Ultrasonic Beam Mixing as a Measure of the Nonlinear Parameters of Fused Silica and Single-Crystal NaCl

The mixing action of two crossed ultrasonic beams has been studied. The theoretical treatment of Taylor and Rollins is extended to include the all-pure-mode cases for the prosess $L \left({\omega }_1\right)-T\left\{\left\{{\omega }_2\right\}\{{\omega }_1-{\omega }_2\}\right\}\to T\left\{\{{\omega }_1-{\omega }_2\}\left\{{\omega }_2\right\}\right\}$ in cubic single crystals. Five such cases exist in cubic crystals; two in the (001) mixing plane and with $L \left({\omega }_1\right)$ propagated in either of two fixed directions [100] and [110]; and the other three in the ($1\overline{1}0$) mixing plane and with $L \left({\omega }_1\right)$ propagated in any of three fixed directions [110], [111], and [001]. The transverse waves are polarized normal to the mixing plane in all five cases and propagate in directions within the plane corresponding to the selection rules on frequency and propagation vector. The conversion efficiency was measured over a range of input frequency ratios, $a=\frac{{\omega }_2}{{\omega }_1}$ for the two independent transverse-polarization states for the above process in fused silica and for the two pure-mode cases in the (001) plane in NaCl. A comparison technique using the interchange equivalence of $T\left({\omega }_2\right)$ and $T({\omega }_1-{\omega }_2)$ effectively eliminated the transducer-bond efficiencies. These measurements were used to determine two of the three independent third-order elastic constants of fused silica. In the case of NaCl, the two ratios of linear combinations of second- and third-order elastic constants corresponding to the two (001) -plane pure-mode cases were determined. The above comparison technique was not applied to the other three pure-mode cases because the transverse anisotropy in the ($1\overline{1}0$) plane leads to refractive effects on the transverse beams that render the technique inapplicable.