Determining the azimuthal index of a light field with orbital angular momentum to high precision using speckle metrology

Light beams possessing orbital angular momentum (OAM) have gained prominence in areas such as optical manipulation, quantum entanglement, and super-resolved imaging. The OAM of such beams is particularly complex to quantify. For a Laguerre-Gaussian beam, the angular momentum per photon is proportional to the azimuthal index, l, which is continuous in nature. The ability to measure precisely non-integer l is challenging and would unlock new potential for using these beams in fields such as sensing or communications. Here we show an innovative approach to measure non-integer values of the azimuthal index, l, of a Laguerre-Gaussian beam to a precision of a few parts in 10^4 based on laser speckle. We apply our speckle-based measurement to sense the refractive index of a liquid in a microfluidic chip at a resolution of 1.6×10^(-5) RIU.