On the modeling of optical systems containing elements of different scales

In optical systems often components of widely varying scales occur. The scale, expressed in units of wavelength, determines what kind of model is needed for the component. For objects with size of the order of the wavelength, rigorous electromagnetic models are required. We discuss several home-made rigorous methods such as the Finite Element Method, the Finite Difference Time Domain Method and the Rigorous Coupled Wave Method and describe our experience with them. For lenses of high numerical aperture, the Extended Nijboer Zernike method is considered. An important issue is how to propagate the field from the exit plane of one component to the entrance plane of the other. We explain a numerical integration method by which the diffraction integral can be computed with an error that is independent of the propagation distance.