# Publications

## 2017

### A deterministic detector for vector vortex states

*Scientific Reports*

##### Ndagano, B., Nape, I., Perez-Garcia, B., Scholes, S., Hernandez-Aranda, R., Konrad, T., Lavery, M. and Forbes, A.

Encoding information in high-dimensional degrees of freedom of photons has led to new avenues in various quantum protocols such as communication and information processing. Yet to fully benefit from the increase in dimension requires a deterministic detection system, e.g., to reduce dimension dependent photon loss in quantum key distribution. Recently, there has been a growing interest in using vector vortex modes, spatial modes of light with entangled degrees of freedom, as a basis for encoding information. However, there is at present no method to detect these non-separable states in a deterministic manner, negating the benefit of the larger state space. Here we present a method to deterministically detect single photon states in a four dimensional space spanned by vector vortex modes with entangled polarisation and orbital angular momentum degrees of freedom….Download

### Comparing mode-crosstalk and mode-dependent loss of laterally displaced orbital angular momentum and Hermite–Gaussian modes for free-space optical communication

*Optics Letters*

##### Ndagano, B., Mphuthi, N., Milione, G. and Forbes, A.

There is interest in using orbital angular momentum (OAM) modes to increase the data speed of free-space optical communication. A prevalent challenge is the mitigation of mode-crosstalk and mode-dependent loss that is caused by the modes’ lateral displacement at the data receiver. Here, the mode-crosstalk and mode-dependent loss of laterally displaced OAM modes are experimentally compared to that of a Hermite–Gaussian (HG) mode subset…Download

### Simultaneous generation of multiple vector beams on a single SLM

*Optics Express*

##### Rosales-Guzmán, C., Bhebhe, N. and Forbes, A.

Complex vector light fields, classically entangled in polarization and phase, have become ubiquitous in a wide variety of research fields. This has triggered the demonstration of a wide variety of generation techniques. Of particular relevance are those based on computer-controlled devices due to their great flexibility. In particular, spatial light modulators have demonstrated their high capabilities to generate any vector beam, with various spatial profiles and polarization distributions. Here, we put forward a novel technique that exploits the superposition principle in optics to enable the simultaneous generation of many vector beams using a single digital hologram…Download

### Simultaneous entanglement swapping of multiple orbital angular momentum states of light

*Nature Communications*

##### Zhang, Y., Agnew, M., Roger, T., Roux, S., Konrad, T., Faccio, D., Leach, J. and Forbes, A.

High-bit-rate long-distance quantum communication is a proposed technology for future communication networks and relies on high-dimensional quantum entanglement as a core resource. While it is known that spatial modes of light provide an avenue for high-dimensional entanglement, the ability to transport such quantum states robustly over long distances remains challenging. To overcome this, entanglement swapping may be used to generate remote quantum correlations between particles that have not interacted; this is the core ingredient of a quantum repeater, akin to repeaters in optical fibre networks. Here we demonstrate entanglement swapping of multiple orbital angular momentum states of light…Download

### Real and virtual propagation dynamics of angular accelerating white light beams

*Optics Express*

##### Vetter, C., Dudley, A., Szameit, A. and Forbes, A.

Accelerating waves have received significant attention of late, first in the optical domain and later in the form of electron matter waves, and have found numerous applications in non-linear optics, material processing, microscopy, particle manipulation and laser plasma interactions. Here we create angular accelerating light beams with a potentially unlimited acceleration rate. By employing wavelength independent digital holograms for the creation and propagation of white light beams, we are able to study the resulting propagation in real and virtual space…Download

### How to shape light with spatial light modulators

*SPIE.SPOTLIGHT*

##### Rosales-Guzmán, C. and Forbes, A.

Structuring light is a ubiquitous laboratory tool, and computer-controlled devices such as spatial light modulators (SLMs) can reshape an input beam into almost any desired output beam. This Spotlight covers the basic principles of these devices as well as some of the most advanced techniques in beam shaping. Many examples have been included to make this guide more comprehensive and help those shaping beams with a SLM for the first time. The provided examples are based in MATLAB (including a dozen downloadable code files), but they can be easily adapted to other programing languages. Readers need only an undergraduate level of mathematics and a basic knowledge of programming…Download

