Monte Carlo transmission line modelling of multilayer optical coatings for performance sensitivity of a dichroic filter for the ARIEL space telescope

Dichroic beamsplitters, or dichroics, are filters that rely on the optical interference that occurs within thin layers to ensure the transmission and reflection of selective wavelengths of an incident beam of light. These optical components consist of a substrate coated on one or both surfaces with multiple layers of thin films, the spectral design and construction of which determine the isolation of particular wavebands. Discrepancies between the measured and expected spectral performance of optical elements with such coatings can largely be attributed to depositions errors and uncertainties in the refractive indices of the materials. Our model uses two-dimensional transmission line modeling to evaluate the transmittance of light through multilayer coatings deposited on a substrate material for given materials, angle of incidence and polarisation. This model allows us to perform Monte Carlo simulations to obtain statistical information about the tolerance of the coating performance to systematic and random uncertainties from the manufacturing process, as well as from environmental changes in space. With the aid of accurate manufacturing recipes and uncertainty amplitudes from commercial manufacturers, this tool can predict variations in the optical performance that result from the propagation of each of these uncertainties for various hypothetical scenarios. One particular application of this study are the dichroics of the ARIEL space telescope. We compare the predicted optical performance with transmission measurements at cryogenic temperatures for one of the ARIEL dichroics, which show the specification compliance of this prototype after many thermal cycles.