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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Measuring the orbital angular momentum of light

Miles J. Padgett, Martin P. J. Lavery, Gregorius C. G. Berkhout, Johannes Courtial, Marco W. Beijersbergen

Published Jan 13, 2011• 2 citations
Publisher

Abstract

We report a new simple optical system for the highly efficient measurement of the Orbital Angular Momentum States of Light. It uses an image reformatter to map each input state onto a different lateral position in the output aperture. This, near perfect, separation of states potentially makes available the high information capacity of OAM in both classical and quantum applications.

DOI
10.1117/12.876119

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We report a new simple optical system for the highly efficient measurement of the Orbital Angular Momentum States of Light. It uses an image reformatter to map each input state onto a different lateral position in the output aperture. This, near perfect, separation of states potentially makes available the high information capacity of OAM in both classical and quantum applications.
The orbital angular momentum of light (OAM) is a fundamental property of light. Beams with OAM have a helical wave front that carries quantized orbital angular momentum L hbar per photon, where L is any integer. This unbounded Hilbert space can increase information capacity of both classical and quantum communications and also improve and extend qubit and qudit quantum algorithms. Additionally, the use of the OAM modes allows for novel imaging techniques to directly observe and measure various topological properties of objects ranging from defects in semiconductors to rotating black holes and extrasolar planets. However, measuring such higher dimensional OAM states is fundamentally important, albeit challenging, in order to use this rich degree of freedom. In the work that follows, I present two novel OAM to time mapping schemes and an application using the higher dimensionality of OAM to non-destructively probe quantum states. These are the first OAM measuring schemes to use the temporal degree of freedom to measure OAM. The use of the novel loop nature allows for high fidelity and high speed measurements of a large number of OAM states without significant increase in experimental resources. The first scheme experimentally demonstrates a compact and practical device to measure the OAM spectrum. I report a fidelity of -21.3 dB for 5 different OAM states. The second scheme extends the first, but uses non-demolition measurements to iteratively test for specific OAM values. While this increases experimental complexity, it allows for the detection of an arbitrarily large OAM value from a single photon. I also discuss details of each technique investigate the affects of misalignment on the OAM spectrum. In the remaining part, I discuss my novel generalized quantum Zeno interrogation. The original quantum Zeno interrogation is limited to the two-dimensional state of a single object; while the generalized version has the ability to non-destructively probe the quantum state a set of objects, and deterministically imprint that information onto a single photon using the OAM degree of freedom.
The desire to increase the amount of information that can be encoded onto a single photon has driven research into many areas of optics. One such area is optical orbital angular momentum (OAM) [1]. These beams have helical phasefronts and carry an orbital angular momentum of mbar per photon, where the integer m is unbounded, giving a large state space in which to encode information. We recently developed a telescope system comprising two bespoke refractive optical elements to transform OAM states into transverse momentum states [2]. This is achieved by mapping the azimuthal position of the input plane to the lateral position in the output [3]. A mapping of this type transforms a set of concentric rings at the input plane into a set of parallel lines in the output plane. A lens can then separate the resulting transverse momentum states into specified lateral positions, allowing for the efficient measurement of multiple OAM states simultaneously. Separating OAM states in this way presents an opportunity for this larger alphabet to improve the data capacity of a free space link and has potential application in both the classical and quantum regimes. We will present our latest design, increasing the bandwidth of measurable states to over 50 OAM modes. In such a system we study the crosstalk introduced by a thin phase turbulence, showing that turbulence similarly degrades the purity of all the modes within this range.
Abstract. We demonstrate high-fidelity detection of the orbital angular momentum (OAM) of light using a compact and practical OAM spectrometer that maps the OAM spectrum to time. The spectrometer consists of a single optical delay loop to achieve timing mapping, a vortex phase plate that iteratively decreases the OAM value, and a single mode fibre to distinguish zero from non-zero OAM states. Light with arbitrarily OAM compositions can be measured. For light with OAM up to 4~, we measured an average crosstalk of-21.3 dB, which is mainly limited by the purity of the input states and optical alignment. ar X iv
We demonstrate high-fidelity detection of the orbital angular momentum (OAM) of light using a compact and practical OAM spectrometer that maps the OAM spectrum to time. The spectrometer consists of a single optical delay loop to achieve timing mapping, a vortex phase plate that iteratively decreases the OAM value and a single mode fiber to distinguish zero from non-zero OAM states. Light with arbitrarily OAM compositions can be measured. For light with OAM up to 4ℏ, we measured an average crosstalk of −21.3 dB, which is mainly limited by the purity of the input states and optical alignment.
Photons are an ideal candidate for encoding both classical and quantum information. Besides spin angular momentum associated with circular polarization, single photon can also carry other fundamentally new degree of freedom of orbital angular momentum related to the spiral phase structure of light. The key significance of orbital angular momentum lies in its potential in realizing a high-dimensional Hilbert space and in encoding a high-dimensional quantum information. Since Allen et al. [Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185] recognized the physical reality of photon orbital angular momentum in 1992, rapidly growing interest has been aroused in orbital angular momentum (OAM) from both classical and quantum points of view. Here we present an overall review on the high-order orbital angular momentum of photon, including its preparation and manipulation based on some specific techniques and also its applications. The spatial light modulator is a commercial device that has been widely employed to generate the OAM beams. We make and identify the optical OAM superposition with very high quantum numbers up to l=360. Recently, the metallic spiral phase mirrors were also developed to produce high-order OAM beams up to l=5050. In addition, the Q-plates made of anisotropic and inhomogeneous liquid crystals were invented to generate high-order OAM beams in a polarization-controllable manner, and the OAM superposition of l=± 50 were achieved. Owing to high rotational symmetry, these high OAM beams have been found to have more and more important applications in the fields of high-sensitivity sensing and high-precision measurements. Two fascinating examples are discussed in detail. The first example is that the research group led by Prof. Zeilinger has prepared and observed the quantum entanglement of high orbital angular momenta up to l=±300 by the technique of polarization-OAM entanglement swapping, and they demonstrated that the angular resolution could be significantly improved by a factor of l. Their result was the first step for entangling and twisting even macroscopic, spatially separated objects in two different directions. The second example is that the research group led by Prof. Padgett has demonstrated an elegant experiment of rotational Doppler effects for visible light with l=±20 OAM superposition. They showed that a spinning object with an optically rough surface might induce a Doppler effect in light reflected from the direction parallel to the rotation axis, and the frequency shift was proportional to both the disk's angular speed and the optical OAM. The potential applications in noncontact measurement of angular speed and in significant improvement of angular resolution for remote sensing will be particularly fascinating.