Generation Of Focused Hollow Beam By A 2π-phase Plate And Its Atomic Lens

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 2Ï€-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.