On the Bertin surfaces of photoelastic crystals

Fabrizio Daví

doi:10.1364/JOSAA.32.002323

On the Bertin surfaces of photoelastic crystals

Fabrizio Daví

Journal of the Optical Society of America A
Vol. 32,
Issue 12,
pp. 2323-2337
(2015)
•https://doi.org/10.1364/JOSAA.32.002323

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Fabrizio Daví, "On the Bertin surfaces of photoelastic crystals," J. Opt. Soc. Am. A 32, 2323-2337 (2015)

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Related Topics
Table of Contents Category
- Physical Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Mathematical methods in physics (000.3860)
- Anisotropic optical materials (160.1190)
- Crystal optics (260.1180)
- Birefringence (260.1440)
- Inhomogeneous optical media (260.2710)

About this Article
History
- Original Manuscript: August 5, 2015
- Revised Manuscript: September 22, 2015
- Manuscript Accepted: September 25, 2015
- Published: November 10, 2015

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Abstract

Conoscopic analysis of interference fringes is one of the most useful tools for investigating the mechanical properties of a crystal. These fringes are generated by a surface of constant phase difference, called the Bertin surface, whose shape depends on the piezo-optic properties of the material and on the applied stress. Here we investigate systematically for the first time, to the best of our knowledge, these surfaces as algebraic surfaces. We also describe their dependence on the stress when these are “small” and give a detailed analysis for all crystallographic classes.

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	$σ_{m}$	$σ_{1}$	$σ_{2}$	$σ_{3}$	$σ_{2 = 3}$	$σ_{1 = 3}$	$σ_{1 = 2}$	$τ_{23}$	$τ_{13}$	$τ_{12}$
Triclinic^a all classes	$B$ , $Q$	$B$ , $Q$	$B$ , $Q$	$B$ , $Q$	$B$ , $Q$	$B$ , $Q$	$B$ , $Q$	$B$ , $Q$	$B$ , $Q$	$B$ , $Q$
Monoclinic^b all classes	$B$ , $Q_{3}$	$B$ , $Q_{3}$	$B$ , $Q_{3}$	$B$ , $Q_{3}$	$B$ , $Q_{3}$	$B$ , $Q_{3}$	$B$ , $Q_{3}$	$B$ , $Q$	$B$ , $Q$	$B$ , $Q_{3}$
Orthorhombic all classes	SP	SP	SP	SP	SP	SP	SP	$B$ , $Q_{1}$	$B$ , $Q_{2}$	$B$ , $Q_{3}$
Tetragonal 4, $\bar{4}$ , $4 / m$	SP	$B$ , $Q_{3}$	$B$ , $Q_{3}$	SP	$B$ , $Q_{3}$	$B$ , $Q_{3}$	SP	$B$ , $Q$	$B$ , $Q$	$B$ , $Q_{3}$
Tetragonal 422, $4 m m$ , $\bar{4} 2 m$ , $4 / m m$	SP	$B_{2}$	$B_{1}$	SP	$B_{1}$	$B_{2}$	SP	$B_{1}$	$B_{2}$	$B$ , $Q_{3}$
Trigonal 3, $\bar{3}$	SP	$B$ , $Q$	$B$ , $Q$	SP	$B$ , $Q$	$B$ , $Q$	SP	$B$ , $Q$	$B$ , $Q$	$B$ , $Q$
Trigonal 32, $3 m$ $\bar{3} m$	SP	$B$ , $Q_{1}$	$B$ , $Q_{2}$	SP	$B_{1}$	$B_{2}$	SP	$B$ , $Q$	$B$ , $Q$	$B$ , $Q$
Hexagonal 6, $\bar{6}$ , $6 / m$	SP	$B$ , $Q_{3}$	$B$ , $Q_{3}$	SP	$B_{1}$	$B_{2}$	SP	$B_{1}$	$B_{2}$	$B$ , $Q_{3}$
Hexagonal 622, $6 m m$ , $\bar{6} 2 m$ , $6 / m m$	SP	$B$ , $Q_{3}$	$B$ , $Q_{3}$	SP	$B_{1}$	$B_{2}$	SP	$B$ , $Q_{3}$	$B$ , $Q_{3}$	$B$ , $Q_{3}$
Cubic all classes	SP	$B_{2, 3}$	$B_{1, 3}$	$B_{1, 2}$	$B_{1, 2, 3}$	$B_{1, 2, 3}$	$B_{1, 2, 3}$	$B_{1}$	$B_{2}$	$B_{3}$
Spherical	SP	$U_{1}$	$U_{2}$	$U_{3}$	$U_{1}$	$U_{2}$	$U_{3}$	$B_{1}$	$B_{2}$	$B_{3}$

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