Generation Of Vectorial Elliptic Hollow Beams And Their Applications

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.