Rigorous and efficient grating-analysis method made easy for optical engineers

TLDR

The coordinate‑transformation‑based differential method of Chandezon et al. is a simple and versatile approach for modeling surface‑relief gratings, yet it has been underused because it traditionally relies on tensor theory. This work aims to reformulate the C method without tensor theory to make it more accessible to optical engineers. The authors rederive the C method using only elementary vector calculus, eliminating tensor formalism. The reformulated method retains the simplicity and versatility of the original C method for modeling surface‑relief gratings.

Abstract

The coordinate-transformation-based differential method of Chandezon et al. [J. Opt. (Paris)11, 235 (1980); J. Opt. Soc. Am.72, 839 (1982)] (the C method) is one of the simplest and most versatile methods for modeling surface-relief gratings. However, to date it has been used by only a small number of people, probably because, traditionally, elementary tensor theory is used to formulate the method. We reformulate the C method without using any knowledge of tensor, thus, we hope, making the C method more accessible to optical engineers.