Magnitude of Electrogyratory Effects

First-order electrogyratory effects can be expressed in terms of a nonlinear gyratory susceptibility ${\chi }_g^{\mathrm{NL}}$ that is defined analogously to the conventional nonlinear optical susceptibility. It is shown that ${\chi }_g^{\mathrm{NL}}$ can be represented as ${\Delta }_g\left(\omega \right){\left[\chi \right(\omega \left)\right]}^2\chi \mathrm{}\left(0\right)\mathrm{}$, where $\chi \left(\omega \right)$ and $\chi \mathrm{}\left(0\right)\mathrm{}$ are linear susceptibilities, and where ${\Delta }_g\left(\omega \right)$ is expected to remain fairly constant for a wide variety of materials. This relationship is formally identical to that commonly used to estimate the conventional nonlinear optical susceptibility. The ratio between ${\Delta }_g\left(\omega \right)$ and the quantity $\Delta \left(\omega \right)$ that describes conventional optical nonlinearities is approximately the ratio of the natural gyration $G$ to the refractive power $n^2-1\mathrm{}$. Values of ${\Delta }_g\left(\omega \right)$ inferred from previously reported measurements of the magnitude of electrogyratory effects are from two to nearly five orders of magnitude larger than the predicted value. It is shown that the observations in these instances can be explained solely in terms of conventional electro-optic (birefringence) effects and therefore have no bearing on the magnitude of electrogyratory effects. A method is described that permits the direct observation of electrogyratory effects in the presence of considerably larger electro-optic birefringence effects. The method is applied to the measurement of electrogyration in bismuth germanium oxide ${\mathrm{Bi}}_{12}$Ge${\mathrm{O}}_{20}$. Even though the sensitivity of the method is limited by indeterminate amounts of stray birefringence in the optical system, the upper limit obtained for the magnitude of the effect is considerably smaller than the previously reported value.