Theory of the Time-Reversal Operator for a Dielectric Cylinder Using Separate Transmit and Receive Arrays

The DORT method applies to scattering analysis with arrays of transceivers. It consists in the study of the time-reversal invariants. In this paper, a large dielectric cylinder is observed by separate transmit and receive arrays with linear polarizations, E or H, parallel to its axis. The decomposition of the scattered field into normal modes and projected harmonics is used to determine the theoretical time-reversal invariants. It is shown that the number of invariants is about 2
k

₁

a
, where
a
is the cylinder radius and
k

₁
the wave number in the surrounding medium. Furthermore, this approach provides approximated expressions of the two first invariants for a sub-resolved cylinder, i.e., when the cylinder diameter is smaller than the resolution width of the arrays. The two first invariants are also expressed in the small object limit for k
₁
a. AMS subject classifications. 35B40, 35P25, 45A05, 74J20,78M35.