。http://lhpg138.me.ncu.edu.tw
[23] Mark Chawla, Chris Baird, “INSIDE A LASER CAVITY -- EXPLORING STABILITY,POLARIZATION, AND MODES” OPTICS AND LASER PHYSICS
　LABORATORY #10 pp.36-41
[24] Peter W. Milonni, Joseph H. Eberly, Laser Physics: Laser Resonators and
　Gaussian Beams, New York (1988)
[25] H. Kogelnik and L. Tigye, Applied: Laser beams and resonator, optics
　infobase(1966)
[26] Peter W. Milonni, Joseph H. Eberly, “Laser Physics,” p.276, Wiley
[27] Hodgson, Norman and H. Weber, Laser resonators and beam propagation.
　Springer(2005)
[28] 楊寶賡。雷射工程。新文京開發出版股份有限公司(2010)
[29] Sasada Lab.Department of Physics, Keio University, “Light possessing orbital angular momenta,” http://www.phys.Keio.ac.jp/guidance/labs/sasada/research/
　orbangmom-en.htnl (2014)
[30] Y. F. Chen, C. H. Jiang, Y. P. Lan and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity” Phys. Rev.
　A 69, 053807 (2007)
[31] T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang “Three-dimensional coherent optical waves localized on trochoidal parametric surfaces” Phys. Lett. 101, 233901
　(2008)