Color dynamics of diffraction gratings: evaluation and applications in optical security

We looked for design methodologies that cope with optical specifications described in terms of trajectories in the CIE (Commission Internationale de l'Eclairage) 1976 chromaticity diagram in the context of low-cost mass-reproduction processes that inevitably introduce changes in the design of a diffractive device for security applications. The mathematics of the design process can be strongly simplified if the theory of planar waveguides (in integrated optics) is used to estimate, with sufficient accuracy, the position of Wood singularities, responsible for the more-interesting visual features of a grating. We show how to use such a model to assess color dynamics variations that are due to production and to estimate domains within the space of grating parameters that enable both first- and second-level security features to be implemented simultaneously. All the results are compared with the values obtained by rigorous coupled-wave analysis.