GEOMETRY OF REFRACTIONS AND REFLECTIONS THROUGH A BIPERIODIC MEDIUM

Paul Glendinning

doi:10.1137/15M1014127

GEOMETRY OF REFRACTIONS AND REFLECTIONS THROUGH A BIPERIODIC MEDIUM

Paul Glendinning

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Abstract

The behavior of light rays obeying Snell's law in a medium made up of two materials with different refractive indices and which are arranged in a periodic chessboard pattern is described. The analysis is in some ways analogous to the study of rational billiards and uses a return map on one surface to prove, among other things, that the number of angles with which any individual ray intersects the lattice is bounded and that if the ratio of refractive indices is large enough, then the dynamics can be described by interval exchange maps.

Original language	English
Pages (from-to)	1219-1238
Number of pages	20
Journal	SIAM Journal of Applied Mathematics
Volume	76
Issue number	4
Early online date	6 Jul 2016
DOIs	https://doi.org/10.1137/15M1014127
Publication status	Published - 2016

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title = "GEOMETRY OF REFRACTIONS AND REFLECTIONS THROUGH A BIPERIODIC MEDIUM",

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JF - SIAM Journal of Applied Mathematics

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GEOMETRY OF REFRACTIONS AND REFLECTIONS THROUGH A BIPERIODIC MEDIUM

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