UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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Conference: Bucharest University Faculty of Physics 2022 Meeting


Section: Theoretical Physics and Applied Mathematics


Title:
Classical and quantum description of Laguerre-Gauss modes of the electromagnetic field and applications


Authors:
Vadim MUNTEANU, Mădălina BOCA


Affiliation:
University of Bucharest, Faculty of Physics, PO-Box MG-11, Magurele, RO-077125


E-mail
vadim.munteanu28@gmail.com


Keywords:
Laguerre Gauss modes; QED; orbital angular momentum of the light; dynamics


Abstract:
The purpose of this work is to present the classical and quantum description of the Laguerre-Gauss modes of the electromagnetic field. These are particular solutions of the Maxwell equations, with a helical structure of the wavefornt which makes them carriers of angular momentum. The present work starts with a classical description of the electromagnetic field, where Hermite/Laguerre-Gauss modes are introduced as solutions of Helmholtz equation in paraxial approximation. Connservation laws of energy, linear and angular momentum are derived from Maxwell equations. Next, a numerical application, consisting in the study of the non-relativistic motion of a charged particle interacting with a LG mode is implemented in Python. The equations of motion are solved numerically using scientific libraries such as Numpy and Scipy. Algebraic manipulations are handled with Sympy library. In the second part, the quantum electrodynamics (QED) framework is introduced briefly and then the second harmonic generation is studied. We present the expression of the transition rate, as obtained in [12], and we show intensity profiles of LG modes emitted in the process.


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