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Abstract: The concept of time reversal TR of scalar wave is reexamined from basicprinciples. Five different time reversal mirrors TRM are introduced and theirrelations are analyzed. For the boundary behavior, it is shown that forparaxial wave only the monopole TR scheme satisfies the exact boundarycondition while for spherical wave only one of the mixed mode TR scheme, aftermultiplication by two, satisfies the exact boundary condition. The asymptoticanalysis of the near-field focusing property is presented. It is shown that tohave a subwavelength focal spot the TRM should involve dipole fields. Themonopole TR is extremely ineffective to focus below wavelength as the focalspot size decreases logarithmically with the distance between the source andTRM. Contrary to the matched field processing and the phase processor, both ofwhich resemble TR, TR in a weak- or non-scattering medium is usually biased inthe 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 theother hand, the TR focal spot has been shown repeatedly in the literature, boththeoretically and experimentally, to be centered at the source point when themedium is multiply scattering. A reconciliation of the two seeminglyconflicting results is found in the random fluctuations in the intensity of theGreen function for a multiply scattering medium and the notion ofscattering-enlarged effective aperture.



Author: Albert C. Fannjiang

Source: https://arxiv.org/







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