Modal decomposition for measuring the orbital angular momentum density of light

We present a novel technique to measure the orbital angular momentum (OAM) density of light. The technique is based on modal decomposition, enabling the complete reconstruction of optical fields, including the reconstruction of the beam's Poynting vector and the OAM density distribution. The modal decomposition is performed using a computer-generated hologram (CGH), which allows fast and accurate measurement of the mode spectrum. The CGH encodes the modes of interest, whose powers and relative phase differences are measured from the far-field diffraction pattern of the incident optical field with the hologram transmission function. In combination with a classical measurement of Stokes parameters, including a polarizer and a quarter-wave plate in front of the hologram, the polarization state of each mode is measured. As a consequence, any arbitrary vector field can be reconstructed, including amplitude, phase, and polarization. Having all information on the optical field, the Poynting vector and the OAM density can be calculated directly. We applied our method to beams emerging from optical fibers and free space beams, which allows us to investigate arbitrary coherent mode superpositions with complexly shaped intensity and polarization distributions. As a reference distinct beams of known OAM density were created using a spatial light modulator (SLM). Comparisons of measured and expected results reveal very good agreement.