Four channel Wigner-Smith matrix formalism applied to the scattering by a fluid layer embedded in semi infinite solids

Abstract

The acoustic scattering by a fluid slab between two semi infinite solid media is revisited from the point of view of a four channel resonant scattering formalism. For a plane and monochromatic longitudinal (P=L) or transversal (P=T) wave incident from each solid, the reflection coefficients r¨PQ and transmission coefficients t¨PQ by the fluid layer (Q=L or T represents the polarization of the scattered waves ) are the components of a 4x4 symmetric, unitary scattering matrix S (S* S = S S* = I). In the particular case of identical solids, it is shown that S has to be written as the product of 2 unitary scattering matrices: S^(b) - corresponding to the scattering by the vacuumed layer-, and S^(*) -denoting the pure resonant part of S-. The Wigner-Smith matrix Q_xi =-j(drond_xi(S) S* is analyzed (drond_xi is the partial derivative with respect to a given input parameter x(i=1,...,4)=f, c_L, c_T, c_F), this formalism being the multichannel extension of the Phase Gradient Method.