Harmonic Generation of Acoustic Surface Waves in Bi₁₂GeO₂₀and LiNbO₃

Harmonic generation of acoustic surface waves has been observed experimentally in different laboratories on quartz, lithium niobate, and bismuth germanium oxide sub- strates and a phenomenological model containing one non- linear elastic constant has been proposed to explain the spatial variation of each observed harmonic on a LiNb03 delay line. In this paper we describe how the surface wave nonlinearities of different materials can be quantitatively compared. Using laser light deflection the growth with distance of the second harmonic was measured in LiNb03 and Bi12GeOzo for fun- damental frequencies of 50 and 100 MHz and of the second, third, and fourth harmonics in LiNb03 for a fundamental of 150 MHz. A one-dimensional, single-parameter model is used from which is obtained a system of coupled differential equa- tions describing the harmonic growth. This system is solved numerically as an initial value problem and a value of the single-parameter found for each material which gave good agreement between the measured data and the model pre- dictions. The parameter values found differ by an order of magnitude in the two materials, LiNb03 being the more strongly nonlinear.