Radial quantum number of Laguerre-Gauss modes



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Karimi, E. and Boyd, R.W. and Hoz Iglesias, Pablo de la and de Guise, H. and Řeháček, J. and Hradil, Z. and Aiello, A. and Leuchs, Gerd and Sánchez Soto, Luis Lorenzo (2014) Radial quantum number of Laguerre-Gauss modes. Physical review A, 89 (6). ISSN 1050-2947

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Official URL: http://dx.doi.org/ 10.1103/PhysRevA.89.063813


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.

Item Type:Article
Additional Information:

© 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).

Uncontrolled Keywords:Orbital angular-momentum; Minimum uncertainty states; Electron vortex beams; Coherent states; Intelligent states; SU(1,1); Vortices; Light; SU(2); Representations.
Subjects:Sciences > Physics > Optics
ID Code:29498
Deposited On:14 Apr 2015 08:48
Last Modified:29 Apr 2022 16:09

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