Derivation of an equivalent multiport description of dielectric periodic gratings based on the coupled-wave theory

This paper deals with the derivation of an equivalent multiport description for modelling and simulation of dielectric periodic gratings. The method presented can be applied to scalar as well as to vectorial diffraction analysis. The approach is based on the coupled-wave theory where the field strengths are represented by infinite sums of their space harmonics. Finally, a vectorial differential equation is obtained which has the same structure as the telegraph's equations in the frequency domain describing the wave propagation on coupled transmission lines. Hence, already existing solution methodologies can be applied and the grating can be interpreted as a multiport where each port represents one diffraction order. Besides the derivation of the approach an intensive study of the important properties of the eigenvalues and eigenvectors of the reduced system is made.