Partial angular coherence and the angular Schmidt spectrum of entangled two-photon fields

Single-shot measurement of the orbital-angular-momentum spectrum of light

“…The OAM-mode index l measures the OAM of each photon in the units of ħ, while the index p characterizes the radial variation in the intensity 1 . The partially coherent fields that we consider in this article are the ones that can be represented as incoherent mixtures of LG modes having different OAM-mode indices 33 . The electric field E in (ρ, ϕ) corresponding to such a field can be written as…”

“…The state of the two-photon field produced by PDC has the following Schmidt-decomposed form when the detection system is sensitive only to the OAM-mode index 33 :…”

“…The angular Schmidt spectrum quantifies the dimensionality and the entanglement of the state in the OAM basis 32,42,43 . There are a variety of techniques for measuring the angular Schmidt spectrum 28,32,33,44,45 . In the context of spatial entanglement, there has even been a theoretical proposal 46 and its subsequent experimental implementation 47 for measuring the spatial Schmidt spectrum in a single-shot manner using coincidence detection.…”

“…One of the major challenges faced in the implementation of OAM-based high-dimensional protocols is the efficient detection of OAM spectrum, and it is currently an active research area [28][29][30][31][32][33][34][35][36][37] . There are several approaches to measuring the OAM spectrum of a field.…”

“…However, due to several experimental challenges, these approaches [35][36][37] have so far been demonstrated only for fields consisting of just a few modes. Thus the existing methods for measuring the OAM spectrum information suffer from either poor efficiency 28,35 or strict interferometric stability requirements 31,32,37 or too much loss 33,34 . In addition, many techniques 28,33,34 inevitably discard part of the field and yield only a post-selected portion of the true spectrum.…”