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arXiv:1401.3512 · Journal of the Optical Society of America B

Limitations to the determination of a Laguerre–Gauss spectrum via projective, phase-flattening measurement

Hammam Qassim, Filippo M. Miatto, Juan P. Torres, Miles J. Padgett, Ebrahim Karimi, Robert W. Boyd

Published Apr 4, 2014• 105 citations
arXivHTMLPDF

Abstract

One of the most widely used techniques for measuring the orbital angular momentum (OAM) components of a light beam is to flatten the spiral phase front of a mode, in order to couple it to a single-mode optical fiber (SMOF). This method, however, suffers from an efficiency that depends on the OAM of the initial mode and on the presence of higher-order radial modes. The reason is that once the phase has been flattened, the field retains its ringed intensity pattern and is therefore a nontrivial superposition of purely radial modes, of which only the fundamental one couples to a SMOF. In this paper, we study the efficiency of this technique both theoretically and experimentally. We find that even for low values of the OAM, a large amount of light can fall outside the fundamental mode of the fiber, and we quantify the losses as functions of the waist of the coupling beam of the OAM and radial indices. Our results can be used as a tool to remove the efficiency bias where fair-sampling loopholes are not a concern. However, we hope that our study will encourage the development of better detection methods of the OAM content of a beam of light.

DOI
10.1364/josab.31.000a20

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One of the most widely used techniques for measuring the orbital angular momentum (OAM) components of a light beam is to flatten the spiral phase front of a mode, in order to couple it to a single-mode optical fiber (SMOF). This method, however, suffers from an efficiency that depends on the OAM of the initial mode and on the presence of higher-order radial modes. The reason is that once the phase has been flattened, the field retains its ringed intensity pattern and is therefore a nontrivial superposition of purely radial modes, of which only the fundamental one couples to a SMOF. In this paper, we study the efficiency of this technique both theoretically and experimentally. We find that even for low values of the OAM, a large amount of light can fall outside the fundamental mode of the fiber, and we quantify the losses as functions of the waist of the coupling beam of the OAM and radial indices. Our results can be used as a tool to remove the efficiency bias where fair-sampling loopholes are not a concern. However, we hope that our study will encourage the development of better detection methods of the OAM content of a beam of light.
Detection of photons in orbital angular momentum (OAM) superposition states is crucial to verification of OAM entanglement. In the past this has been realized by laterally shifting a hologram designed to remove a charge 1 phase singularity at its center. Such a laterally shifted hologram converts a beam with an off-center singularity (similar to that created by superposing an m = 0 beam and an m = 1 beam, where in is the OAM mode number) into a Gaussian beam, which is then filtered through a single mode fiber (SMF). However, it has been shown that a photon detected by this method is not a simple superposition of a photon in the m = 0 Gaussian mode and the m = 1 mode detected with an unshifted hologram, making it necessary to apply complicated analysis. One problem is that the radial distributions of the detected m = 0 and 1 components as determined by the SMF change as the hologram is shifted. Another, possibly more serious problem is the mixing of other OAM components. To overcome this problem we propose a new scheme for the detection of OAM superposition states consisting of a hologram and a path interferometer. The hologram is designed so that the output is equally distributed between the 0th and 1st order diffraction beams. The 0th order is the input beam itself, whose m = 0 Gaussian component is filtered through an SMF. In the 1st order beam the m = 1 component is converted to m = 0 and is filtered through a second SMF. The filtered beams now have the same spatial distribution, and can be superposed by a beam splitter. By inserting attenuators and phase modulators within the interferometer, superpositions with varying amplitude ratios and relative phases can be detected without shifting the hologram.
The most common approach to create orbital angular momentum (OAM) carrying vortex beams is by modulating a Gaussian beam with an azimuthal phase profile. This results in a beam with many radial modes and hence reduced power in the desired mode. Here we show that it is possible to select the mode size of the Laguerre-Gaussian basis so that the power in the detected p = 0 mode is maximised. We outline the idea theoretically and confirm it experimentally with both classical and quantum tests, demonstrating a power increase by as much as 50x. The consequence is higher signal-to- noise in optical communication and larger available dimensions in quantum entanglement experiments when using OAM modes as a basis.
Abstract The orbital angular momentum (OAM) of light has been at the center of several classical and quantum applications for imaging, information processing and communication. However, the complex structure inherent in OAM states makes their detection and classification nontrivial in many circumstances. Most of the current detection schemes are based on models of the OAM states built upon the use of Laguerre–Gauss (LG) modes. However, this may not in general be sufficient to capture full information on the generated states. In this paper, we go beyond the LG assumption, and employ hypergeometric-Gaussian (HyGG) modes as the basis states of a refined model that can be used—in certain scenarios—to better tailor OAM detection techniques. We show that enhanced performances in OAM detection are obtained for holographic projection via spatial light modulators in combination with single-mode fibers (SMFs), and for classification techniques based on a machine learning approach. Furthermore, a three-fold enhancement in the SMF coupling efficiency is obtained for the holographic technique, when using the HyGG model with respect to the LG one. This improvement provides a significant boost in the overall efficiency of OAM-encoded single-photon detection systems. Given that most of the experimental works using OAM states are effectively based on the generation of HyGG modes, our findings thus represent a relevant addition to experimental toolboxes for OAM-based protocols in quantum communication, cryptography and simulation.
Abstract Laguerre-Gauss beams, and more generally the orbital angular momentum of light (OAM) provide valuable research tools for optical manipulation, processing, imaging and communication. High-efficiency frequency conversion of OAM is possible via four-wave mixing in rubidium vapour. Conservation of the OAM in the two pump beams determines the total OAM shared by the generated light fields at 420 nm and 5.2 μm—but not its distribution between them. Here we experimentally investigate the spiral bandwidth of the generated light modes as a function of pump OAM. A small pump OAM is transferred almost completely to the 420 nm beam. Increasing the total pump OAM broadens the OAM spectrum of the generated light, indicating OAM entanglement between the generated light fields. This clears the path to high-efficiency OAM entanglement between widely disparate wavelengths.
Accurate reconstruction of the complex spectrum of orbital angular momentum (OAM) superposition states is crucial for their application in high-capacity optical communications and quantum information, yet existing methods are often constrained by system complexity, extensive data requirements, or incomplete information retrieval. Here, we propose and experimentally demonstrate an iterative algorithm that enables high-fidelity recovery of the complex OAM spectrum of high-dimensional superpositions from only a few sparsely sampled patterns. The method integrates the Laguerre-Gaussian (LG) modal basis as an a priori constraint, which enables the direct retrieval of spectral coefficients by circumventing intermediate field reconstruction. To validate its performance, we reconstructed a test field composed of a random superposition of 21 LG modes, achieving fidelities of 99.3% in simulation and 97.2% in experiment using only four sparse sampling patterns. This work provides an efficient and robust tool for characterizing high-dimensional structured light, with significant potential in optical communication and quantum science.
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.