Reflection and transmission of Rayleigh waves by the edge of a deposited thin film

The reflection and transmission of Rayleigh waves by the edge of an isotropic thin film deposited on an isotropic substrate is solved within the first-order approximation relying on the Wiener-Hopf technique under the assumption that the film is thin enough compared to the wavelength. Straight-crested Rayleigh waves are assumed to impinge on the edge of the film perpendicularly from the unplated side of the substrate. In formulating the problem mathematically, Tiersten's boundary condition is employed to take into account the effects which the deposited film imposes on the elastic waves in the substrate. Expressions for the radiation coefficients of both of the bulk waves, longitudinal and transverse, and for the reflection coefficient of the Rayleigh wave are derived and evaluated numerically for gold, aluminum, nickel, and copper films deposited on the fused-silica substrate. It is found that the radiation coefficients, especially the one for the transverse bulk wave, exceed the reflection coefficient by a factor of 10 or more in magnitude. The reflection and transmission of the Rayleigh wave is influenced mainly by the shear velocity and shear modulus μ′ of the film material, whereas the Lamé constant λ′ of the film does not have as much effect on both the reflection and transmission.