Cold atom confinement in hollow laser beams with high charge number

We investigate experimentally and numerically the focusing properties of hollow laser beams suitable for cold atom confinement, and use these properties to confine atoms in a blue-detuned optical trap. A Gaussian beam modified by a spatial light modulator to have an azimuthally varying phase exp(i$n\phi )$ creates a hollow laser beam with charge number $n$. When focused through an imaging lens, these hollow beams are found to attain peak intensity farther from the focal plane as $n$ is increased. We demonstrate the properties of these beams by confining atoms in a box potential with steep intensity walls formed by crossed blue-detuned hollow beams with high charge number.