Simulating the Interaction between Atom Clouds
and Laguerre-Gaussian Laser Beams

Stefan Evans, John Noé and Harold Metcalf

Laser Teaching Center
Department of Physics and Astronomy
Stony Brook University

Among certain atomic transitions is a class called electric quadrupole transitions, which require properties of the light field that conflict with those of ordinary laser beams. However, certain kinds of beams, including Laguerre Gaussian (LG) beams possessing orbital angular momentum (OAM), satisfy the needed conditions [1,2]. The OAM comes about from the unique helical wave front of these LG beams [3]. The energy flow of the light (Poynting vector) circulates around the beam axis similar to the way water rotates in a whirlpool; the exact center of the beam is a phase singularity and thus has no intensity. LG beams containing such a singularity are often called optical vortex beams. The OAM is quantified by the "topological charge": the number of times the phase varies from 0 to 2π as one moves once around the beam axis in a plane perpendicular to the axis of propagation.

As a first step, we have simulated the effect of partially obstructing such beams in MATLAB, where an optical vortex with dark spots was computed and propagated into the far field. The dark spots caused by small obstructions rotate around the beam axis and become smeared out as the beam propagates. Our preliminary experiments have involved creating optical vortices by means of a vortex phase plate, a manufactured film varying in thickness around a center point so as to transform the incident light beam into a helical wavefront. We obtained high quality vortices after eliminating diffraction artifacts via spatial filtering. We recently passed a order 4 vortex so obtained in the reverse direction through the phase plate to remove the helical phase pattern. In the far field we observed a ring of light with a bright center spot, similar to an Airy pattern.

Our next experimental step is to observe the changes to a vortex beam as obstructions are placed in its path. We plan to understand how these beams interact with clusters of atoms, with regard to the size and location of the obstructions, with the eventual goal of experimenting on the atomic level.

We thank Giovanni Milione (CCNY) for assistance with the MATLAB simulations, and RPC Photonics (Rochester) for providing the VPP-633 vortex phase plate.


[1] V. E. Lembessis and M. Babiker, "Enhanced Quadrupole Effects for Atoms in Optical Vortices," Phys. Rev. 110, 083002 (2013)

[2] Basil S. Davis, L. Kaplan, and J.H. McGuire, "On Exchange of Orbital Angular Momentum Between Twisted Photons and Atomic Electrons," J. Opt. 15 (2013) 035403

[3] L. Allen, M.W. Beijersbergen, R.J.C. Spreeuw, J.P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45 (1992) 8185.