Orbital angular momentum 25 years on [invited]

Twenty-five years ago Allen, Beijersbergen, Spreeuw, and Woerdman published their seminal paper establishing that light beams with helical phase-fronts carried an orbital angular momentum. Previously orbital angular momentum had been associated only with high-order atomic/molecular transitions and hence considered to be a rare occurrence. The realization that every photon in a laser beam could carry an orbital angular momentum that was in excess of the angular momentum associated with photon spin has led both to new understandings of optical effects and various applications. These applications range from optical manipulation, imaging and quantum optics, to optical communications. This brief review will examine some of the research in the field to date and consider what future directions might hold

An introduction to ghost imaging: quantum and classical

Ghost imaging has been a subject of interest to the quantum optics community for the past 20 years. Initially seen as manifestation of quantum spookiness, it is now recognized as being implementable in both single- and many-photon number regimes. Beyond its scientific curiosity, it is now feeding novel imaging modalities potentially offering performance attributes that traditional approaches cannot match

Image reconstruction from photon sparse data

We report an algorithm for reconstructing images when the average number of photons recorded per pixel is of order unity, i.e. photon-sparse data. The image optimisation algorithm minimises a cost function incorporating both a Poissonian log-likelihood term based on the deviation of the reconstructed image from the measured data and a regularization-term based upon the sum of the moduli of the second spatial derivatives of the reconstructed image pixel intensities. The balance between these two terms is set by a bootstrapping technique where the target value of the log-likelihood term is deduced from a smoothed version of the original data. When compared to the original data, the processed images exhibit lower residuals with respect to the true object. We use photon-sparse data from two different experimental systems, one system based on a single-photon, avalanche photo-diode array and the other system on a time-gated, intensified camera. However, this same processing technique could most likely be applied to any low photon-number image irrespective of how the data is collected

Two-photon optics of Bessel-Gaussian modes

In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum and Schmidt number in this basis and show how this may be varied by control over the radial degree of freedom, a continuous parameter in Bessel-Gaussian modes. As a test we first implement a back-projection technique to classically predict, by experiment, the quantum correlations for Bessel-Gaussian modes produced by three holographic masks, a blazed axicon, binary axicon and a binary Bessel function. We then proceed to test the theory on the down-converted photons using the binary Bessel mask. We experimentally quantify the number of usable OAM modes and confirm the theoretical prediction of a flattening in the OAM spectrum and a concomitant increase in the OAM bandwidth. The results have implications for the control of dimensionality in quantum states.Comment: 8 pages, 10 figure

Polarisation structuring of broadband light

Spatial structuring of the intensity, phase and polarisation of light is useful in a wide variety of modern applications, from microscopy to optical communications. This shaping is most commonly achieved using liquid crystal spatial light modulators (LC-SLMs). However, the inherent chromatic dispersion of LC-SLMs when used as diffractive elements presents a challenge to the extension of such techniques from monochromatic to broadband light. In this work we demonstrate a method of generating broadband vector beams with dynamically tunable intensity, phase and polarisation over a bandwidth of 100 nm. We use our system to generate radially and azimuthally polarised vector vortex beams carrying orbital angular momentum, and beams whose polarisation states span the majority of the Poincaré sphere. We characterise these broadband vector beams using spatially and spectrally resolved Stokes measurements, and detail the technical and fundamental limitations of our technique, including beam generation fidelity and efficiency. The broadband vector beam shaper that we demonstrate here may find use in applications such as ultrafast beam shaping and white light microscopy

Measuring orbital angular momentum superpositions of light by mode transformation

We recently reported on a method for measuring orbital angular momentum (OAM) states of light based on the transformation of helically phased beams to tilted plane waves [Phys. Rev. Lett.105, 153601 (2010)]. Here we consider the performance of such a system for superpositions of OAM states by measuring the modal content of noninteger OAM states and beams produced by a Heaviside phase plate

Polarisation structuring of broadband light

Spatial structuring of the intensity, phase and polarisation of light is useful in a wide variety of modern applications, from microscopy to optical communications. This shaping is most commonly achieved using liquid crystal spatial light modulators (LC-SLMs). However, the inherent chromatic dispersion of LC-SLMs when used as diffractive elements presents a challenge to the extension of such techniques from monochromatic to broadband light. In this work we demonstrate a method of generating broadband vector beams with dynamically tunable intensity, phase and polarisation over a bandwidth of 100 nm. We use our system to generate radially and azimuthally polarised vector vortex beams carrying orbital angular momentum, and beams whose polarisation states span the majority of the Poincaré sphere. We characterise these broadband vector beams using spatially and spectrally resolved Stokes measurements, and detail the technical and fundamental limitations of our technique, including beam generation fidelity and efficiency. The broadband vector beam shaper that we demonstrate here may find use in applications such as ultrafast beam shaping and white light microscopy

The transition from a coherent optical vortex to a Rankine vortex: beam contrast dependence on topological charge

Spatially coherent helically phased light beams carry orbital angular momentum (OAM) and contain phase singularities at their centre. Destructive interference at the position of the phase singularity means the intensity at this point is necessarily zero, which results in a high contrast between the centre and the surrounding annular intensity distribution. Beams of reduced spatial coherence yet still carrying OAM have previously been referred to as Rankine vortices. Such beams no longer possess zero intensity at their centre, exhibiting a contrast that decreases as their spatial coherence is reduced. In this work, we study the contrast of a vortex beam as a function of its spatial coherence and topological charge. We show that beams carrying higher values of topological charge display a radial intensity contrast that is more resilient to a reduction in spatial coherence of the source

Heralded phase-contrast imaging using an orbital angular momentum phase-filter

We utilise the position and orbital angular momentum (OAM) correlations between the signal and idler photons generated in the down-conversion process to obtain ghost images of a phase object. By using an OAM phase filter, which is non-local with respect to the object, the images exhibit isotropic edge-enhancement. This imaging technique is the first demonstration of a full-field, phase-contrast imaging system with non-local edge enhancement, and enables imaging of phase objects using significantly fewer photons than standard phase-contrast imaging techniques