On the Bertin surfaces of photoelastic crystals

Fabrizio Daví

doi:10.1364/JOSAA.32.002323

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

On the Bertin surfaces of photoelastic crystals

Fabrizio Daví

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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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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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Journal of the Optical Society of America A