Lucia Cascio, Giampaolo Tardioli and Wolfgang J.R. Hoefer
The analysis of microwave structures with time domain methods (such as TLM and FDTD) is a well established technique which offers extreme flexibility in the geometry of the structure to be analyzed. An entirely new application of these methods is based on their possibility to treat time reversed Maxwell's equations. In this way it is feasible to perform an inverse analysis of a scattered field in order to reconstruct the original source distribution and, therefore, the shape of the scatterer. This procedure has been introduced in  to reconstruct sources in closed structures. A further step is the utilization of the reverse method for synthesis procedures. The goal is to synthesize the geometry of a passive structure from its desired frequency or time domain response using alternate forward and backward simulations.
This work presents a new approach to the synthesis of thin scatterers in waveguides based on the TLM time reverse process. The procedure begins by establishing a relation between the properties of the reconstructed field (in particular of its dominant mode) and the geometry of the scatterer. For simple geometries, such as a thin inductive iris in parallel plate, this can be accomplished with a single reconstruction. Once the fundamental mode of the scattered field is modified according to the synthesis specifications and then reinjected into the empty waveguide, a modal analysis of the reconstructed field at the section of the scatterer will contain the information about the desired dimensions of the obstacle.
The proposed synthesis method has been tested for a parallel plate waveguide of width a=62 delta_l and length l=98 delta_l (delta_l=1mm). The fundamental mode has been extracted from a target structure having w/a= 0.2258. A guess structure with w/a = 0.8065 has been used as starting point for the synthesis. The synthesized mean value after only one synthesis step is 0.3025, which corresponds to the exact value of the desired scatterer w/a = 0.2258, as it can be seen in Fig. 1 (TR-TLM).
Further details can be found in:
L Cascio, G. Tardioli and W. J. R. Hoefer, "Synthesis Procedure via TLM Time Reverse Process" Proceedings of the 1st Int. Workshop on TLM Modeling, pp. 263-266, Victoria, Canada, August 1995.
 R. Sorrentino, P. P. M. So, W. J. R. Hoefer, "Numerical Microwave Synthesis by Inversion of the TLM Process", 21st European Microwave Conference Digest, pp. 1273-1277, Stuttgart, Germany, Sept. 1991
Fig. 1: Fundamental mode amplitude of the reconstructed field for a parallel plate waveguide and synthesis example