XXXVIII Workshop on Geometric Methods in Physics 30.06-6.07.2019
VIII School on Geometry and Physics 24-28.06.2019

Pedro Raúl Jiménez Macías

Laguerre-Gaussian optical beams as boson realizations of either $SU(1,1)$ or $SU(2)$ groups

The paraxial wave equation for the propagation of light in a weakly guiding inhomogeneous medium with quadratic refractive index can be addressed via the eigenvalue problem that includes the (stationary) guided Laguerre-Gaussian modes as eigenvectors and the spectrum of propagation constants as the set of eigenvalues. We are interested in non stationary wave-packet solutions of the above problem to construct the representation space of either $SU(1,1)$ or $SU(2)$ Lie groups. It is found that the generators of the related Lie algebras can be expressed in terms of the Laguerre-Gaussian intertwining operators, so the related coherent states can be constructed such that their propagation factors depend on the discrete parameters that define the group representation.
Joint work with S. Cruz y Cruz, Z. Gress, O. Rosas-Ortiz.

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