Non-Euclidean symmetries of first-order optical systems

We revisit the basic aspects of first-order optical systems from a geometrical viewpoint. In the paraxial regime, there is a wide family of beams for which the action of these systems can be represented as a Möbius transformation. We examine this action from the perspective of non-Euclidean hyperbol...

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Bibliographic Details
Published in:Journal of the Optical Society of America. A, Optics, image science, and vision Optics, image science, and vision, 2020-02, Vol.37 (2), p.225-230
Main Authors: Monzón, J J, Montesinos-Amilibia, J M, Sánchez-Soto, L L
Format: Article
Language:English
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Summary:We revisit the basic aspects of first-order optical systems from a geometrical viewpoint. In the paraxial regime, there is a wide family of beams for which the action of these systems can be represented as a Möbius transformation. We examine this action from the perspective of non-Euclidean hyperbolic geometry and resort to the isometric-circle method to decompose it as a reflection followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations for basic elements, such as free propagation and thin lenses, and link them with physical parameters of the system.
ISSN:1084-7529
1520-8532
DOI:10.1364/JOSAA.378661