Analysis of the time-reversal operator for a single cylinder under two-dimensional settings

The time-reversal operator (TRO) for a cylindrical rod with circular cross section illuminated by an array of line antennas is investigated in order to locate the target and determine its electromagnetic property. In the two-dimensional settings, the number of eigenvalues of the time-reversal operator is determined by the polarization of the incident wave, as well as the composing material of the rod. This statement is proved mathematically and its physical meaning is explained in terms of the induced line current and two-dimensional dipolar current. Numerical simulations show that the eigenvector of the TRO allows one to focus the time-reversed wave on the target.