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

• Published in: Advanced photonics Vol. 5; no. 3; p. 036006
• Main Authors: Lin, Zhongzheng, Hu, Jianqi, Chen, Yujie, Brès, Camille-Sophie, Yu, Siyuan
• Format: Journal Article
• Language: English
• Published: Bellingham Society of Photo-Optical Instrumentation Engineers 01.05.2023; S P I E - International Society for
• Subjects: Angular momentum; Cameras; Electrons; Interferometry; Measurement techniques; Retrieval; Spectra; phase retrieval; orbital angular momentum; Kramers–Kronig relations; single-shot measurement
• ISSN: 2577-5421; 2577-5421
• DOI: 10.1117/1.AP.5.3.036006

Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few shots. Yet, its single-shot retrieval remains elusive, due to the signal–signal beat interference inherent in the measurement. Here, we introduce 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 and the requirement of the KK method and then apply the technique to precisely measure various characteristic OAM states. In addition, we discuss the effects of the carrier-to-signal power ratio and the number of sampling points essential for rigorous retrieval and evaluate the performance on a large set of random OAM spectra and high-dimensional spaces. Single-shot KK interferometry shows enormous potential for characterizing complex OAM states in real time.