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Conference on Lasers and Electro-Optics

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

Girish Ashok Kulkarni, Rishabh Sahu, Omar S. Magaña‐Loaiza, Robert W. Boyd, Anand K. Jha

Published Jan 1, 2018• 3 citations
Publisher

Abstract

We propose a single-shot scheme to measure the orbital-angular-momentum (OAM) spectrum of a partially coherent field. We first test the scheme for a known field, and then use it to measure the OAM spectrum of the signal-idler field from parametric down-conversion with Schmidt number K = 82:1.
DOI
10.1364/cleo_qels.2018.fw4f.7

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The existing methods for measuring the orbital-angular-momentum (OAM) spectrum suffer from issues such as poor efficiency, strict interferometric stability requirements, and too much loss. Furthermore, most techniques inevitably discard part of the field and measure only a post-selected portion of the true spectrum. Here, we propose and demonstrate an interferometric technique for measuring the true OAM spectrum of optical fields in a single-shot manner. Our technique directly encodes the OAM-spectrum information in the azimuthal intensity profile of the output interferogram. In the absence of noise, the spectrum can be fully decoded using a single acquisition of the output interferogram, and, in the presence of noise, acquisition of two suitable interferograms is sufficient for the purpose. As an important application of our technique, we demonstrate measurements of the angular Schmidt spectrum of the entangled photons produced by parametric down-conversion and report a broad spectrum with the angular Schmidt number 82.1.
The existing methods for measuring the orbital-angular-momentum (OAM) spectrum suffer from issues such as poor efficiency, strict interferometric stability requirements, and too much loss. Furthermore, most techniques inevitably discard part of the field and measure only a post-selected portion of the true spectrum. Here, we propose and demonstrate an interferometric technique for measuring the true OAM spectrum of optical fields in a single-shot manner. Our technique directly encodes the OAM-spectrum information in the azimuthal intensity profile of the output interferogram. In the absence of noise, the spectrum can be fully decoded using a single acquisition of the output interferogram, and, in the presence of noise, acquisition of two suitable interferograms is sufficient for the purpose. As an important application of our technique, we demonstrate measurements of the angular Schmidt spectrum of the entangled photons produced by parametric down-conversion and report a broad spectrum with the angular Schmidt number 82.1.
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.
We implement an interferometric method using two angular slits to measure the orbital-angular-momentum (OAM) mode spectrum of a field with partial angular coherence. As the angular separation of the slits changes, an interference pattern for a particular OAM mode is obtained. The visibility of this interference pattern as a function of angular separation is equivalent to the angular correlation function of the field. By Fourier transforming the angular correlation function obtained from the double-angular-slit interference, we are able to calculate the OAM spectrum of the partially coherent field. This method has potential application for characterizing the OAM spectrum in high-dimensional quantum information protocols.
It is tough work to measure the orbital angular momentum (OAM) spectrum due to the requirement of a reference light or photodetector arrays, while measuring the spin angular momentum (SAM) is readily convenient and matured. In this work, the so-called OAM-SAM nonseparable states are employed, and the OAM spectrum can be obtained only by measuring the Stokes parameters of an arbitrary light beam with low loss noncascading structure and a single point detector. According to the experimental results, the fidelity of the measured OAM spectrum can be as high as 95.2% and 94.3% for OAM eigenstates and superposed states, respectively.