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Orbital angular momentum (OAM) spectrum diagnosis is a fundamental buildingblock for diverse OAM-based systems. Among others, the simple on-axisinterferometric measurement can retrieve the amplitude and phase information ofcomplex OAM spectra in a few shots. Yet, its single-shot retrieval remainsillusive, due to the signal-signal beat interference inherent in themeasurement. Here, we introduce the concept of Kramers-Kronig (KK) receiver incoherent communications to the OAM domain, enabling rigorous, single-shot OAMspectrum measurement. We explain in detail the working principle and therequirement of the KK method, and then apply the technique to precisely measurevarious characteristic OAM states. In addition, we discuss the effects of thecarrier-to-signal power ratio and the number of sampling points essential forrigorous retrieval, and evaluate the performance on a large set of random OAMspectra and high-dimensional spaces. Single-shot KK interferometry showsenormous potential for characterizing complex OAM states in real-time.

Single-shot Kramers-Kronig complex orbital angular momentum spectrum retrieval