A new look at computational time reversal in TLM

Abstract

A fundamental rule in Transmission Line Matrix (TLM) modeling is to ensure that the shortest wavelength in the model is always large compared to the discretization parameter. This rule is appropriate for electromagnetic analysis, but when the TLM model is used to solve inverse problems, such as computational imaging, source reconstruction, or structure synthesis - procedures that involve computational reversal of time - this wavelength restriction severely compromises the spatial resolution of the procedure by virtue of the Abbe limit. By discarding this rule we achieve super-resolution in source reconstruction using time reversal. We leverage the Johns Matrix concept and the reciprocity of TLM to achieve a breakthrough where previous attempts at structure synthesis through time reversal have been unsatisfactory.