Modal Diversity for Robust Free-Space Optical Communications
Physical Review Applied
Cox M., Cheng L., Rosales-Guzmán C., and Forbes A.
Free-space communication links are severely affected by atmospheric turbulence, which causes degradation in the transmitted signal. One of the most common solutions to overcome this is to exploit diversity. In this approach, information is sent in parallel over different paths using two or more transmitters that are spatially separated, with each beam therefore experiencing different atmospheric turbulence, lowering the probability of a receive error. In this work we propose and experimentally demonstrate a alternative method of diversity based on spatial modes of light, which we call modal diversity. We remove the need for a physical separation of the transmitters by exploiting the fact that spatial modes of light experience… Download
Brightness enhancement in a solid-state laser by mode transformation
Naidoo D., Litvin A. I. and Forbes A.
Laser brightness is a measure of the ability to deliver intense light to a target and encapsulates both the energy content and the beam quality. High-brightness lasers require that both parameters be maximized, yet standard laser cavities do not allow this. For example, multimode beams, a mix of many transverse modes, have a high energy content but low beam quality, while single transverse mode Gaussian beams have a good beam quality, but their small mode volume means a low energy extraction. Here we overcome this fundamental limitation and demonstrate an optimal approach to realizing high-brightness lasers. We employ… Download
A compact diffractive sorter for high-resolution demultiplexing of orbital angular momentum beams
Ruffato G., Girardi M., Massari M,. Mafakheri E., Sephton B., Capaldo P., Forbes A. and Romanato F.
The design and fabrication of a compact diffractive optical element is presented for the sorting of beams carrying orbital angular momentum (OAM) of light. The sorter combines a conformal mapping transformation with an optical fan-out, performing demultiplexing with unprecedented levels of miniaturization and OAM resolution. Moreover, an innovative configuration is proposed which simplifies alignment procedures and further improves the compactness of the optical device. Samples have been fabricated in the form of phase-only diffractive optics… Download
The first iteration of Grover’s algorithm using classical light with orbital angular momentum
Journal of Modern Optics
Perez-Garcia B., Hernandez-Aranda I. R., Forbes, A and Konrad T.
We present an experimental realization of the first iteration in Grover’s quantum algorithm using classical light and linear optical elements. The algorithm serves to find an entry marked by an oracle in an unstructured database. In our scheme, the quantum states encoding the database are represented by helical modes generated by means of a Spatial Light Modulator, while the marking corresponds to a π phase shift of the hidden mode. The optical implementation of Grover’s algorithm then selectively amplifies the intensity of the marked mode such that it can be revealed by a modal decomposition. The core of the algorithm… Download
Classical and quantum analysis of propagation invariant vector flat-top beams
Bhebhe N., Rosales-Guzman C. and Forbes A.
Laser beams with a near uniform intensity profile, such as flat-top and super-Gaussian beams, have found many applications, particularly in laser materials processing. Unfortunately such beams are not eigenmodes of free space and, thus, alter their intensity profile during propagation. This may be overcome by creating vector flat-top beams. Here, we exploit the polarization dependent efficiency of spatial light modulators to create a vector flat-top beam that maintains its intensity profile and vector nature during propagation. We apply a holistic classical and quantum toolkit to analyze the dynamics of the vector state during propagation and demonstrate the versatility of these beams in an optical trapping and tweezing application. Download
Are Bessel beams resilient to aberrations and turbulence?
Journal of the Optical Society of America
Mphuti, N., Botha, R. and Forbes, A.
It is understood from the conical wave picture that Bessel beams may self-heal after certain opaque obstructions, but the extrapolation to transparent phase screens is not self-evident. Here we consider the propagation of Bessel beams through aberrated obstacles and show that the self-healing is not guaranteed, but rather a function of the severity of the aberration. Paradoxically, we explain why strong aberrations may show self-healing while weak aberrations will not… Download
Tackling Africa’s digital divide
Lavery, M., Abadi, M., Bauer, R., Brambilla, G., Cheng, L., Cox, M., Dudley, A., Ellis, A., Fontaine, N., Kelly, A., Marquardt, C., Matlhane, S., Ndagano, B., Petruccione, F., Slavík, R., Romanato, F., Rosales-Guzmán, C., Roux, F., Roux, K., Wang, J. and Forbes, A.
