dorsal/arxiv
View SchemaGeometrical aspects of first-order optical systems
| Authors | A. G. Barriuso, J. J. Monzon, L. L. Sanchez-Soto, J. F. Carinena |
|---|---|
| Categories | |
| ArXiv ID | physics/0506112 |
| URL | https://arxiv.org/abs/physics/0506112 |
| DOI | 10.1088/1464-4258/7/9/002 |
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.
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"abstract": "We reconsider the basic properties of ray-transfer matrices for first-order\noptical systems from a geometrical viewpoint. In the paraxial regime of scalar\nwave optics, there is a wide family of beams for which the action of a\nray-transfer matrix can be fully represented as a bilinear transformation on\nthe upper complex half-plane, which is the hyperbolic plane. Alternatively,\nthis action can be also viewed in the unit disc. In both cases, we use a simple\ntrace criterion that arranges all first-order systems in three classes with a\nclear geometrical meaning: they represent rotations, translations, or parallel\ndisplacements. We analyze in detail the relevant example of an optical\nresonator.",
"arxiv_id": "physics/0506112",
"authors": [
"A. G. Barriuso",
"J. J. Monzon",
"L. L. Sanchez-Soto",
"J. F. Carinena"
],
"categories": [
"physics.optics"
],
"doi": "10.1088/1464-4258/7/9/002",
"title": "Geometrical aspects of first-order optical systems",
"url": "https://arxiv.org/abs/physics/0506112"
},
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