Analysis of parameteric mixing and harmonic generation of surface acoustic waves

The parametric mixing and harmonic generation of surface acoustic waves (SAW) has been treated by a new formalism in which the nonlinear wave equation and boundary conditions are rigorously satisfied at the sum and difference frequencies. The key features are analytical expressions for the spatial structure of modes which can be synchronously driven by volume forces and surface‐boundary conditions. After a propagation distance of a few acoustic wavelengths, the acoustic fields evolve into a linearly growing normal‐mode SAW. Equations are derived from which the nonlinear interaction cross sections can be evaluated and numerical results are given for a number of materials. Good agreement was obtained between experiment and theory for y‐x and x‐y α‐quartz in the limit that the piezoelectricity is neglected.

[1]  G. Stegeman,et al.  Brillouin scattering from isotropic metals , 1978 .

[2]  G. Stegeman,et al.  Theory of non phase-matched second harmonic generation of surface plasmons , 1978 .

[3]  D. Mills.  Theory of second harmonic generation by surface polaritons on metals , 1977 .

[4]  A. Alippi,et al.  Phase and amplitude relations between fundamental and second harmonic acoustic surface waves on SiO2 and LiNbO3 , 1977 .

[5]  G. Stegeman.  Normal‐mode surface waves in the pseudobranch on the (001) plane of gallium arsenide , 1976 .

[6]  H. Tiersten,et al.  Second harmonic generation and parametric excitation of surface waves in elastic and piezoelectric solids , 1974 .

[7]  J. W. Gibson,et al.  Nonlinearly generated harmonics and attenuation of Rayleigh waves on crystalline quartz , 1974 .

[8]  G. Stegeman,et al.  Nonlinear surface‐wave interactions: Parametric mixing and harmonic generation , 1974 .

[9]  K. Yamanouchi,et al.  Third‐order elastic constants of lithium niobate , 1973 .

[10]  R. Graham.  Strain dependence of the piezoelectric polarization of z-cut lithium niobate☆ , 1973 .

[11]  R. White,et al.  Surface Elastic‐Wave Velocity and Second‐Harmonic Generation in an Elastically Nonlinear Medium , 1972 .

[12]  E. Lean,et al.  Nonlinear Effects in Surface Acoustic Waves , 1970 .

[13]  A. J. Slobodnik.  Nonlinear Effects in Microwave Acoustic LiNbO3 Surface‐Wave Delay Lines , 1970 .

[14]  L. Kuhn,et al.  ACOUSTIC SURFACE WAVE MIXING ON α‐QUARTZ , 1969 .

[15]  P. O. L. pen.  Second‐Harmonic Generation in an Elastic Surface Wave in α‐Quartz , 1968 .

[16]  G. Stegeman,et al.  Surface‐wave harmonic generation on y‐z, x‐z, and 41 1/2‐x lithium niobate , 1977 .

[17]  E. Dieulesaint,et al.  Harmonic Generation of Acoustic Surface Waves in Bi12GeO20and LiNbO3 , 1973, IEEE Transactions on Sonics and Ultrasonics.

[18]  W. Tanski,et al.  Further investigation of noncollinear surface‐wave interactions , 1973 .