The measurement and generation of orbital angular momentum using an optical geometric transformation

Previously we have demonstrated that the orbital angular momentum (OAM) of the light beam may be measured by image transformation that maps the azimuthal to linear transverse co-ordinate (Berkhout et al 2010 Phys. Rev. Lett. 105 153601). For each input OAM state the transmitted light is focussed to a different transverse position enabling simultaneous measurement over many states. We present a significant improvement to our earlier design, extending the measurement bandwidth to greater than 50 OAM states and showing simultaneous measurement of the radial co-ordinate. We further demonstrate the transformation working in reverse, potentially allowing for the rapid switching of OAM modes.