Geometrical aspects of first-order optical systems

Details Geometrical aspects of first-order optical systems Geometrical aspects of first-order optical systems

2005-06-13

arxiv.org/abs/physics/0506112v1

Physics

Optics

11 pages. 4 figures. Accepted for publication in Journal of Optics A: Pure and Applied Optics

Scientific paper

10.1088/1464-4258/7/9/002

We reconsider the basic properties of ray-transfer matrices for first-order optical systems from a geometrical viewpoint. In the paraxial regime of scalar wave optics, there is a wide family of beams for which the action of a ray-transfer matrix can be fully represented as a bilinear transformation on the upper complex half-plane, which is the hyperbolic plane. Alternatively, this action can be also viewed in the unit disc. In both cases, we use a simple trace criterion that arranges all first-order systems in three classes with a clear geometrical meaning: they represent rotations, translations, or parallel displacements. We analyze in detail the relevant example of an optical resonator.

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