Radial quantum number of Laguerre-Gauss modes

(Received 31 January 2014; published 16 June 2014)We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensionalharmonicoscillatorincylindricalcoordinates.Wediscussladderoperatorsforthisvariable,andconfirmthattheyobey the commutation relations of the su(1,1) algebra. Using this fact, we examine how basic quantum opticalconcepts can be recast in terms of radial modes.DOI: 10.1103/PhysRevA.89.063813 PACS number(s): 42