Surface-wave nonlinearities: Nonlinear bulk-wave generation by two oppositely directed collinear surface waves

The nonlinear interaction between two oppositely directed surface acoustic waves (SAW) of frequencies ω1 and ω2 and wave vectors κ1 and κ2 is analyzed theoretically. It is shown from the general theory of thermoelasticity that nonlinear volume forces and surface stresses are created at the frequencies ω1±ω2 and wave vectors κ1∓κ2, respectively. For the difference frequency case the forces and stresses are relieved by evanescent SAW. In the sum frequency case, up to three bulk waves are generated depending on the value of κ2/κ1. The nonlinear interaction is characterized by normalized surface displacement and bulk-wave power parameters. The upshift case is examined as a function of κ2/κ1 for fused quartz, yz sapphire, and zx sapphire and the cross sections for bulk-wave generation are discussed in detail. Numerical calculations are presented (with ω1=ω2) for the (001), (110), and (111) planes of gallium arsenide, the principal planes of sapphire, and for some cuts of piezoelectric α-quartz and lithium niobate (in the quasi-static approximation). The quantity and type of bulk modes generated is discussed in light of SAW propagation plane reflection symmetry, rotational symmetry, and confinement of SAW displacements to the saggital plane.