Synthesis of optical thin film filters under boundary conditions

Abstract

An exact synthesis algorithm for dielectric thin film filters with uniform optical phase thickness was first presented in 2004. This algorithm computes at least one thin film stack which realizes a given filter function. The feasibility is guaranteed by a set of necessary and sufficient conditions the filter function has to fulfill. This set of conditions only guarantees strictly positive refractive index values for all thin film layers. For a technological realization strictly positive refractive index values are insufficient since only certain refractive index values can be realized for a thin film layer. In this paper an additional condition for the location of the zeros of the filter response function is derived. Starting point is a boundary condition for the refractive index value for each of the N layers of the filter stack. Each refractive index value can be selected arbitrarily from an interval which is bounded by a lower and an upper refractive index boundary value. This additional zero location condition is necessary that at least one filter stack exists which fulfills these boundary conditions to a given filter function. Since the boundary conditions are determined by the used fabrication process for thin film filters the presented additional condition for the location of the zeros has to be calculated only once when a new process is installed.