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Journal of Applied Physics

LP 01 -mode output beam from a micro-sized hollow optical fiber: A simple theoretical model and its applications in atom optics

Jianping Yin, Yifu Zhu

Published Mar 1, 1999• 18 citations
Publisher

Abstract

We calculate electric field distributions of the output beam from a LP01 mode in a micro-sized hollow optical fiber under the Fresnel approximation and find that the output beam characteristics in free space is similar to that of a TEM01* doughnut laser beam. We propose a simple theoretical model, a modified TEM01* doughnut beam, to simulate the free-space output beam from the LP01 mode in hollow fibers, and discuss potential applications of the LP01-mode output beam in atomic guiding, funneling, cooling, and trapping. Our study shows that this model is in good agreement with the numerical results derived from the Fresnel diffraction theory (except near the weak first-order diffraction ring around the zero-order diffraction peak). The model can be conveniently used to calculate the optical potential, gradient force, light-induced acceleration, spontaneous-emission rate, and quantum tunneling loss in atomic guiding, funneling, and trapping with the LP01-mode output beam in free space. It can be also used to study the optical-potential evaporative cooling of cold atoms in a gravito-optical trap constructed by the LP01-mode output beam.

DOI
10.1063/1.369608

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Acta Physica Sinica•Jan 1, 2016•3 citations
We calculate electric field distributions of the output beam from a LP01 mode in a micro-sized hollow optical fiber under the Fresnel approximation and find that the output beam characteristics in free space is similar to that of a TEM01* doughnut laser beam. We propose a simple theoretical model, a modified TEM01* doughnut beam, to simulate the free-space output beam from the LP01 mode in hollow fibers, and discuss potential applications of the LP01-mode output beam in atomic guiding, funneling, cooling, and trapping. Our study shows that this model is in good agreement with the numerical results derived from the Fresnel diffraction theory (except near the weak first-order diffraction ring around the zero-order diffraction peak). The model can be conveniently used to calculate the optical potential, gradient force, light-induced acceleration, spontaneous-emission rate, and quantum tunneling loss in atomic guiding, funneling, and trapping with the LP01-mode output beam in free space. It can be also used to study the optical-potential evaporative cooling of cold atoms in a gravito-optical trap constructed by the LP01-mode output beam.
The diffracted near field distribution from an LP 01 mode in a hollow optical fibre was recently calculated using a scalar model based on the weakly waveguiding approximation (Yoo et al 1999 J. Opt. B: Quantum Semiclass. Opt. 1 364 ). It showed a dominant Gaussian-like distribution with an increased axial intensity in the central region (not a doughnut-like distribution), so the diffracted output beam from the hollow fibre cannot be used to form an atomic funnel. Using exact solutions of the Maxwell equations based on a vector model, however, we calculate the electric field and intensity distributions of the HE 11 mode in the same hollow fibre and study the diffracted near- and far-field distributions of the HE 11 -mode output beam under the Fresnel approximation. We analyse and compare the differences between the output beams from the HE 11 and LP 01 modes. Our study shows that both the near- and far-field intensity distributions of the HE 11 -mode output beam are doughnut-like and can be used to form a simple atomic funnel. However, it is not suitable to use the weakly waveguiding approximation to calculate the diffracted near-field distribution of the hollow fibre due to the greater refractive-index difference between the hollow region ( n 0 = 1) and the core ( n 1 = 1.45 or 1.5). Finally, the 3D intensity distribution of the HE 11 -mode output beam is modelled and the corresponding optical potentials for cold atoms are calculated. Some potential applications of the HE 11 -mode output beam in an atomic guide and funnel are briefly discussed.
Using exact solutions of Maxwell equations based on the vector model, we calculate the diffracted near- and far-field distributions of the HE 11 -mode output beam from a micron-sized hollow optical fibre under the Fresnel approximation, and compare the differences between the HE 11 - and LP 01 -mode output beams. Our study shows that it is unsuitable to calculate the diffracted near-field distribution of the hollow fibre by using weakly waveguiding approximation, and the near- and far-field intensity distributions of the HE 11 -mode output beam are doughnut-like, which can be used to form a simple atomic funnel as it is blue-detuned.
