Topology and geometry of caustics in relation with experiments

Alain Joets

Banach Center Publications (1999)

  • Volume: 50, Issue: 1, page 169-177
  • ISSN: 0137-6934

Abstract

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Caustics of geometrical optics are understood as special types of Lagrangian singularities. In the compact case, they have remarkable topological properties, expressed in particular by the Chekanov relation. We show how this relation may be experimentally checked on an example of biperiodic caustics produced by the deflection of the light by a nematic liquid crystal layer. Moreover the physical laws may impose a geometrical constraint, when the system is invariant by some group of symmetries. We show, on the example of polyhedral caustics, how the two constraints force degenerate umbilics of integer index to appear and determine their spatial organization.

How to cite

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Joets, Alain. "Topology and geometry of caustics in relation with experiments." Banach Center Publications 50.1 (1999): 169-177. <http://eudml.org/doc/209005>.

@article{Joets1999,
abstract = {Caustics of geometrical optics are understood as special types of Lagrangian singularities. In the compact case, they have remarkable topological properties, expressed in particular by the Chekanov relation. We show how this relation may be experimentally checked on an example of biperiodic caustics produced by the deflection of the light by a nematic liquid crystal layer. Moreover the physical laws may impose a geometrical constraint, when the system is invariant by some group of symmetries. We show, on the example of polyhedral caustics, how the two constraints force degenerate umbilics of integer index to appear and determine their spatial organization.},
author = {Joets, Alain},
journal = {Banach Center Publications},
keywords = {caustics; geometrical optics; Lagrangian singularities; Chekanov relation},
language = {eng},
number = {1},
pages = {169-177},
title = {Topology and geometry of caustics in relation with experiments},
url = {http://eudml.org/doc/209005},
volume = {50},
year = {1999},
}

TY - JOUR
AU - Joets, Alain
TI - Topology and geometry of caustics in relation with experiments
JO - Banach Center Publications
PY - 1999
VL - 50
IS - 1
SP - 169
EP - 177
AB - Caustics of geometrical optics are understood as special types of Lagrangian singularities. In the compact case, they have remarkable topological properties, expressed in particular by the Chekanov relation. We show how this relation may be experimentally checked on an example of biperiodic caustics produced by the deflection of the light by a nematic liquid crystal layer. Moreover the physical laws may impose a geometrical constraint, when the system is invariant by some group of symmetries. We show, on the example of polyhedral caustics, how the two constraints force degenerate umbilics of integer index to appear and determine their spatial organization.
LA - eng
KW - caustics; geometrical optics; Lagrangian singularities; Chekanov relation
UR - http://eudml.org/doc/209005
ER -

References

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