A rigorous study of diffraction effects on the transmission of linear dielectric micro-reflector arrays

Linear micro-reflector arrays are used in various lighting applications where the selectivity between high reflectance for a defined range of angles of incidence and transmittance for other angles of incidence is most interesting. One goal is to miniaturize the unit elements in order to make the devices thinner and to give them a more homogeneous appearance. Diffraction effects then have to be taken into consideration. The scalability of the unit element in linear micro-reflector arrays was studied by using rigorous diffraction theories for periods between 1 and 60 µm. Two principally different geometries of the single micro-reflector were compared: a prism at which two prism surfaces enclose an angle of 90°, and a compound parabolic concentrator. The results show that the scalability depends on the structure geometry and the refractive index of the transparent material. The role of evanescent waves on the scalability of micro-reflector arrays is emphasized. In a first approximation, considerations based on the longitudinal Goos-Hänchen shift are helpful in addressing decreasing period-to-wavelength ratios when the unit cell is miniaturized. The detailed analysis of this approach raises open questions.