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Field theory of monochromatic optical beams I. classical fields

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Aiello,  Andrea
Marquardt Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Aiello_2020_J._Opt._22_014001.pdf
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Field_theory_I.png
(Supplementary material), 46KB

Citation

Aiello, A. (2019). Field theory of monochromatic optical beams I. classical fields. Journal of Optics, 22(1): 014001. doi:10.1088/2040-8986/ab5c5c.


Cite as: http://hdl.handle.net/21.11116/0000-0005-4732-3
Abstract
We study monochromatic, scalar solutions of the Helmholtz and paraxial wave equations from a field-theoretic point of view. We introduce appropriate time-independent Lagrangian densities for which the Euler-Lagrange equations reproduces either Helmholtz and paraxial wave equations with the $z$-coordinate, associated with the main direction of propagation of the fields, playing the same role of time in standard Lagrangian theory. For both Helmholtz and paraxial scalar fields, we calculate the canonical energy-momentum tensor and determine the continuity equations relating ``energy'' and ``momentum'' of the fields. Eventually, the reduction of the Helmholtz wave equation to a useful first-order Dirac form, is presented. This work sheds some light on the intriguing and not so acknowledged connections between angular spectrum representation of optical wavefields, cosmological models and physics of black holes.