GEOMETRY OF REFRACTIONS AND REFLECTIONS THROUGH A BIPERIODIC MEDIUM

被引：6

作者：

Glendinning, Paul ^{[1
]}

机构：

[1] Univ Manchester, Sch Math, Oxford Rd, Manchester M13 9PL, Lancs, England

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2016年 / 76卷 / 04期

关键词：

composite billiards; refraction; reflection; ergodicity; geometric ray theory; interval exchange maps;

D O I：

10.1137/15M1014127

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1219 / 1238

页数：20

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