Periodic Structures, Admittance Grid

→ See also Mechel, Vol. I, Ch. 12 (1989)

An object with a periodic surface is a special case of an object with an inhomogeneous surface (other inhomogeneous surfaces which are amenable to analysis are those in which either the scale of the inhomogeneities and their distances is small compared to $\lambda _{{0}}$, then the average admittance is relevant, or the inhomogeneities are at large distances from each other, then scatter matrices can be set up). The method to be applied with periodic structures will be displayed in this and the next sections with some typical examples.

In principle, the quantities that describe the periodic surface, such as its surface admittance or the sound field at the surface, are synthesised with a Fourier series. The Fourier terms are waves which have different names in the literature: “spatial harmonics” (used here), “Hartree harmonics” (often used in microwave technology), or “Bloch waves” (used in solid state physics). The most important quality of...