Karimi, E.Boyd, R.W.Hoz Iglesias, Pablo de lade Guise, H.Řeháček, J.Hradil, Z.Aiello, A.Leuchs, GerdSánchez Soto, Luis Lorenzo2023-06-192023-06-192014-06-161050-294710.1103/PhysRevA.89.063813https://hdl.handle.net/20.500.14352/33972© 2014 American Physical Society. E.K. and R.W.B. acknowledge the support of the Canada Excellence Research Chairs (CERC) Program. The work of H.G. is supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. J.R. and Z.H. are grateful for the financial assistance of the Technology Agency of the Czech Republic (Grant No. TE01020229) and the Czech Ministry of Industry and Trade (Grant No. FR-TI1/364). G.L. is partially funded by EU FP7 (Grant Q-ESSENCE). Finally, P.H. and L.L.S.S. acknowledge the support from the Spanish MINECO (Grant No. FIS2011-26786).We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensional harmonic oscillator in cylindrical coordinates. We discuss ladder operators for this variable, and confirm that they obey the commutation relations of the su(1,1) algebra. Using this fact, we examine how basic quantum optical concepts can be recast in terms of radial modes.engjournal articlehttp://dx.doi.org/ 10.1103/PhysRevA.89.063813http://journals.aps.org/open access535Orbital angular-momentumMinimum uncertainty statesElectron vortex beamsCoherent statesIntelligent statesSU(11)VorticesLightSU(2)Representations.Óptica (Física)2209.19 Óptica Física