Radial quantum number of Laguerre-Gauss modes

Karimi, E.; Boyd, R. W.; de la Hoz, P.; de Guise, H.; Rehacek, J.; Hradil, Z.; Aiello, A.; Leuchs, G.; Sanchez-Soto, L. L.

doi:10.1103/PhysRevA.89.063813

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Radial quantum number of Laguerre-Gauss modes

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Aiello, A.
Optical Quantum Information Theory, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Leuchs, G.
Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Sanchez-Soto, L. L.
Guests, Max Planck Institute for the Science of Light, Max Planck Society;

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Citation

Karimi, E., Boyd, R. W., de la Hoz, P., de Guise, H., Rehacek, J., Hradil, Z., et al. (2014). Radial quantum number of Laguerre-Gauss modes. PHYSICAL REVIEW A, 89(6): 063813. doi:10.1103/PhysRevA.89.063813.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-65E5-8

Abstract

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.