Publication: Non-Euclidean symmetries of first-order optical systems
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2020-02
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The Optical Society of America
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Abstract
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.
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Received 23 September 2019; revised 1 December 2019; accepted 6 December 2019; posted 6 December 2019 (Doc. ID 378661); published 10 January 2020