第一部分以四面鏡共振腔搭配腔內黑點來產生環形渦流光束，藉由調控黑點直徑與腔內光束直徑的比值參數M去調控拓樸荷數大小，最多能做到l=4的渦流光束。第二部分以三面鏡系統搭配軸稜錐對，藉由調控軸稜追位置與輸出耦合鏡位置等參數來改變腔內光束之光路做出可調直徑與發散角之環性光束，並在特定操作位置具有圓柱向量光束偏振特性。

Summary
In the first part of experiment, we set up a four mirror laser cavity, by adds a 250 μm defect spot in the middle of two focal lens to generate hollow beams which have optical vortex, by adjust the output couple’s distance from lens 2 or fix the position of output couple and move the defect spot along the propogation axis, we can adjust the ratio of defect spot diameter and cavity spot size, consider the different ratio we can produce vortex beam with different magnitudes topology charges, and the highest we can produce a vortex beam which topology charge equal to 4. In the second part, we set up a three mirrors laser cavity, by adds a γ equal to 175° axicon pairs which head to head in the cavity to generate hollow beams ,by move the axicon pairs close to or adjuste the output couple away from lens 2, the average diameter and divergence angle of hollow beams will become bigger continuously, the most important, in the operating position where z_a=30.3 cm, d = 4.9 cm, we produce a hollow beam which divergency angle relatively small, no multiple Bessel rings effect and have azimuthal polarization(AP) characteristics.
Key word : Hollow beam、Optical vortex beam、Cylindrical vector beam
Introduction
As the name of hollow beam, it has annular intensity distribution, and doesn’t exist intensity in the center of beam, according to different optical characteristic we can divide into two hollow beams, the vortex beam and cylindrical vector beam. Optical vortex beam is a special hollow beams, different from normal plan wave, it has the amplitude and phase singularities in the center of beam, and the wavefront which rotates around the propogation direction continuously, called helical wavefront, it’s poynting vector perpendicular to wavefront also rotate with propogation axis. thus the phase will dependence of azimuthal degree in the transverse plan, written in exp⁡(ilϕ), where ϕ is the angular coordinate from 0 to 2π and l is integer called topology charge. The vortex beam have orbital angular momentum (OAM), and the value of OAM is (_-^+)lℏ per photon. In the general solid state laser system, this king of vortex beam called Laguerre-Gaussian mode.
On the other hand, different from normal linear polarization, circular polarization which the polarization is homogeneous distribution in the free space, the cylindrical vector beam which the polarization is dependence of spatial distribution, it’s polarization is cylindrical symmetrical arrangement in the beam cross section, according to arrangement, divide into two kinds : azimuthal polarization(AP) and radial polarization(RP).
In recent years, the hollow beam with special properties is very popular research topics and has been developed of potential applications, like particals trapping and manipulation、resolution microscope、materials processing、quantum information.

EXPERIMENT
In the first part of experiment, we set up a four mirror laser cavity with Nd:YVO4 gain medium, by adjusting the three part of cavity length for 5.1 cm, 14.6 cm and variable length d = 5.8 cm, the cavity is in critical situation, the varity of cavity spot size is very slow in the middle of two focal lens, we can see the beam as plan wave in this rigion, and then put a 250 μm defect spot 13.1 cm distance from lens 2, in this condition, we generate a hollow beam, to observerse and verificate it’s phase structure have votex phase, we set up a Mach-Zehnder interferometer, after this hollow beam interfere with a plan wave we confirm it is a optical vortex beam which topology charge is 2. After, we move the output couple away from lens 2 to change the cavity spot size,so that we can change the ratio of defect spot diameter to cavity spot size, when we set the d from 6.2 cm to 6.8cm, in this cavity length, the cavity spot sizes are smaller compare to d is 5.8, so that we can produce a hollow beam with topology charge is 1. To generate the higer topology charge, we set cavity length d = 6.8 cm, in this cavity length, there exist a continuous change cavity spot size from about 255 μm to 480 μm, so we move defect spot along propogation axis in this rigion we can generate a topology charge adjustable vortex beam from

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