On the Limiting Bandwidth of Interference Filters : Influence of Temperature during Production

Abstract

Computer simulation of thin-film multilayer production has shown that the effects of errors in the layers on the performance of complete coatings depends strongly on the particular monitoring process used. Deposition of dielectric quarter-wave multilayers is usually controlled by a method which involves the detection of the maxima and minima of transmission for the centre wavelength of the filter, the turning value method, and we know that this technique profits from an exceptionally efficient error compensation. The true tolerances in stack production are much larger than we would calculate neglecting this compensation. However, the analysis of experimental results shows that we must consider other effects which have so far been neglected in the computer simulation and which affect the monitoring process enough to prevent the fabrication of interference filters with very narrow transmission bands. Here we describe how the computer simulation is modified to take account of the influence of temperature changes during filter manufacture. First, it is necessary, for each material used, to determine the dilatation coefficients of both refractive index and thickness; they may be deduced from measurements of shifts with temperature of the centre wavelength of narrow-band filters of two different designs. Then, as a first approximation, we assume in the simulation a gradual temperature change which is always proportional to the deposited thickness and which reaches a total of 60°C for the complete filter. The calculations show that the effects of such a temperature change cannot be neglected even if the actual monitoring is perfect, that is if the deposition is always terminated exactly at a turning value of transmittance. The optical characteristics of very narrow-band filters, and especially of double half-wave filters, are seriously degraded. If, in addition, errors in determination of the turning values are included, then the effects are considerably worse. This can explain why it is so difficult to make filters with passband width less than 8 Å. The results of this study can be used to choose optimal conditions for the production of narrow-band filters.