### Chapter 7: Laser isotope separation with shaped light

*Taylor & Francis Group*

##### Botha, L. and Forbes, A.

Laser-induced chemistry is an exciting and expanding field, which has led to commercial spin-off opportunities, such as the separation of isotopes of a given atom by means of selective laser-induced dissociation of a molecular structure containing those isotopes. This process, sometimes referred to as isotope enrichment, or just plain enrichment, is often the result of the molecule absorbing multiple photons, usually from an intense laser source. When a molecule is highly excited, it absorbs laser radiation by resonance, leading to dissociation of the weakest bonds…. In this chapter, we will introduce some of the important variables in an isotope separation process and show how the beam shape influences the commercial success of the process. Rather than discuss the topic from a general perspective, we will use carbon isotope separation as a case study to illustrate the practical aspects of this application…Download

### Multiplexing 200 modes on a single digital hologram

*Journal of Optics*

##### Rosales-Guzmán, C., Bhebhe, N., Mahonisi, N. and Forbes, A.

The on-demand tailoring of light’s spatial shape is of great relevance in a wide variety of research areas. Computer-controlled devices, such as Spatial Light Modulators (SLMs) or Digital Micromirror Devices (DMDs), offer a very accurate, flexible and fast holographic means to this end. Remarkably, digital holography affords the simultaneous generation of multiple beams (multiplexing), a tool with numerous applications in many fields. Here, we provide a self-contained tutorial on light beam multiplexing…Download

### Hybrid quantum erasure scheme for channel disturbance characterization

*Optics Communications*

##### Nape, I., Kyeremah, C. Vallés, A., Rosales-Guzmán, C., Buah-Bassuah, P. and Forbes, A.

We demonstrate a simple projective measurement based on the quantum eraser concept that can be used to characterize the disturbances of any communication channel. Quantum erasers are commonly implemented as spatially separated path interferometric schemes. Here we exploit the advantages of redefining the which-path information in terms of spatial modes, replacing physical paths with abstract paths of orbital angular momentum (OAM)…Download

### Erasing the orbital angular momentum information of a photon

*Physical Review A*

##### Nape, I., Ndagano, B. and Forbes, A.

Quantum erasers with paths in the form of physical slits have been studied extensively and proven instrumental in probing wave-particle duality in quantum mechanics. Here we replace physical paths (slits) with abstract paths of orbital angular momentum (OAM). Using spin-orbit hybrid entanglement of photons, we show that the OAM content of a photon can be erased with a complementary polarization projection of one of the entangled pair…Download

### Instrumentation limitation on a polarization-based entangled photon source

*Journal of the Optical Society of America B*

##### Ismail, Y., Joshi, S., Forbes, A. and Petruccione, F.

Free-space optical communication is hindered by turbulence resulting in spatial modal dispersion of the optical beam. Here we mimic in the laboratory the far-field turbulence effects on entangled photons in the polarization basis. We make use of a diffractive optical element to simulate turbulence distortions and measure the entanglement as a function of the turbulence strength. We show that the standard method of coincidence detection using single-mode-fiber coupling to single-photon counters results in spatial mode dependence of entanglement even though it is not measured with spatial modes…Download

### Digital spiral-slit for bi-photon imaging

*Journal of Optics*

##### McLaren, M. and Forbes, A.

Quantum ghost imaging using entangled photon pairs has become a popular field of investigation, highlighting the quantum correlation between the photon pairs. We introduce a technique using spatial light modulators encoded with digital holograms to recover both the amplitude and the phase of the digital object. Down-converted photon pairs are entangled in the orbital angular momentum basis, and are commonly measured using spiral phase holograms. Consequently, by encoding a spiral ring-slit hologram into the idler arm, and varying it radially we can simultaneously recover the phase and amplitude of the object in question…Download

