Average the instantaneous elastic-wave energy flux over one temporal period at fixed position. For complex amplitudes,
Write the evanescent P displacement amplitude as
For an isotropic linear elastic material with Lamé parameters , its stress and velocity amplitudes are
Apart from a real common factor,
which is purely imaginary. Its real part vanishes, and hence
The converted P-wave is a reactive near-boundary field and transports no time-averaged acoustic energy in the normal direction.