Elastic-wave propagation in anharmonic media with resonant absorption and dispersion
Harris, Frederick Henry
Donoho, Paul L.
Master of Arts
Wetsel et al and Meyer et al have experimentally observed anomalous resonances at harmonics of the fundamental resonant field in CaF24:U4+ using 9.0 GHz elastic waves. Wetsel has explained the observed phenomena by invoking multiphonon spinlattice interactions while Meyer et al have attributed it to the natural anharmonicity of the crystal lattice. In this paper a model for elastic-wave propagation in anharmonic media with resonant absorption and dispersion is developed. The anharmonicity is represented by including third-order elastic energy, which leads to a nonlinear wave equation. Further, the resonant absorption and dispersion is included by assuming a Gaussian lineshape for a linear one-phonon spin-lattice interaction. The solution of the resulting equations of motion in terms of a harmonic series of sinusoidal waves leads to an infinite set of coupled nonlinear differential equations. The numerical solutions obtained by truncating the set at the fifth harmonic are given, and their close qualitative agreement with the experimental data is described. In view of the close qualitative agreement between the model and experiment, it is concluded that the observed anomalous resonances can be explained on the basis of lattice anharmonicity without including multiphonon spin-lattice interactions. Also, further experimental tests are suggested to test the results of the model.