By T. S. Narasimhamurty
This complete treatise reports, for the 1st time, all of the crucial paintings over the last one hundred sixty years at the photoelastic and the heavily similar linear and quadratic electro-optic results in isotropic and crystalline mate rials. Emphasis is put on the exceptional progress of the topic in past times decade and a part with the arrival of the laser, with using high-frequency acousto-optic and electro-optic options, and with the invention of recent piezoelectric fabrics, all of that have provided a suggestions to the large curiosity in those components of solid-state physics. the 1st of those matters, the photoelastic influence, was once came across via Sir David Brewster in 1815. He first discovered the impact in gels and as a result stumbled on it in glasses and crystals. whereas the influence remained of educational curiosity for almost 100 years, it turned of functional price whilst Coker and Filon utilized it to measuring stresses in laptop elements. With one picture and next research, the strain in any planar version might be decided. by way of taking sections of a third-dimensional version, entire third-dimensional stresses are available. for this reason this impression is broadly utilized in industry.
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Extra info for Photoelastic and Electro-Optic Properties of Crystals
1). A rotation of axes and a reflection in a plane are examples of such a pair of Cartesian coordinate systems. 1) X/ with respect X3 X 2' a 21 (X22 a 23 X' 3 a 31 a 32 a 33 Thus, for example, (Xll' (X12' and a l3 are the direction cosines of Xl' with respect to XI' X 2 , and X 3 . Transformation of the coordinates of P from one system to another is called a linear transformation. A rotation of 9 10 Chapter 2 X~ x! -":O~---X2 X, ''; x, / Fig. 1. Transformation of axes : a rotation of the axes of one coordinate system X/ with respect to another system Xj, both having a common origin O.
It was Pockels who originated the phenomenological theory of photoelasticity of crystals. His work on crystal photoelasticity formed his doctoral dissertation at Gottingen in 1889. The phenomenon of photoelasticity, discovered by Brewster and systematically investigated by Pockels, attracted a number of workers in this field. A brief historical survey follows. 3. 1. Amorphous Solids Sir David Brewster [192; 193] discovered the phenomenon of artificial birefringence first in jellies in 1815 and then in other transparent solids like glasses and cubic crystals in 1816.
While studying such anisotropic properties of crystals, we make extensive use of transformations of the components of vectors and tensors from one coordinate system to another. The linear transformations between two coordinate systems are greatly facilitated by the use of matrix algebra. It is essentially an operational tool. , the elastic stiffness constants and compliance constants, which bear an inverse but not a reciprocal relationship. Similarly the stress-optical and strain-optical coefficients in Pockels' scheme of photoelastic constants can be interrelated in an elegant way.