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978-3-8439-1117-7, Reihe Elektrotechnik

Bastian Diehm Synthese optischer Dünnschichtfilter unter Randbedingungen

157 Seiten, Dissertation Universität Stuttgart (2012), Softcover, A5

In the thesis of A. Rowinska-Schwarzweller an exact synthesis method for dielectric optical thin film filters with uniform optical phase thickness was presented for the first time. This method provides not only one but the set of all solutions which realize a given filter function. The choice between different solutions is a crucial advantage over present methods which typically deliver only one solution.

If a specified filter function satisfies a set of conditions, the synthesis method provides only solutions with all positive refractive index values. However positive values are insufficient for a technological realization. One way to evade this restriction is co-deposition of multiple materials with different refractive indices during layer fabrication. Another option is to replace the layer with the non manufacturable refractive index value by a system consisting of three layers. By using these methods thin film layers with an arbitrary refractive index value lying in an interval bounded by a lower and an upper value can be fabricated. With regard to the technological realizability one is interested in solutions with preferably all refractive index values lying in an interval which is determined by the materials and the fabrication process used.

In this thesis it is investigated in which way the synthesis method can be optimized to incorporate the technological boundary conditions mentioned above. Because the optimization methods presented later on use methods which originate from the field of algebraic geometry and interval analysis an introduction to these topics is also given. In the main part of this thesis two methods of resolution are presented. The first approach is to efficiently find equivalent solutions which fulfill the stated boundary conditions by using sophisticated search methods. Another option is to consider the set of all equivalent solutions as the solution set of a polynomial equation system and to determine solely the solutions which fulfill the boundary conditions. The option presented here employs Groebner bases. Although this method is only useful for low order filters it is a symbolic approach and therefore parameters can be taken into account during the search process. The second approach takes advantage of the interval analysis methods to derive conditions for the filters transfer function from given technological boundary conditions. In the last chapter results of two fabricated thin film filters are presented.