A direct method for Bloch wave excitation by scattering at the edge of a lattice. Part II: Finite size effects

A method for determining the reflection and transmission properties of a periodic structure occupying a half-space, previously developed for lattices formed from point scatterers, is generalized to allow for finite size effects. This facilitates the consideration of much higher frequencies (or more precisely, much higher scatterer size to wavelength ratios), and also a wider range of boundary conditions. The method is presented in a general context of linear wave theory, and physical interpretations are given for acoustics, elasticity, electromagnetism and water waves.