Completeness and Modal Expansion Methods in Diffraction Theory

As a consequence of their structure, modal formulations for diffraction gratings may satisfy reciprocity and conservation of energy criteria exactly, independently of the errors incurred when using truncated field expansions. We consider completeness relations, which provide a means of assessing truncation errors in modal formulations. Taking the lamellar diffraction grating as an example, we describe the completeness relations as they apply to infinitely conducting, dielectric and lossy structures.