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The optical singularities of birefringent dichroic chiral crystals

The optical singularities of birefringent dichroic chiral crystals
The optical singularities of birefringent dichroic chiral crystals
Using a new formalism involving projection from the sphere of directions to the stereographic plane, and associated complex variables, explicit formulae are obtained for the two refractive indices and polarizations in optically anisotropic crystals that are both dichroic (absorbing) and chiral (optically active). This enables three types of polarization singularity to be classified and explored: singular axes, which are degeneracies where the two refractive indices are equal, and which for a transparent non-chiral crystal condense pairwise onto the optic axes; C points, where the polarization is purely circular (right- or left-handed), with topological index +1, +12 or +14 and whose positions are independent of the chirality; and L lines, where the polarization is purely linear, dividing direction space into regions with rightand left-handedness. A local model captures essential features of the general theory. Interference figures generated by slabs of crystal viewed directly or through a polarizer and/or analyser enable the singularities to be displayed directly.
polarization, crystal optics, singularities, degeneracies, stereographic projection
1364-5021
1261-1292
Berry, M.V.
ab44fe7c-0c8c-4c7a-981f-50fe4a5bc6ad
Dennis, M.R.
ff55cf66-eb8b-4eb9-83eb-230c2f223d61
Berry, M.V.
ab44fe7c-0c8c-4c7a-981f-50fe4a5bc6ad
Dennis, M.R.
ff55cf66-eb8b-4eb9-83eb-230c2f223d61

Berry, M.V. and Dennis, M.R. (2003) The optical singularities of birefringent dichroic chiral crystals. Proceedings of the Royal Society A, 459 (2033), 1261-1292. (doi:10.1098/rspa.2003.1155).

Record type: Article

Abstract

Using a new formalism involving projection from the sphere of directions to the stereographic plane, and associated complex variables, explicit formulae are obtained for the two refractive indices and polarizations in optically anisotropic crystals that are both dichroic (absorbing) and chiral (optically active). This enables three types of polarization singularity to be classified and explored: singular axes, which are degeneracies where the two refractive indices are equal, and which for a transparent non-chiral crystal condense pairwise onto the optic axes; C points, where the polarization is purely circular (right- or left-handed), with topological index +1, +12 or +14 and whose positions are independent of the chirality; and L lines, where the polarization is purely linear, dividing direction space into regions with rightand left-handedness. A local model captures essential features of the general theory. Interference figures generated by slabs of crystal viewed directly or through a polarizer and/or analyser enable the singularities to be displayed directly.

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Published date: 2003
Keywords: polarization, crystal optics, singularities, degeneracies, stereographic projection

Identifiers

Local EPrints ID: 29382
URI: https://eprints.soton.ac.uk/id/eprint/29382
ISSN: 1364-5021
PURE UUID: 886d87eb-67fd-4d77-8252-63a39716c957

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Date deposited: 12 May 2006
Last modified: 14 Aug 2019 17:49

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