Atom guiding in an atomic funnel is very useful for many interesting atom optical experiments requiring the precise control of atomic motion. We have obtained a doughnut-shaped laser beam by coupling a Ti:sapphire laser into a hollow core optical fiber and collimating the output laser beam of the fiber with a microscope objective lens. Using such a doughnut-shaped laser beam [2 mm inner diameter and a 5 mm outer diameter at the trapping position (about 1m away from the objective lens)l, we have guided the trapped cold Rb atoms in the atomic funnel.
We analyze the optical potential for atom guidance in a dark hollow laser beam and compare it with that generated by the evanescent wave in a micrometer-sized hollow optical fiber. We calculate dependence of the optical potential on various parameters: radial position r, laser–atom detuning Δ, beam power P0, and propagation distance Z. We experimentally generated a dark hollow laser beam from a hollow optical fiber with a 7-μm hole diameter and obtained a coupling efficiency of ∼50% for the LP01 mode. Our study shows that a dark hollow laser beam can produce an optical potential deep enough to guide cold atoms from a magneto-optical trap.
We propose an atomic funnel consisting of a dark hollow, divergent laser beam and an evanescent light in a short micron-sized hollow optical fiber. The cold atoms extracted from a magneto-optical trap experience effective Sisyphus cooling in the dark hollow beam. We calculate the potential barriers for atomic guiding in the evanescent light and the dark hollow beam, and analyze the atomic losses during the guiding and funneling process. Our results show that the equilibrium three-dimensional root-mean-square momentum of about $4.5\ensuremath{\Elzxh}k$ (temperature $\ensuremath{\sim}2.5\ensuremath{\mu}\mathrm{K}$) and the funneling efficiency of about 95% could be obtained. A low-velocity, intense coherent atomic beam can be generated in this funnel scheme and its potential applications in atom optics are briefly discussed.
In order to generate a submicron localized hollow laser beam and realize the more efficient laser cooling and trapping of a single atom, a simple and promising scheme with using the system of a single mode fiber a circle binary phase plate and a microlens is proposed in this paper. From Rayleigh-Sommerfeld diffraction theory, the intensity distribution of the generated localized hollow laser beam near the focal plane and its propagating properties in free space are calculated. Also, the dependences of the dark-spot size of the localized hollow beam on the mode radius of single mode fiber and the focal length of the mocrolens are studied. The calculated results show that the intensity distribution of the localized hollow beam presents approximately symmstrical distribution near the focal plane. In the center of the focal plane, the light intensity is 0 and increases gradually around it. So a closed spherical light field (i.e., localized hollow laser beam) with a radius of 0.4 m is generated. The calculated results also show that the dark-spot size of the localized hollow laser beam decreases with the increasing of the microlens focal length and the decreasing of the single mode fiber mode radius. So proper parameters of this optical system can be chosen to generate localized hollow laser beams with different sizes for various applications. When the localized hollow laser beam is blue detuned, atoms will be trapped in the minimum light filed. If a repumping laser beam is applied, the trapped atoms will be also cooled by the intensity-gradient Sisyphus cooling. In this paper, we build a device for trapping and cooling a single atom by using the generated blue detuned submicron localized hollow laser beam. We study the dynamical process of intensity-gradient cooling of a single 87Rb atom trapped in the localized hollow beam by Monte-Carlo method. Our study shows that a single 87Rb atom with a temperature of 120 K (the corresponding momentum is 30ħk) from a magneto-optical trap (MOT) can be directly cooled to a final tempreture of ～ 5.8 K (the corresponding momentum is ～ 6.6ħk). So an ultracold single atom is generated and trapped in our submicro localized hollow beam. This device for obtaining ultralcold single atom can be widely uesd in the regions of the optical physics, the atom and molecule optics, such as the detecting of the fundamental physical parameters, realizing the quantum computer, studying the cold collision of singe atoms, and realizing the single atom laser.