Innovations in ‘sustainable’ photonics technologies such as free-space optical links and solar-powered equipment provide developing countries with new cost-effective opportunities for deploying future-proof telecommunication networks…. Download
Purity of vector vortex beams through a birefringent amplifier
Physical Review Applied
Sroor, H., Nyameko, L., Naidoo, D., Litvin, I., and Forbes, A.
Creating high-quality vector vortex (VV) beams is possible with a myriad of techniques at low power, and while a few studies have produced such beams at high power, none have considered the impact of amplification on the vector purity. Here we employ tools to study the amplification of VV beams and, in particular, the purity of such modes. We outline a versatile toolbox for such investigations and demonstrate its use in the general case of VV beams through a birefringent gain medium. Intriguingly, we show that it is possible to enhance the purity… Download
Entanglement beating in free space through spin-orbit coupling
Light: Science & Application
Otte, E., Rosales-Guzman, C., Ndagano, B., Denz, C., and Forbes, A.
It is well known that the entanglement of a quantum state is invariant under localunitary transformations. This rule dictates, for example, that the entanglement of internal degrees of freedom of a photon remain invariant during free-space propagation. Here, we outline a scenario in which this paradigm does not hold. Using local Bell states engineered from classical vector vortex beams with non-separable degrees of freedom, so-called classically entangled states, we demonstrate that the entanglement evolves during propagation, oscillating between maximally entangled (purely vector) and product states (purely scalar). We outline… Download
Turbulence and the Hong-Ou-Mandel effect
Physical Review A
Prabhakar, S., Mabena, C., Konrad, K., and Roux, F.
The effect of a decoherence channel, such as a turbulent atmosphere, on the second order quantum interference in the Hong-Ou-Mandel (HOM) effect is investigated. The investigation includes both theoretical analyses and an experimental implementation of the process. In our experiment, entangled input states are prepared with spontaneous parametric down-conversion. The atmospheric turbulence is modelled as a single-phase screen and… Download
Structured Laguerre-Gaussian beams for mitigation of spherical aberration in tightly focused regimes
Journal of Optics
Haddadi, S., Bouzid, O., Fromager, M., Hasnaoui, A., Harfouche, A., Cagniot, E., Forbes, A., and Ait-Ameur, K.
Many laser applications utilise a focused laser beam having a single-lobed intensity profile in the focal plane, ideally with the highest possible on-axis intensity. Conventionally, this is achieved with the lowest-order Laguerre–Gaussian mode (LG00), the Gaussian beam, in a tight focusing configuration. However, tight focusing often involves significant spherical aberration due to the high numerical aperture of the systems involved, thus degrading the focal quality. Here, we demonstrate that a high-order radial LGp0 mode can be tailored to meet and in some instancesexceed the performance of the Gaussian. We achieve… Download
Creation and detection of vector vortex modes for classical and quantum communication
Journal of Lightwave Technology
Ndagano, B., Nape, I.,Cox M., Rosales-Guzmán C. and Forbes, A.
Vector vortex beams are structured states of light that are nonseparable in their polarisation and spatial mode, they are eigenmodes of free-space and many fiber systems, and have the capacity to be used as information carriers for both classical and quantum communication. Here, we outline recent progress in our understanding of these modes, from their creation to their characterization and detection. We then use these tools to study their propagation behavior in free-space and optical fiber and show that modal cross-talk results in a decay of vector states into separable scalar modes, with a concomitant loss of information. We present… Download
A hybrid quantum eraser scheme for characterization of free-space and fiber communication channels
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). Remarkably, vector modes (natural modes of free-space and fiber) have a non-separable feature of spin–orbit coupled states, equivalent to the description of two independently marked paths. We explore… Download
Bouzid O., Haddadi, S., Fromager, M., Cagniot, E., Ferria, K., Forber, A. and Ait-Ameur, K. (2017). Focusing anomalies with binary diffractive optical elements, Applied Optics 56, 9735.
