Geometrical aspects of first-order optical systems
Abstract
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.
Cite
@article{arxiv.physics/0506112,
title = {Geometrical aspects of first-order optical systems},
author = {A. G. Barriuso and J. J. Monzon and L. L. Sanchez-Soto and J. F. Carinena},
journal= {arXiv preprint arXiv:physics/0506112},
year = {2009}
}
Comments
11 pages. 4 figures. Accepted for publication in Journal of Optics A: Pure and Applied Optics