On the analysis of microstructured surfaces

The study of general microstructures in 2D geometry and rotational 3D microstructures is presented. The study is based on infinitesimal microstructures for some calculations and the macro-profile of the surface can be treated as a new type of optical surface with a certain deflection law, which will be different of the reflection law or the Snell law. In two dimensions, we discuss the propagation of wavefronts by general microstructured surfaces (which do not fulfill the Fermat principle) and the discontinuity of the eikonal function at the microstructure. Naturally, a classification of the microstructures is obtained (regular and anomalous) and the concept of 2D ideal microstructures is also introduced, as those that perfectly couple two macroscopic extended bundles in 2D geometry. In 3D, after classifying the rotational optical systems into point-spot and ring-spot types, the first-order properties of both regular and anomalous rotational microstructured surfaces are discussed. Finally, an application of anomalous rotational microstructured surfaces to the problem of mixing the light from three RGB LED chips is introduced.