The ability to measure polarisation, spectrum, temporal dynamics, and spatial amplitude and phase of optical beams is essential to study fundamental phenomena in laser dynamics, telecommunications and nonlinear optics. Current characterisation techniques only apply in limited contexts. Non-interferometric methods typically lack access to spatial phase, while phase-sensitive approaches necessitate either an auxiliary reference source or an adequate self-reference, neither of which is universally available. Regardless of the reference, deciphering complex wavefronts of multiple co-propagating incoherent fields remains particularly challenging. Here, we harness the principles of quantum state tomography to circumvent these limitations. A full description of an unknown beam is retrieved by measuring its temporally and spectrally resolved density matrices for both polarisations, using a spatial light modulator to display projective holograms and a single-mode fibre to guide the collected signal to a high-speed photodiode and a spectrometer. Despite no spatial resolution of the detector and the intensity-only character of the collected signal, the method resolves multiple arbitrary spatial fields within a single beam, including their phase and amplitude, as well as their spatial coherence. Leveraging the coherence information unlocks unambiguous determination of the spectral and temporal evolution of mutually incoherent fields, even when these spectrally overlap or have an identical time delay. We demonstrate these hallmark features by characterising the rich spatiotemporal and spectral output of a vertical-cavity surface-emitting laser diode that has so far resisted full analysis using existing techniques.
Sub-nanometer 3D morphometric precision of polarisation-resolved wide-field optical extinction microscopy determines the roundness of individual gold nanospheres
Polarisation-resolved identification of spontaneous four-wave mixing processes in a multimode fused tapered fibre coupler
University of Ottawa（渥太华大学）；National Research Council of Canada（加拿大国家研究委员会）；Nexus for Quantum Technologies, Department of Physics, University of Ottawa（渥太华大学物理系量子技术联盟）；Département de physique et astronomie, Université de Moncton（蒙克顿大学物理与天文学系）；Quantinuum；Corning Incorporated（康宁公司）
Ultra-high-speed chemiluminescence tomography of spinning-mode detonation waves
Pennsylvania State University（宾夕法尼亚州立大学）；Spectral Energies, LLC（光谱能源有限责任公司）；Innovative Scientific Solutions, Inc.（创新科学解决方案公司）；Air Force Research Laboratory（空军研究实验室）
Spatially or temporally resolved phase-based optoretinography with actively-tracked point-scanning optical coherence tomography
Medical Laser Center Lübeck GmbH（吕贝克医学激光中心有限公司）；Institute of Biomedical Optics, University of Lübeck（吕贝克大学生物医学光学研究所）；Heidelberg Engineering GmbH（海德堡工程有限公司）；Airway Research Center North (ARCN), Member of the German Center for Lung Research (DZL)（北气道研究中心（ARCN），德国肺病研究中心（DZL）成员）
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；KAIST Institute for Health Science and Technology, KAIST（韩国科学技术院健康科学与技术研究所）；Graduate School of Medical Science and Engineering, KAIST（韩国科学技术院医学科学与工程研究生院）；Department of Mechanical Engineering, KAIST（韩国科学技术院机械工程系）；Graduate School of Stem Cell and Regenerative Biology, KAIST（韩国科学技术院干细胞与再生生物学研究生院）；Department of Pathology, Gangnam Severance Hospital, Yonsei University College of Medicine（延世大学医学院江南世福兰斯医院病理科）；Center for Genome Engineering, Institute for Basic Science（基础科学研究院基因组工程中心）；BioMedical Research Center (BMRC), KAIST（韩国科学技术院生物医学研究中心）；Tomocube Inc.（Tomocube公司）
Single-shot coherent process tomography and mid-infrared polarimetry with undetected photons
Humboldt-Universität zu Berlin（柏林洪堡大学）；University of Science and Technology of China（中国科学技术大学）；Ferdinand-Braun-Institut, Leibniz-Institut für Höchstfrequenztechnik（费迪南德·布劳恩研究所，莱布尼茨高频技术研究所）
