Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C. & Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992).
Stav, T. et al. Quantum entanglement of the spin and orbital angular momentum of photons using metamaterials. Science 361, 1101–1104 (2018).
Karimi, E. et al. Spin-orbit hybrid entanglement of photons and quantum contextuality. Phys. Rev. A 82, 022115 (2010).
Pan, J.-W. et al. Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777–838 (2012).
Gorodetski, Y., Niv, A., Kleiner, V. & Hasman, E. Observation of the spin-based plasmonic effect in nanoscale structures. Phys. Rev. Lett. 101, 043903 (2008).
Bliokh, K. Y., Rodríguez-Fortuño, F. J., Nori, F. & Zayats, A. V. Spin–orbit interactions of light. Nat. Photon. 9, 796–808 (2015).
Li, C.-F. Spin and orbital angular momentum of a class of nonparaxial light beams having a globally defined polarization. Phys. Rev. A 80, 063814 (2009).
Zhao, Y., Edgar, J. S., Jeffries, G. D. M., McGloin, D. & Chiu, D. T. Spin-to-orbital angular momentum conversion in a strongly focused optical beam. Phys. Rev. Lett. 99, 073901 (2007).
Krenn, M., Tischler, N. & Zeilinger, A. On small beams with large topological charge. New J. Phys. 18, 033012 (2016).
Defienne, H., Reichert, M. & Fleischer, J. W. General model of photon-pair detection with an image sensor. Phys. Rev. Lett. 120, 203604 (2018).
Ndagano, B. et al. Imaging and certifying high-dimensional entanglement with a single-photon avalanche diode camera. npj Quantum Inf. 6, 94 (2020).
Wang, J., Sciarrino, F., Laing, A. & Thompson, M. G. Integrated photonic quantum technologies. Nat. Photon. 14, 273–284 (2020).
Madsen, L. S. et al. Quantum computational advantage with a programmable photonic processor. Nature 606, 75–81 (2022).
Faraon, A. et al. Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade. Nat. Phys. 4, 859–863 (2008).
O’Brien, J. L., Furusawa, A. & Vučković, J. Photonic quantum technologies. Nat. Photon. 3, 687–695 (2009).
Reddy, D. V., Nerem, R. R., Nam, S. W., Mirin, R. P. & Verma, V. B. Superconducting nanowire single-photon detectors with 98% system detection efficiency at 1550 nm. Optica 7, 1649 (2020).
Harrow, A. W. & Montanaro, A. Quantum computational supremacy. Nature 549, 203–209 (2017).
Krenn, M., Hochrainer, A., Lahiri, M. & Zeilinger, A. Entanglement by path identity. Phys. Rev. Lett. 118, 080401 (2017).
Halder, M. et al. Entangling independent photons by time measurement. Nat. Phys. 3, 692–695 (2007).
Reimer, C. et al. Generation of multiphoton entangled quantum states by means of integrated frequency combs. Science 351, 1176–1180 (2016).
Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001).
Nagali, E. et al. Quantum information transfer from spin to orbital angular momentum of photons. Phys. Rev. Lett. 103, 013601 (2009).
Molina-Terriza, G., Torres, J. P. & Torner, L. Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum. Phys. Rev. Lett. 88, 013601 (2001).
Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).
Simon, C. & Pan, J.-W. Polarization entanglement purification using spatial entanglement. Phys. Rev. Lett. 89, 257901 (2002).
Müller, M., Bounouar, S., Jöns, K. D., Glässl, M. & Michler, P. On-demand generation of indistinguishable polarization-entangled photon pairs. Nat. Photon. 8, 224–228 (2014).
Fabre, C. & Treps, N. Modes and states in quantum optics. Rev. Mod. Phys. 92, 035005 (2020).
Devlin, R. C., Ambrosio, A., Rubin, N. A., Mueller, J. P. B. & Capasso, F. Arbitrary spin-to–orbital angular momentum conversion of light. Science 358, 896–901 (2017).
Beth, R. A. Mechanical detection and measurement of the angular momentum of light. Phys. Rev. 50, 115–125 (1936).
Fickler, R. et al. Quantum entanglement of high angular momenta. Science 338, 640–643 (2012).
Wang, J. et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photon. 6, 488–496 (2012).
Fickler, R. et al. Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information. Nat. Commun. 5, 4502 (2014).
Ostrovsky, E., Cohen, K., Tsesses, S., Gjonaj, B. & Bartal, G. Nanoscale control over optical singularities. Optica 5, 283 (2018).
Tsesses, S., Cohen, K., Ostrovsky, E., Gjonaj, B. & Bartal, G. Spin–orbit interaction of light in plasmonic lattices. Nano Lett. 19, 4010–4016 (2019).
Van Enk, S. J. & Nienhuis, G. Commutation rules and eigenvalues of spin and orbital angular momentum of radiation fields. J. Mod. Opt. 41, 963–977 (1994).
Das, P., Yang, L.-P. & Jacob, Z. What are the quantum commutation relations for the total angular momentum of light? tutorial. J. Opt. Soc. Am. B 41, 1764 (2024).
Shitrit, N. et al. Spin-optical metamaterial route to spin-controlled photonics. Science 340, 724–726 (2013).
Kher-Aldeen, J. et al. Dynamic control and manipulation of near-fields using direct feedback. Light Sci. Appl. 13, 298 (2024).
Lopez-Mago, D. & Gutiérrez-Vega, J. C. Shaping Bessel beams with a generalized differential operator approach. J. Opt. 18, 095603 (2016).
Soares, W. C., Caetano, D. P. & Hickmann, J. M. Hermite–Bessel beams and the geometrical representation of nondiffracting beams with orbital angular momentum. Opt. Express 14, 4577 (2006).
