【作者】 李会容；

【导师】 印建平；

【作者基本信息】 华东师范大学 ， 光学， 2011， 博士

【摘要】 矢量椭圆空心光束不仅具有一般空心光束的优点,而且具有独特的传输特性、偏振特性和分数的轨道角动量,在原子分子物理、原子分子光学、光学测量、光信息处理、生物光子学、生物医学、纳米科技、材料科学等领域都有广阔的应用前景。随着人们对光束角动量的认识,具有角动量的光束在光学镊子、光学扳手、微机械马达、纳米科技、量子保密通信、光信息存储等领域也有重要应用。而无衍射光束由于其传输不变性,一直是人们追求的热点之一。本文致力于自聚焦矢量椭圆空心光束和无衍射矢量椭圆空心光束的产生及其应用的理论研究。首先,我们基于麦克斯韦方程的矢量模型,采用马提厄函数对椭圆介质空心光纤中传输的部分椭圆空心模式进行了详细研究；我们的研究表明：椭圆空心光纤中可以传输一些椭圆空心模式,并且光纤中传输的单个模式的平均光子角动量为零,而双模传输可以获得随传输距离正弦变化的平均光子角动量。在此基础上,我们利用椭圆空心光纤中传输的单模衍射输出,产生了角动量为零的矢量椭圆空心光束；并利用椭圆空心光纤中的双模衍射输出,产生了具有位置依赖的分数角动量的矢量椭圆空心光束。得到的两种矢量椭圆空心光束都具有自聚焦效应,光束在穿过其自聚焦平面时,椭圆长轴和短轴将发生交换。此外,两种矢量椭圆空心光束都具有位置依赖的任意偏振态。接着,我们提出了一种采用双模传输的椭圆空心光纤和圆锥形透镜构成的光学系统来产生矢量的准马提厄空心光束的新方案。我们成功得到了一束在长达1m的传输距离内近似无衍射的椭圆空心光束,并且证明了这种光束是一种矢量准马提厄空心光束。研究表明：产生的矢量准马提厄空心光束在1.2～2.2m的区域内具有传输不变的光强分布(即无衍射特性)和随传输距离周期性旋转的径向依赖的偏振态,并且在此区域内光束中心的椭圆环具有传输不变的分数轨道角动量。此外,我们通过数值拟合,给出了描述矢量准马提厄空心光束在自由空间的光强分布和轨道角动量分布的简单表达式。最后,本文还对产生的矢量椭圆空心光束在原子分子光学中的应用进行了理论研究。我们首先讨论了产生的自聚焦矢量椭圆空心光束在原子透镜中的应用,计算了激光失谐量和原子束的初始速率对原子透镜像差的影响。当失谐量为70GHz,原子束的初始速率为28ms时,总的像差达到最小,为26.2nm,远低于光波的衍射极限。并且我们产生的矢量椭圆空心光束在自聚焦过程中始终保持中心光强为零,十分适合于用作高分辨的原子透镜。此外,蓝失谐的矢量准马提厄空心光束在导引冷原子或冷分子的同时,可以实现对冷原子或者冷分子的旋转操控。85Rb原子在矢量准马提厄空心光束中运动的平均旋转角频率与原子在光场中所处的初始位置和入射激光的功率大小有关。初始位置距离光束中心较近的原子其平均旋转角频率较大,入射光功率较大时,原子的平均旋转频率也较大。我们清楚地看到了光束的轨道角动量对原子运动轨迹的明显扭转。重氨分子在矢量准马提厄空心光束中的质心运动也与在光束中所处的初始位置有关,当处于特定初始位置时,分子会沿椭圆形轨道作螺旋进动。此外,在矢量准马提厄空心光束中重氨分子的平均旋转角频率很高,可达9.33kHz。更多还原

【Abstract】 Vectorial elliptical hollow beams not only have the same advantages of common hollow beams, but also unique propagation characteristics, polarization states and fractional orbital angular momentum. They have some wide applications in atomic and molecular physics, atomic and molecular optics, optical measurement, optical information processing, bio-photonics, bio-medical, nanotechnology and materials science, etc. Light beams with angular momentum have also important applications in optical tweezers, optical spanner, micro-mechanical motors, nanotechnology, quantum cryptography and optical information storage, etc. In addition, due to the propagation invariance, diffraction-free beams have been one of the hot research topics in nowadays. This thesis is dediated to the study of production of vectorial elliptical hollow beams with self-focusing effect or diffraction-free property and their applications.Firstly, based on the vector model of Maxwell’s equations, we study some elliptic hollow modes guided in an elliptic dielectric hollow fiber by using Mathieu functions. Our study shows that there are some closed elliptic hollow modes guided in the elliptical hollow fiber, and the angular momentum of a single mode in the elliptical hollow fiber exactly equals zero, however, the synthesized dual-mode field has a fractional angular momentum, which oscillates in a sinusoidal manner along the axis of the fiber. Then, we proposed a handy scheme to generate a vectorial elliptic hollow beam without angular momentum by a single mode output from the elliptic hollow fiber, and a vectorial elliptic hollow beam with a position-dependent fractional angular momentum by a dual-mode output from the fiber. Both vectorial elliptic hollow beams have a self-focusing effect in near field, and the directions of the major and minor axes of the elliptical intensity profile will be interchanged after the self-focusing plane. Both vectorial elliptic hollow beams have a position-dependent arbitrary polarization.Secondly, we propose a promising and practical scheme to generate a vectorial Mathieu-like hollow beam by using an axicon optical system and a dual-mode elliptic hollow fiber. The intensity and polarization distributions of the beam and its fractional orbital angular momentum are investigated. Our study shows that the generated beam is a vectorial Mathieu-like hollow beam within the propagation region of 1.2～2.2 m, owing an diffraction-free intensity-profile, periodically-rotated polarization property as well as an invariant fractional orbital angular momentum. Some simple but practical formulus to describe three-dimensional propagation characteristics of such a Mathieu-like hollow beam are obtained by fitting its intensity distribution numerically.Finally, we study the applications of the generated vectorial elliptic hollow beam in atomic and molecular optics. By using the self-focusing effect of the elliptic hollow beam, we obtain an atomic lense with a high resolution. Moreover, a blue-detuned vectorial Mathieu-like hollow beam can be used to guide cold atoms and molecules, rotating them meanwhile. When an 85Rb atom is moving in the vectorial Mathieu-like hollow beam, its average rotation angular frequency depends on the initial position and the power of the incident laser. Closer initial position to the beam center or larger incident laser power will result in higher rotation angular frequency. Our study shows that the trajectory of the atom is obviously twisted by the orbital angular momentum of the vectorial Mathieu-like hollow beam. Similarly, the center-of-mass trajectory of a ND3 molecule in the vectorial Mathieu-like hollow beam is also determined by its initial position. And molecules of certain initial position do make spiral precession along the elliptical orbit. The average rotation angular frequency of a ND3 molecule in the vectorial Mathieu-like hollow beam can be up to 9.33kHz.更多还原