Construction of the temporal invariants of the time-reversal operator

This paper proposes a method to construct the temporal Green's function from a scatterer to an array of transducers in a waveguide using free-space back propagation of the eigenvectors of the time-reversal operator (TRO). The monostatic Green's function is obtained as an eigenvector of the TRO which is known with an arbitrary phase; thus the impulse response cannot be obtained by a simple inverse Fourier transform. Assuming that the monochromatic fields obtained by the back propagation of the eigenvectors are in phase at the focal point, the phase correction is determined. Simulations and laboratory experiments are presented.