High efficiency measurement of all orbital angular momentum modes in a light beam

We present an experimental demonstration of a Laguerre-Gauss (LG) spectrum measurement technique using variable focus lenses that is able to measure the strengths of all modes present in an unknown, incoming light beam with the highest possible efficiency. The experiment modifies the classical projective, phase flattening technique by including a variable sized pinhole and a two electronic lens variable imaging system that is tuned for each mode to give the highest possible detection efficiency irrespective of the beam waist of LG mode chosen for the projection/decomposition. The modified experiment preserves the orthogonality between the modes with only a 4 \% cross-talk so that superposition states may also be detected efficiently. Our experiment results show efficient detection of OAM vortex beams with topological charge, $l$, values ranging from 0 to 4 with various different beam waists chosen for the decomposition.