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

Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverseOAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve theamplitude and phase information of complex OAM spectra in a few shots. Yet, its single-shot retrievalremains elusive, due to the signal–signal beat interference inherent in the measurement. Here, weintroduce the concept of Kramers–Kronig (KK) receiver in coherent communications to the OAM domain,enabling rigorous, single-shot OAM spectrum measurement. We explain in detail the working principle andthe requirement of the KK method and then apply the technique to precisely measure variouscharacteristic OAM states. In addition, we discuss the effects of the carrier-to-signal power ratio and thenumber of sampling points essential for rigorous retrieval and evaluate the performance on a large set ofrandom OAM spectra and high-dimensional spaces. Single-shot KK interferometry shows enormouspotential for characterizing complex OAM states in real time.