Mabena, C. and Roux, F. (2017). High-dimensional quantum channel estimation using classical light, Phys. Rev. A. 96, 053860. Download
Ndagano, B., Mphuthi, N., Milione, G. and Forbes, A. (2017). Comparing mode-crosstalk and mode-dependent loss of laterally displaced orbital angular momentum and Hermite–Gaussian modes for free-space optical communication. Optics letters, 42(20), 4175-4178. Download
Rosales-Guzmán, C., Bhebhe, N. and Forbes, A. (2017). Simultaneous generation of multiple vector beams on a single SLM. Optics express, 25(21), 25697-25706. Download
Zhang, Y., Agnew, M., Roger, T., Roux, F.S., Konrad, T., Faccio, D., Leach, J. and Forbes, A. (2017). Simultaneous entanglement swapping of multiple orbital angular momentum states of light. Nature Communications, 8(1), 632. Download
Vetter, C., Dudley, A., Szameit, A. and Forbes, A. (2017). Real and virtual propagation dynamics of angular accelerating white light beams. Optics express, 25(17), 20530-20540. Download
Rosales-Guzmán, C. and Forbes, A. (2017). How to shape light with spatial light modulators. SPIE.SPOTLIGHT Download
Forbes, A. and Botha, L., (2017). Laser Isotope Separation. Laser Beam Shaping Applications (2nd ed.), Ch. 7, eds. F.M. Dickey and T. Lizotte. CRC Taylor & Francis Group (New York) Download
Rosales-Guzmán, C., Bhebhe, N., Mahonisi, N. and Forbes, A. (2017). Multiplexing 200 modes on a single digital hologram. Journal of Optics, 19 113501 Download
Nape, I., Kyeremah, C., Vallés, A., Rosales-Guzmán, C., Buah-Bassuah, P.K. and Forbes, A., (2017). Hybrid quantum erasure scheme for channel disturbance characterization. Optics Communications 408, 53-57 Download
Roux F.S. (2017). Biphoton states in correlated turbulence, Phys. Rev. A.Download
Nape, I., Ndagano, B. and Forbes, A., (2017). Erasing the orbital angular momentum information of a photon. Physical Review A, 95 (5), 053859 Download
Ismail, Y., Joshi, S., Forbes, A. and Petruccione, F., (2017). Instrumentation limitation on a polarization-based entangled photon source. JOSA B, 34(6), 1084-1089 Download
McLaren, M. and Forbes, A., (2017). Digital spiral-slit for bi-photon imaging. Journal of Optics, 19(4), 044006 Download
Webster, J., Rosales-Guzmán, C. and Forbes, A., (2017). Radially dependent angular acceleration of twisted light. Optics letters, 42(4), 675-678. Download
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., (2017). Characterizing quantum channels with non-separable states of classical light. Nature Physics, 13(4), 397 Download
Forbes, A., (2017). Controlling light’s helicity at the source: orbital angular momentum states from lasers. Phil. Trans. R. Soc. A, 375(2087), 20150436 Download
Sephton, B., Dudley, A. and Forbes, A. (2017). Quantum Walks. Quest, 13(4), 15-18. Download
Forbes, A. (2017). Blurring the classical quantum divide. Optics and photonics news, 17(12), 36. Download
Rubinsztein-Dunlop, H., Forbes, A., Berry, M., Dennis, M., Andrews, D., Mansuripur, M., Denz, C., Alpmann, C., Banzer, P., Bauer, T. and Karimi, E., (2016). Roadmap on structured light. Journal of Optics, 19(1), 013001. 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
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
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
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
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
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.