Thermo-optic behaviour of silicon carbide

Summary

The dispersion and birefringence of carborundum are well represented by the formulæ

$$\begin{gathered} \omega ^2 = 1 + \frac{{k_1 \lambda ^2 }}{{\lambda ^2 - \lambda _1 ^2 }} + \frac{{k_2 \lambda ^2 }}{{\lambda ^2 - \lambda _2 ^2 }} \hfill \\ \varepsilon ^2 = 1 + \frac{{k_3 \lambda ^2 }}{{\lambda ^2 - \lambda _1 ^2 }} + \frac{{k_4 \lambda ^2 }}{{\lambda ^2 - \lambda _2 ^2 }}, where \hfill \\ \lambda _1 = 155 m\mu , \lambda _2 = 175 m\mu , k_1 = 3 \cdot 657, k_2 = 1 \cdot 898, \hfill \\ k_3 = 1 \cdot 626, k_4 = 4 \cdot 11. \hfill \\ \end{gathered} $$

The theory of thermo-optic behaviour of solids when applied to the case of carborundum explains the observed positive temperature coefficient of both the indices.