【作者】 夏勇；

【导师】 印建平；

【作者基本信息】 苏州大学 ， 光学， 2003， 硕士

【摘要】 从90年代起，各种技术，如几何光学法、模式转换法、光学全息法、计算全息法、横模选择法、中空光纤法、非线性方法等，被相继用来产生暗中空光束，并得到一些很好的实验结果。同时，其他的一些研究小组开展了暗中空光束在光阱与微粒的操纵、中性原子的激光导引、冷却与囚禁以及相干物质波（如玻色-爱因斯坦凝聚，BEC）的操纵与控制等领域的应用研究。本文提出了采用2π位相板法产生聚焦中空光束的新方法。当一束准直的高斯光束通过具有2π位相分布的位相片和一个薄透镜时，这将导致在入射高斯光束中心的完全和部分相消干涉效应，于是在透镜后就会形成一束聚焦中空光束（FHB）。根据菲涅耳衍射理论，我们数值计算了傍轴近似条件下聚焦中空光束的场分布。发现在焦平面之前有一个非常有趣的传播性质，即随着传播距离z的增加，这一聚焦中空光束的暗斑尺寸（DSS）先从另变大然后再变小，最大的暗斑尺寸的位置在z=f/2处。当选择较大的入射准直高斯光束的束腰w₀和较短的薄透镜焦距f时，可以在焦平面上产生一个很小的DSS（或束半径R₀），甚至可以接近衍射极限。经过焦点后，这一聚焦中空光束将以一定的角度发散，它的DSS会变得越来越大，光强度变得越来越弱。同时我们还提出了两种聚焦中空光束的理论模型，一种是修改的TEM₀₁模式的doughnut光束模型，另一种是宽、窄高斯光束模型。从这两种拟合的效果来看，在径向位置-R₀到R₀的范围内，这两种光束模型与数值计算结果拟合的非常好。本文还讨论了这一蓝失谐聚焦中空光束的可能应用。由于这一聚焦中空光束在它的焦平面上具有很小的DSS，可以用来聚焦原子束以形成原子透镜。在焦平面上，聚焦中空光束的DSS越小，光学势越大，相应的最佳失谐量δ越大，这对原子透镜的性能越有利。因为这不仅容易得到高分辨率的原子透镜，而且还可以减少在聚焦中空光束中原子的自发辐射和光子散射效应。同时还考虑了各项象差对聚焦⁸⁵Rb原子束分辨率的影响。如果选取合适的参数，则可得到一焦距为f=3.88um和分辨率约为6A^o的⁸⁵Rb原子透镜。此外，这一蓝失谐的聚焦中空光束还可以用于中性原子的激光冷却与囚禁，甚至用于研究冷原子在聚焦中空光束中的绝热压缩（加热）和绝热膨胀（冷却）过程。更多还原

【Abstract】 Since 1990’s, a variety of methods, such as geometrical optical method, mode-conversion method, optical holographic method, computer-generated holography method, transverse-mode selection method, hollow fiber method and nonlinear optical method, have been used to generate the dark hollow beams （DHBs）. On the other hand, various techniques using the DHBs have been applied in optical traps for microscopic particles, guiding, cooling and trapping for neutral atoms as well as in manipulations and control of coherent matter waves （i.e., Bose-Einstein condensations （BEC）） and so on.In this thesis, we propose a new method to generate a focused hollow laser beam by using an azimuthally-distributed 2π-phase plate and a convergent thin lens. When a collimated-well Gaussian laser beam passes through a 27i-phase plate and then focused by a lens, a focused hollow beam （FHB） will be generated behind the lens, as a result of the completely （r = 0） and partially （r ≠ 0） destructive interference effects around the central region of the beam. From the Fresnel diffraction equation, we calculated the intensity distribution of the FHB in free space, and found that there is an interested propagation property of the FHB before the focal plane. That is, with the increase of the propagation distance z, the dark spot size （DSS） of the FHB is first increased, and then decreased, the DSS has the maximum value at the position of z=-f/2. When a larger waist w of the incident Gaussian beam and a shorter focal length/of the lens are chosen, we can obtain an extremely-small dark spot size of the focused hollow beam, even approach the diffraction limit. After the focal plane, the focused hollow beam propagated according to a constant angle of divergence, the DSS become larger, and the intensity become weaker. We also propose two models to describe the propagation charcteristic of the focused hollowbeam in 3D free space: One is the modified TEM₀₁ mode doughnut beam model, the otheris the width and narrow Gaussian beam model. Our study shows that two models are in good agreement with the numerical results derived from the Fresnel diffraction theoryfrom - R0 to + R0 in the radial position.We discuss some potential applications of the blue-detuned FHB. Due to the extremely-small dark spot size of the focused hollow beam in the focal plane, it can be used to form an atomic lens with a high resolution. In the focal plane of z= 0, the smaller the DSS of the FHB, the higher the optical potential, and the greater the corresponding optimal detuning 8, which are beneficial to atomic lens because it cannot only be profitable to obtain an atomic lens with a higher resolution, but also helpful to reduce the spontaneous emission and photon scattering effects of atoms in the FHB. We considered the effects of the spherical aberration, chromatic aberration, diffusive aberration and diffraction aberration on the atomic lens. In this case, the minimum focal length offocused 85Rb atomic beam is 3.88 (am, the resolution of our atomic lens is 6 angstoms or so.In addition, the blue-detuned FHB can also be used cool and trap neutral atoms, even to study the adiabatic compression （heating） and expansion （cooling） of atoms in the FHB.更多还原