### Radially dependent angular acceleration of twisted light

*Optics Letters*

##### Webster, J., Rosales-Guzman, C. and Forbes, A.

While photons travel in a straight line at constant velocity in free space, the intensity profile of structured light may be tailored for acceleration in any degree of freedom. Here we propose a simple approach to control the angular acceleration of light. Using Laguerre–Gaussian modes as our twisted beams carrying orbital angular momentum, we show that superpositions of opposite handedness result in a radially dependent angular acceleration as they pass through a focus (waist plane)…Download

### Characterizing quantum channels with non-separable states of classical light

*Nature Physics*

##### Ndagano, B., Perez-Garcia, B., Roux, F.S., McLaren, M., Rosales-Guzman, C., Zhang, Y., Mouane, O., Hernandez-Aranda, R.I., Konrad, T. and Forbes, A.

High-dimensional entanglement with spatial modes of light promises increased security and information capacity over quantum channels. Unfortunately, entanglement decays due to perturbations, corrupting quantum links that cannot be repaired without performing quantum tomography on the channel. Paradoxically, the channel tomography itself is not possible without a working link. Here we overcome this problem with a robust approach to characterize quantum channels…Download

### Controlling light’s helicity at the source: orbital angular momentum states from lasers

*Philosophical Transactions A*

##### Forbes, A.

Optical modes that carry orbital angular momentum (OAM) are routinely produced external to the laser cavity and have found a variety of applications, thus increasing the demand for integrated solutions for their production. Yet such modes are notoriously difficult to produce from lasers due to the strict symmetry requirements for their creation, together with the need to break the degeneracy in helicity. Here, we review the progress made since 1992 in producing such twisted light modes directly at the source…Download

### Roadmap on structured light

*Journal of Optics*

##### Rubinsztein-Dunlop, H., Forbes, A., Berry, M. V., Dennis, M. R., Andrews, D. L., Mansuripur, M.,… & Karimi, E.

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized…Download

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##### 2016

Roux, F. S. (2016). Topological charge conservation in stochastic optical fields. *Journal of Optics*, *18*(5), 054005. download

Roux, F. S. (2016). Non-Markovian evolution of photonic quantum states in atmospheric turbulence. *Journal of Optics*, *18*(5), 055203. download

Zhang, Y., Prabhakar, S., Rosales-Guzmán, C., Roux, F. S., Karimi, E., & Forbes, A. (2016). Hong-Ou-Mandel interference of entangled Hermite-Gauss modes. *Physical Review A*, *94*(3), 033855. download

Zhang, Y., Prabhakar, S., Roux, F. S., Forbes, A., & Konrad, T. (2016). Experimentally observed decay of high-dimensional entanglement through turbulence. *Physical Review A*, *94*(3), 032310. download

Sephton, B., Dudley, A., & Forbes, A. (2016). Revealing the radial modes in vortex beams. *Applied optics*, *55*(28), 7830-7835. download

Cox, M. A., Rosales-Guzmán, C., Lavery, M. P., Versfeld, D. J., & Forbes, A. (2016). On the resilience of scalar and vector vortex modes in turbulence. *Optics express*, *24*(16), 18105-18113. download

Perez-Garcia, B., Yepiz, A., Hernandez-Aranda, R. I., Forbes, A., & Swartzlander, G. A. (2016). Digital generation of partially coherent vortex beams. *Optics Letters*, *41*(15), 3471-3474. download

Ndagano, B., Sroor, H., McLaren, M., Rosales-Guzmán, C., & Forbes, A. (2016). Beam quality measure for vector beams. *Optics Letters*, *41*(15), 3407-3410. download

Trichili, A., Salem, A. B., Dudley, A., Zghal, M., & Forbes, A. (2016). Encoding information using Laguerre Gaussian modes over free space turbulence media. *Optics Letters*, *41*(13), 3086-3089. download

Gossman, D., Perez-Garcia, B., Hernandez-Aranda, R. I., & Forbes, A. (2016). Optical interference with digital holograms. *American Journal of Physics*, *84*(7), 508-516. download

