EXPERIMENTAL DETECTION OF OPTICAL VORTICES USING A SHACK-HARTMANN WAVEFRONT SENSOR KEVIN MURPHY AND CHRIS DAINTY 1. Background Optical vortices (also know as branch points or phase singularities) occur when the phase of an optical field becomes undefined in a region of zero amplitude. The phase of the wavefront is discontinuous about the vortex and with a 2mπ radian jump across the discontinuity, where m is an integer number corresponding to the charge of the vortex. This leads to a spiral phase change going from 0 to 2mπ around the undefined phase at the centre, [Fig. 1]. Vortices occur in pairs which consist of both a positive and a negative vortex with the sign determined by the direction of the rotation of the spiral phase pattern around the centre of the vortex. The wavefront dislocation which joins the two oppositely signed vortices is along the line where the 2mπ discontinuity is present and is sometimes referred to as a branch cut. Figure 1. A2π radian vortex. This shows the spiral phase around the centre of the vortex as well as the wavefront dislocation created by the vortex. There is much interest in trying to correct for the distortions induced the atmosphere on a propagating laser beam of which optical vortices are a large part, with one the main techniques for accomplishing this being Adaptive Optics (AO). AO systems look to measure the wavefront and correct for it’s aberrations by using a controllable optical element and generally consist of a wavefront sensor, a camera, a deformable element and a control system along with static optical elements. Optical vortices can cause a number of difficulties for AO systems, in both the hardware and the control system, which try to correct for them. The operation of the Shack-Hartmann wavefront sensor is shown below [Fig.2]. Initially a plane wavefront is passed through the lenslet array and falls onto the detector. The lenlets split the beam up into the same number of beamlets and these will all form an in-focus spot on the detector. The position of these spots are noted and called the reference positions. Then when an aberrated wavefront is passed through the lenslet array another set of spot positions are noted. The difference in these spot locations compared to the reference spot positions gives us the phase gradients (or slopes) of the aberrated wavefront we are measuring. Figure 2. Operation of a Shack Hartmann wavefront sensor. 1