Near-perfect measuring of full-field transverse-spatial modes of light

Along with the growing interest in using the transverse-spatial modes of light in quantum and classical optics applications, developing an accurate and efficient measurement method has gained importance. Here, we present a technique relying on a unitary mode conversion for measuring any full-field transverse-spatial mode. Our method only requires three consecutive phase modulations followed by a single mode fiber and is, in principle, error-free and lossless. We experimentally test the technique using a single spatial light modulator and achieve an average error of 4.2% for a set of 9 different full-field Laguerre-Gauss and Hermite-Gauss modes with an efficiency of up to 70%. Moreover, as the method can also be used to measure any complex superposition state, we demonstrate its potential in a quantum cryptography protocol and in high-dimensional quantum state tomography.