Trichili, A., Rosales-Guzmán, C., Dudley, A., Ndagano, B., Salem, A. B., Zghal, M., & Forbes, A. (2016). Optical communication beyond orbital angular momentum. *Scientific reports*, *6*. download

Forbes, A., Dudley, A., & McLaren, M. (2016). Creation and detection of optical modes with spatial light modulators. *Advances in Optics and Photonics*, *8*(2), 200-227. download

Perez-Garcia, B., McLaren, M., Goyal, S. K., Hernandez-Aranda, R. I., Forbes, A., & Konrad, T. (2016). Quantum computation with classical light: Implementation of the Deutsch–Jozsa algorithm. *Physics Letters A*, *380*(22), 1925-1931. download

Naidoo, D., Roux, F. S., Dudley, A., Litvin, I., Piccirillo, B., Marrucci, L., & Forbes, A. (2016). Controlled generation of higher-order Poincaré sphere beams from a laser. *Nature Photonics*, *10*(5), 327-332. download

Goyal, S. K., Roux, F. S., Konrad, T., & Forbes, A. (2016). The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum. *Journal of Optics*, *18*(6), 064002. download

Naidoo, D., Harfouche, A., Fromager, M., Ait-Ameur, K., & Forbes, A. (2016). Emission of a propagation invariant flat-top beam from a microchip laser. *Journal of Luminescence*, *170*, 750-754. download

Zhang, Y., Roux, F. S., Konrad, T., Agnew, M., Leach, J., & Forbes, A. (2016). Engineering two-photon high-dimensional states through quantum interference. *Science advances*, *2*(2), e1501165. download

Brüning, R., Ndagano, B., McLaren, M., Schröter, S., Kobelke, J., Duparré, M., & Forbes, A. (2016). Data transmission with twisted light through a free-space to fiber optical communication link. *Journal of Optics*, *18*(3), 03LT01. download

Dudley, A., Majola, N., Chetty, N., & Forbes, A. (2016). Implementing digital holograms to create and measure complex-plane optical fields. *American Journal of Physics*, *84*(2), 106-112. download

##### 2015

Naidoo, D., Fromager, M., Ait-Ameur, K., & Forbes, A. (2015). Radially polarized cylindrical vector beams from a monolithic microchip laser. *Optical Engineering*, *54*(11), 111304-111304. download

Brüning, R., Flamm, D., Ngcobo, S. S., Forbes, A., & Duparré, M. (2015, February). Rapid measurement of the fiber’s transmission matrix. In *SPIE OPTO* (pp. 93890N-93890N). International Society for Optics and Photonics. download

Goyal, S. K., Roux, F. S., Forbes, A., & Konrad, T. (2015). Implementation of multidimensional quantum walks using linear optics and classical light.*Physical Review A*, *92*(4), 040302. download

Brüning, R., Zhang, Y., McLaren, M., Duparré, M., & Forbes, A. (2015). Overlap relation between free-space Laguerre Gaussian modes and step-index fiber modes. *JOSA A*, *32*(9), 1678-1682. download

McLaren, M., Konrad, T., & Forbes, A. (2015). Measuring the nonseparability of vector vortex beams. *Physical Review A*, *92*(2), 023833. download

Litvin, I. A., Mhlanga, T., & Forbes, A. (2015). Digital generation of shape-invariant Bessel-like beams. *Optics express*, *23*(6), 7312-7319. download

Schulze, C., Roux, F. S., Dudley, A., Rop, R., Duparré, M., & Forbes, A. (2015). Accelerated rotation with orbital angular momentum modes. *Physical Review A*, *91*(4), 043821. download

Ndagano, B., Bruning, R., McLaren, M., Duparre, M., & Forbes, A. (2015) Fiber propagation of vector modes. *Optics Express*, 23(13), 17330-17336. download

Perez-Garcia, B., Francis, J., McLaren, M., Hernandez-Aranda, R. I., Forbes, A., & Konrad, T. (2015). Quantum computation with classical light: The Deutsch Algorithm. *Physics Letters A*, *379*(28), 1675-1680. download

