Calculation of the Six-Beam Diffraction in Layered Media Using Polynomials of Principal Minors

Abstract

The scattering of plane elastic waves by an anisotropic layered medium in the case of the six-beam diffraction is considered. The matrix method for solving wave equations is developed. The conversion coefficients [Formula: see text] for the three types of incident waves (horizontally polarized shear wave, vertically polarized shear wave and longitudinal wave) are defined. Representations of coefficients [Formula: see text] through elements of transfer matrix are found. The method for coefficients [Formula: see text] calculations is presented. It does not require the solving of algebraic problem on eigenvalues for waves in an anisotropic layer. Some features of the functional dependencies of [Formula: see text] on the angles of incidence, wave frequency and layer thickness are demonstrated on several examples of the crystals in a three-layer model. It is shown that the conversions SH wave into SV waves and SV wave into SH waves are equivalent.