Single-shot measurement of the orbital-angular-momentum spectrum of light (original) (raw)
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Simplified measurement of the orbital angular momentum of single photons
Optics Communications, 2003
We describe a simplification of a recent approach for sorting photons according to their orbital angular momentum (OAM) [Leach et al., Phys. Rev. Lett. 88 (2002) 257901]. The original cascade of Mach-Zehnder interferometers required optical elements that can increase the OAM per photon of any passing light by a fixed amount, which in practice introduced loss. Our simplification, which we demonstrate experimentally, does not require these lossy elements but instead shifts the phase in one arm of each interferometer. We also point out that an earlier scheme for sorting Hermite-Gaussian (HG) modes [Xue et al., Opt. Lett. 26 (2001) 1746] could be modified to sort photons according to their OAM.
Precise quantum tomography of photon pairs with entangled orbital angular momentum
New Journal of Physics, 2009
We report a high fidelity tomographic reconstruction of the quantum state of photon pairs generated by parametric down-conversion with orbital angular momentum (OAM) entanglement. Our tomography method allows us to estimate an upper and lower bound for the entanglement between the downconverted photons. We investigate the two-dimensional state subspace defined by the OAM states ±`and superpositions thereof, with`= 1, 2, . . . , 30. We find that the reconstructed density matrix, even for OAMs up to around`= 20, is close to that of a maximally entangled Bell state with a fidelity in the range between F = 0.979 and F = 0.814. This demonstrates that, although the single count-rate diminishes with increasing`, entanglement persists in a large dimensional state space.
Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states
New Journal of Physics, 2013
A light beam may be separated into its orbital-angular momentum (OAM) components by a geometric optical transformation that converts each OAM component into a plane wave with a transverse phase gradient. Subsequent focusing produces a spot the lateral position of which is proportional to the input OAM state (Lavery et al 2012 Opt. Express 20 3). In this paper, we improve this approach, extending the measurement bandwidth to >50 OAM states and showing a simultaneous measurement of the radial coordinate.
Fourier Relationship between Angular Position and Orbital Angular Momentum of Entangled Photons
2008
We demonstrate the Fourier relationship between angular position and angular momentum for a light mode. In particular we measure the distribution of orbital angular momentum states of light that has passed through an aperture and verify that the orbital angular momentum distribution is given by the complex Fourier-transform of the aperture function. We use spatial light modulators, configured as diffractive optical components, to define the initial orbital angular momentum state of the beam, set the defining aperture, and measure the angular momentum spread of the resulting beam. These measurements clearly confirm the Fourier relationship between angular momentum and angular position, even at light intensities corresponding to the single photon level.
We introduce and experimentally demonstrate a method for measuring at the same time the mean and the variance of the photonic orbital angular momentum (OAM) distribution in any paraxial optical field, without passing through the acquisition of its entire angular momentum spectrum. This method hence enables one to reduce the infinitely many output ports required in principle to perform a full OAM spectrum analysis to just two. The mean OAM, in turn, provides direct access to the average mechanical torque that the optical field in any light beam is expected to exert on matter, for example in the case of absorption. Our scheme could also be exploited to weaken the strict alignment requirements usually imposed for OAM-based free-space communication.
Orbital angular momentum analysis of high-dimensional entanglement
Physical Review A, 2007
We describe a simple experiment that is ideally suited to analyze the high-dimensional entanglement contained in the orbital angular momenta ͑OAM͒ of entangled photon pairs. For this purpose we use a two-photon interferometer with a built-in image rotator and measure the two-photon visibility versus rotation angle. Mode selection with apertures allows one to tune the dimensionality of the entanglement; mode selection with spiral phase plates and fibers allows detection of a single OAM mode. The experiment is analyzed in two different ways: either via the continuous two-photon amplitude function or via a discrete modal ͑Schmidt͒ decomposition of this function. The latter approach proves to be very fruitful, as it provides a complete characterization of the OAM entanglement.
Measuring the Orbital Angular Momentum State of Light by Coordinate Transformation
IEEE Photonics Technology Letters, 2017
We present a method to measure the orbital angular momentum (OAM) state of light by coordinate transformation. The input OAM mode with annular shape is uniaxially compressed into a linear-shaped light, so that the upper and lower portions of OAM mode overlap to produce an interference pattern, showing easily recognizable fringes both in the near field and far field. The far-field measurement is more suitable for detecting large OAM but with the cost of additional diffractive element. The incident light can illuminate any position of the device, showing good tolerance to adjust the optical path. In a practical application, the proposed scheme can be realized only by one or two elliptical lenses, which provides a convenient and economic method for measurement of OAM state.
Partial angular coherence and the angular Schmidt spectrum of entangled two-photon fields
Physical Review A, 2011
We study partially coherent fields that have a coherent-mode representation in the orbital-angular-momentummode basis. For such fields, we introduce the concepts of the angular coherence function and the coherence angle. Such fields are naturally produced by the process of parametric down-conversion-a second-order nonlinear optical process in which a pump photon breaks up into two entangled photons, known as the signal and idler photons. We show that the angular coherence functions of the signal and idler fields are directly related to the angular Schmidt (spiral) spectrum of the down-converted two-photon field and thus that the angular Schmidt spectrum can be measured directly by measuring the angular coherence function of either the signal or the idler field, without requiring coincidence detection.
Journal of Modern Optics, 2002
We calculate the anticipated correlation between measurements of the orbital angular momentum of the signal and idler beams for parametric down-conversion. These calculations apply to the experiments where the orbital angular momentum state is measured by the use of computer-generated holograms. Displacement of these holograms with respect to the beam axis allows the measurement of superpositions of Laguerre±Gaussian modes. The correlations between such superposition modes of the signal and idler beams show their entanglement and could be used for Bell-type tests of nonlocality. Over the past 20 years many experiments have been performed to study polarization entanglement of photon pairs. The experiments of Aspect and coworkers [1] in the early 1980s are generally regarded as having provided the ®rst experimental support for nonlocal interpretations of quantum mechanics. Since that time, other experiments on photon pairs have successfully shown entanglement in their polarization states [2], their arrival times [3, 4] and their transverse position [5]. In addition to investigating the interpretation of quantum mechanics, entanglement also plays important roles in quantum cryptography [6] and teleportation [7]. Recently, Mair et al. [8] reported the ®rst experiments to investigate the entanglement of the orbital angular momentum of photon pairs using computergenerated holograms to measure the orbital angular momentum of individual photons. While the polarization of light, related to the spin angular momentum, can be characterized by two orthogonal states, the orbital angular momentum is higher dimensional [9]. The multi-dimensional entanglement of orbital angular momentum states could ®nd interesting applications in quantum cryptography and communication. This paper seeks to apply our recently derived theoretical treatment [10] of the correlation between orbital angular momentum states to experiments of their type. We also suggest more detailed experiments to observe the entanglement of the