Abstract:
This paper outlines a theoretical formulation for the diffraction of plane waves
by capacitive grids consisting of perfectly conducting cylinders, and focuses on
the importance of the acoustic (lowest frequency) mode as the mechanism for
long wavelength energy transmission. Particular attention is paid to boundary
conditions and the form of the modes in the quasistatic limit as the wavenumber
k approaches O. We develop a scattering matrix formulation and elucidate its
properties in the long wavelength limit (for which there is only a single propagating
order) using the Sherman-Woodbury formula. With this, we demonstrate
a circuit model for grids of infinitesimal thickness, and a thin film model for
thick grids. Questions of homogenisation are considered and results applicable
to finitely conducting grids are discussed.