Litvin, I. A., Mhlanga, T., & Forbes, A. (2015). Digital generation of shape-invariant Bessel-like beams. *Optics express*, *23*(6), 7312-7319. download

McLaren, M. G., Roux, F. S., & Forbes, A. (2015). Realising high-dimensional quantum entanglement with orbital angular momentum. *South African Journal of Science*, *111*(1-2), 01-09. download

Burger, L., Litvin, I., Ngcobo, S., & Forbes, A. (2015). Implementation of a spatial light modulator for intracavity beam shaping. *Journal of Optics*, *17*(1), 015604. download

Milione, G., Dudley, A., Nguyen, T. A., Chakraborty, O., Karimi, E., Forbes, A., & Alfano, R. R. (2015). Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams. *Journal of Optics*, *17*(3), 035617. download

##### 2014

Aspden, R.S. et al., 2014. Experimental demonstration of Klyshko’s advanced-wave picture using a coincidence-count based, camera-enabled imaging system. *Journal of Modern Optics*, 61(March), pp.1–5. doi: 10.1080/09500340.2014.899645 download

Ismail, Y. et al., 2014. Characterization of a Polarisation Based Entangled Photon Source. *The African Review of Physics*, 9, pp.217–226.download

Litvin, I. a et al., 2014. Doughnut laser beam as an incoherent superposition of two petal beams. *Optics letters*, 39(3), pp.704–7. doi: 10.1364/OL.39.000704. download

Schulze, C. et al., 2014. Measurement of the orbital angular momentum density of Bessel beams by projection into a Laguerre-Gaussian basis. *Applied optics*, 53(August), pp.5924 – 5933. doi: 10.1364/AO.53.005924. download

Spangenberg, D.-M. et al., 2014. White light wavefront control with a spatial light modulator. *Optics Express*, 22(11), p.13870. doi: 10.1364/OE.22.013870.download

Trichili, A., Mhlanga, T. & Ismail, Y., 2014. Detection of Bessel beams with digital axicons. *Optics Express*, 22(14), pp.17553 – 17560. doi: 10.1364/OE.22.017553.download

##### 2013

Boubaha, B. et al., 2013. Spatial properties of coaxial superposition of two coherent Gaussian beams. *Applied optics*, 52(23), pp.5766–72. doi: 10.1364/AO.52.005766. download

Chaibi, A., Mafusire, C. & Forbes, A., 2013. Propagation of orbital angular momentum carrying beams through a perturbing medium. *Journal of Optics*, 15(10), p.105706. doi: 10.1088/2040-8978/15/10/105706. download

Giovannini, D. et al., 2013. Characterization of high-dimensional entangled systems via mutually unbiased measurements. *Physical Review Letters*, 110(14), pp.1–5. doi: 10.1103/PhysRevLett.110.143601.download

Goyal, S.K. et al., 2013. Implementing quantum walks using orbital angular momentum of classical light. *Physical Review Letters*, 110(26), pp.1–5. doi: 10.1103/PhysRevLett.110.263602. download

Litvin, I. a, Burger, L. & Forbes, A., 2013. Angular self-reconstruction of petal-like beams. *Optics letters*, 38(17), pp.3363–5. doi: 10.1364/OL.38.003363. download

Schulze, C. et al., 2013a. Measurement of the orbital angular momentum density of light by modal decomposition. *New Journal of Physics*, 15(July), p.073025. doi: 10.1088/1367-2630/15/7/073025 download

Schulze, C. et al., 2013b. Reconstruction of laser beam wavefronts based on mode analysis. *Applied optics*, 52(21), pp.5312–7. doi: 10.1364/AO.52.005312.download

##### 2012

Dudley, A. & Forbes, A., 2012. From stationary annular rings to rotating Bessel beams. *Journal of the Optical Society of America A*, 29(4), p.567. doi: 10.1364/JOSAA.29.000567.download

Flamm, D. et al., 2012. Mode analysis with a spatial light modulator as a correlation filter. *Optics Letters*, 37(13), p.2478. doi: 10.1364/OL.37.002478. download