Frischwasser, K. et al. Real-time sub-wavelength imaging of surface waves with nonlinear near-field optical microscopy. Nat. Photon. 15, 442–448 (2021).
Milione, G., Sztul, H. I., Nolan, D. A. & Alfano, R. R. Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light. Phys. Rev. Lett. 107, 053601 (2011).
Dieleman, F., Tame, M. S., Sonnefraud, Y., Kim, M. S. & Maier, S. A. Experimental verification of entanglement generated in a plasmonic system. Nano Lett. 17, 7455–7461 (2017).
Tame, M. S. et al. Quantum plasmonics. Nat. Phys. 9, 329–340 (2013).
Fakonas, J. S., Mitskovets, A. & Atwater, H. A. Path entanglement of surface plasmons. New J. Phys. 17, 023002 (2015).
Dowling, J. P. Quantum optical metrology—the lowdown on high-N00N states. Contemp. Phys. 49, 125–143 (2008).
Howell, J. C., Bennink, R. S., Bentley, S. J. & Boyd, R. W. Realization of the Einstein–Podolsky–Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion. Phys. Rev. Lett. 92, 210403 (2004).
Bavaresco, J. et al. Measurements in two bases are sufficient for certifying high-dimensional entanglement. Nat. Phys. 14, 1032–1037 (2018).
Dai, D. Silicon nanophotonic integrated devices for on-chip multiplexing and switching. J. Lightwave Technol. 35, 572–587 (2017).
Orcutt, J. S. et al. Nanophotonic integration in state-of-the-art CMOS foundries. Opt. Express 19, 2335 (2011).
Olivieri, L. et al. Terahertz nonlinear ghost imaging via plane decomposition: toward near-field micro-volumetry. ACS Photon. 10, 1726–1734 (2023).
Ryczkowski, P., Barbier, M., Friberg, A. T., Dudley, J. M. & Genty, G. Ghost imaging in the time domain. Nat. Photon. 10, 167–170 (2016).
Popov, E. (ed.) Gratings: Theory and Numeric Applications, Second Revisited Edition (Institut Fresnel, 2014).
Johnson, K. C. Projection operator method for biperiodic diffraction gratings with anisotropic/bianisotropic generalizations. J. Opt. Soc. Am. A 31, 1698 (2014).
Hong, M., Dawkins, R. B., Bertoni, B., You, C. & Magaña-Loaiza, O. S. Nonclassical near-field dynamics of surface plasmons. Nat. Phys. 20, 830–835 (2024).
Lawrie, B. J., Evans, P. G. & Pooser, R. C. Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons. Phys. Rev. Lett. 110, 156802 (2013).
Huck, A. et al. Demonstration of quadrature-squeezed surface plasmons in a gold waveguide. Phys. Rev. Lett. 102, 246802 (2009).
Fasel, S. et al. Energy-time entanglement preservation in plasmon-assisted light transmission. Phys. Rev. Lett. 94, 110501 (2005).
Altewischer, E., van Exter, M. P. & Woerdman, J. P. Plasmon-assisted transmission of entangled photons. Nature 418, 304–306 (2002).
Chang, D. E., Sørensen, A. S., Hemmer, P. R. & Lukin, M. D. Quantum optics with surface plasmons. Phys. Rev. Lett. 97, 053002 (2006).
Ren, X. F., Guo, G. P., Huang, Y. F., Li, C. F. & Guo, G. C. Plasmon-assisted transmission of high-dimensional orbital angular-momentum entangled state. Europhys. Lett. 76, 753–759 (2006).
Machado, F., Rivera, N., Buljan, H., Soljačić, M. & Kaminer, I. Shaping polaritons to reshape selection rules. ACS Photon. 5, 3064–3072 (2018).
Bliokh, K. Y., Niv, A., Kleiner, V. & Hasman, E. Geometrodynamics of spinning light. Nat. Photon. 2, 748–753 (2008).
Spektor, G., David, A., Gjonaj, B., Bartal, G. & Orenstein, M. Metafocusing by a metaspiral plasmonic lens. Nano Lett. 15, 5739–5743 (2015).
Kam, A. et al. Non-classical correlation between mode-entangled pairs of surface plasmon polaritons. In Proc. CLEO: Fundamental Science FF2C.5 (Optica Publishing Group, 2023).
Wright, W. E. Parallelization of Bresenham’s line and circle algorithms. IEEE Comput. Graph. Appl. 10, 60–67 (1990).
Gareth, J., Daniela, W., Trevor, H. & Robert, T. An Introduction to Statistical Learning Vol. 112 (Springer, 2013).
Ilin, Y. & Arad, I. Learning a quantum channel from its steady-state. New J. Phys. 26, 073003 (2024).
Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. Preprint at https://arxiv.org/abs/1412.6980 (2014).
Pelucchi, E. et al. The potential and global outlook of integrated photonics for quantum technologies. Nat. Rev. Phys. 4, 194–208 (2021).
Loredo, J. C. et al. Generation of non-classical light in a photon-number superposition. Nat. Photon. 13, 803–808 (2019).
Crespi, A. et al. Integrated photonic quantum gates for polarization qubits. Nat. Commun. 2, 566 (2011).
Marsili, F. et al. Detecting single infrared photons with 93% system efficiency. Nat. Photon. 7, 210–214 (2013).
Wang, J. et al. Multidimensional quantum entanglement with large-scale integrated optics. Science 360, 285–291 (2018).
Sit, A. et al. High-dimensional intracity quantum cryptography with structured photons. Optica 4, 1006 (2017).
Reid, M. D. et al. The Einstein–Podolsky–Rosen paradox: from concepts to applications. Rev. Mod. Phys. 81, 1727–1751 (2009).