Nonlinear planar forward and backward projection

Abstract

Planar projection methods have been shown to rapidly relate fields between two planes. Such an approach is particularly useful for characterizing transducers, since only a single plane needs to be measured in order to characterize an entire field. The present work considers the same approach for the case of a nonlinear field in the presence of an arbitrary dispersion relation. Unlike traditional methods that use Fourier solutions of the time-domain wave equation, the approach forms a frequency-domain integral equation for waves in a dispersive medium. It is shown that a transfer function similar to that derived from time domain equations can be utilized. Both the forward- and backward-projection behaviors are examined and it is demonstrated that the approach is invariant to propagation direction.