Ismail, Y. et al., 2012. Shape invariant higher-order Bessel-like beams carrying orbital angular momentum. *Journal of Optics*, 14(8), p.085703. doi: 10.1088/2040-8978/14/8/085703. download

Litvin, I. a. et al., 2012. Azimuthal decomposition with digital holograms. *Optics Express*, 20(10), p.10996. doi: 10.1364/OE.20.010996. download

Naidoo, D. et al., 2012. Observing mode propagation inside a laser cavity. *New Journal of Physics*, 14(May), p.053021. doi: 10.1088/1367-2630/14/5/053021. download

Schulze, C., Flamm, D., et al., 2012. Beam-quality measurements using a spatial light modulator. *Optics Letters*, 37(22), pp.4687–9. doi: 10.1364/OL.37.002478.Decomp_Schulze2012 (1)

Schulze, C., Ngcobo, S., et al., 2012. Modal decomposition without a priori scale information. *Optics Express*, 20(25), pp.27866–73. doi: 10.1364/OE.20.027866.download

Schulze, C., Naidoo, D., et al., 2012. Wavefront reconstruction by modal decomposition. *Optics Express*, 20(18), p.19714. doi: 10.1364/OE.20.019714.Decomposition_Schulze2012

##### 2011

Agnew, M. et al., 2011. Tomography of the quantum state of photons entangled in high dimensions. *Physical Review A – Atomic, Molecular, and Optical Physics*, 84(6), p.062101. doi: 10.1103/PhysRevA.84.062101.

Godin, T. et al., 2011. Transverse correlation vanishing due to phase aberrations. *Optics Communications*, 284(19), pp.4601–4606. doi: 10.1016/j.optcom.2011.05.062.

Lavery, M.P.J. et al., 2011. Robust interferometer for the routing of light beams carrying orbital angular momentum. *New Journal of Physics*, 13(September), p.093014. doi: 10.1088/1367-2630/13/9/093014.

Litvin, I. a., Dudley, A. & Forbes, A., 2011. Poynting vector and orbital angular momentum density of superpositions of Bessel beams. *Optics Express*, 19(18), p.16760. doi: 10.1364/OE.19.016760.

McLaren, M., Sidderas-Haddad, E. & Forbes, A., 2011. Accurate measurement of microscopic forces and torques using optical tweezers. *South African Journal of Science*, 107(9-10), pp.1–8. doi: 10.4102/sajs.v107i9/10.579.

Naidoo, D. et al., 2011. Transverse mode selection in a monolithic microchip laser. *Optics Communications*, 284(23), pp.5475–5479. doi: 10.1016/j.optcom.2011.08.017.

##### 2010 & older

Bernhardi, E.H. et al., 2008. Estimation of thermal fracture limits in quasi-continuous-wave end-pumped lasers through a time-dependent analytical model. *Optics Express*, 16(15), pp.11115–11123. doi: 10.1364/OE.16.011115.

Burger, L. & Forbes, A., 2008. Kaleidoscope modes in large aperture Porro prism resonators. *Optics Express*, 16(17), pp.12707–12714. doi: 10.1364/OE.16.012707.

Litvin, I. A. & Forbes, A., 2009. Gaussian mode selection with intracavity diffractive optics. *Optics Letters*, 34(19), pp.2991–2993. doi: 10.1364/OL.34.002991.

Litvin, I. A. & Forbes, A., 2008. Bessel-Gauss resonator with internal amplitude filter. *Optics Communications*, 281(9), pp.2385–2392. doi: 10.1016/j.optcom.2007.12.052.

Litvin, I.A. & Forbes, A., 2009. Intra – cavity flat – top beam generation. *Optics Express*, 17(18), pp.15891–15903. doi: 10.1364/OE.17.015891.

Mafusire, C. et al., 2008. Optical aberrations in a spinning pipe gas lens. *Optics Express*, 16(13), pp.9850–9856. doi: 10.1364/OE.16.009850.

Vasilyeu, R. et al., 2009. Generating superpositions of higher-order Bessel beams. *Optics Express*, 17(26), pp.23389–23395. doi: 10.1364/OE.17.023389.