On time reversal mirrors

Abstract

The concept of time reversal (TR) of a scalar wave is reexamined from basic principles. Five different time-reversal mirrors (TRMs) are introduced and their relations are analyzed. For the boundary behavior, it is shown that for a paraxial wave only the monopole TR scheme satisfies the exact boundary condition while for the spherical wave only the MD-mode TR scheme satisfies the exact boundary condition. The asymptotic analysis of the near-field focusing property is presented for two dimensions and three dimensions. It is shown that to have a subwavelength focal spot, the TRM should consist of dipole transducers. The transverse resolution of the dipole TRM is linearly proportional to the distance between the point source and the TRM. The mixed mode TRM has the similar (linear) behavior in three dimensions, but in two dimensions the transverse resolution behaves as the square root of the distance between the point source and the TRM. The monopole TRM is ineffective in focusing below the wavelength. Contrary to the matched field processing and the phase processor, both of which resemble TR, TR in a weak- or non-scattering medium is usually biased in the longitudinal direction, especially when TR is carried out on a single plane with a finite aperture. This is true for all five TR schemes. On the other hand, the TR focal spot has been shown repeatedly in the literature, both theoretically and experimentally, to be centered at the source point when the medium is multiple scattering. A reconciliation of the two seemingly conflicting results is found in the random fluctuations in the intensity of the Green function for a multiple scattering medium and the notion of scattering-enlarged effective aperture.