Design of microwave and optical filters using the inverse scattering method

Abstract

Summary form only given. We consider particular applications of one-dimensional inverse scattering theory towards the direction of the design of microwave and optical filters of particular form. In particular, we consider the following two problems of filter design. (i) The design of continuous microstrip tapers with prescribed filter characteristics (microwave filters): here the width w(x) of a microstrip is to be designed, once the input reflection coefficient r(k) of the filter is given. The design procedure uses the one-dimensional2-D) inverse scattering theory. (ii) The design of optical corrugated waveguide filters: in this application the corrugation function of a planar optical waveguide is designed with given the frequency characteristics of the corresponding filter. In the present formulation, coupled Gel'fand-Levitan-Marchenko (GLM) integral equations have to be solved as a part of the design algorithm. This solution is implemented in several ways, such as a special numerical technique, called 'leapfrogging' technique, or through a method which transforms the coupled GLM equations to linear algebraic systems of equations, which are easily solved numerically. The comparison of these methods checks the accuracy of the proposed design method. This is also accomplished, as usually, through the numerical solution of the corresponding Riccati differential equation. After the solution of the GLM equations, the amplitude and phase functions of the corrugation design directly follow.