Equivalent network representation of planar gratings with periodic distribution of dielectric constant

An equivalent network representation of planar gratings with periodic distribution of dielectric constant is presented. The method is applicable in the same way to scalar as well as to vectorial diffraction problems. The approach is based on the coupled-wave theory which leads to a set of ordinary differential equations describing the tangential components of the electrical and magnetic field strengths. This set of equations is solved by using transmission line theory. The introduction of equivalent currents and voltages allows a diffraction analysis by using methods already known from conventional network theory. Thus, an impedance matrix and, after the introduction of power waves, a scattering matrix can be defined for describing the dynamical grating behaviour.