On reflectance optimisation of absorbing material stack

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Abstract
Reviews the reflectance method suitable for optimising thin film performance. In this method one follows the complex amplitude p(z) reflected from the partial stack obtained when the incident medium is extended up to the height z. Several formulations of the differential equation yielding p(z) in s polarisation are presented and some homographic transformations are discussed; namely, those due to a change of the incident medium and occurring when the admittance eta is substituted for p(z). These transformations, and specially the last one, are likely to facilitate the treatment of some problems discussed below such as thickness optimisation for a single layer, whereby a criterion is given to indicate when the highest reflectance is reached by increasing the film thickness and film thickness determination in a stack made of two materials. In the latter case curves are plotted in the rho or eta planes for all interfaces and at least one limiting cycle is derived. For refractive indices near unity, this approach validates the deposition monitoring whereby the reflectance is continuously measured and another material substituted when an extremum is observed. Although in the general case this method fails, the condition is given for it to remain valid.