On time reversal mirrors

TL;DR

This paper reexamines the principles of time reversal of scalar waves, introduces five different TRMs, analyzes their boundary behaviors, and discusses their focusing properties, especially in scattering media, revealing limitations and conditions for subwavelength focusing.

Contribution

It introduces and analyzes five distinct time reversal mirror schemes, clarifies their boundary conditions, and explores their effectiveness in focusing, especially in scattering environments, providing new insights into TR performance.

Findings

Monopole TR satisfies boundary conditions for paraxial waves.

Dipole fields are necessary for subwavelength focusing.

TR in scattering media centers the focal spot at the source.

Abstract

The concept of time reversal (TR) of scalar wave is reexamined from basic principles. Five different time reversal mirrors (TRM) are introduced and their relations are analyzed. For the boundary behavior, it is shown that for paraxial wave only the monopole TR scheme satisfies the exact boundary condition while for spherical wave only one of the mixed mode TR scheme, after multiplication by two, satisfies the exact boundary condition. The asymptotic analysis of the near-field focusing property is presented. It is shown that to have a subwavelength focal spot the TRM should involve dipole fields. The monopole TR is extremely ineffective to focus below wavelength as the focal spot size decreases logarithmically with the distance between the source and TRM. 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 {\em 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 multiply scattering. A reconciliation of the two seemingly conflicting results is found in the random fluctuations in the intensity of the Green function for a multiply scattering medium and the notion of scattering-enlarged effective aperture.