Hyperbolic reflections as fundamental building blocks for multilayer optics

Details Hyperbolic reflections as fundamental building blocks for multilayer optics Hyperbolic reflections as fundamental building blocks for multilayer optics

2003-05-12

arxiv.org/abs/physics/0305040v1

Physics

Optics

7 pages, 7 figures, accepted for publication in J. Opt. Soc. Am. A

Scientific paper

10.1364/JOSAA.20.001812

We reelaborate on the basic properties of lossless multilayers by using bilinear transformations. We study some interesting properties of the multilayer transfer function in the unit disk, showing that hyperbolic geometry turns out to be an essential tool for understanding multilayer action. We use a simple trace criterion to classify multilayers into three classes that represent rotations, translations, or parallel displacements. Moreover, we show that these three actions can be decomposed as a product of two reflections in hyperbolic lines. Therefore, we conclude that hyperbolic reflections can be considered as the basic pieces for a deeper understanding of multilayer optics.

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