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SIAM J. APPL. MATH. c 2008 Society for Industrial and Applied Mathematics
Vol. 69, No. 3, pp. 830844
FAR FIELD MODELING OF ELECTROMAGNETIC TIME
REVERSAL AND APPLICATION TO SELECTIVE FOCUSING
ON SMALL SCATTERERS
X. ANTOINE, B. PINC¸ON, K. RAMDANI, AND B. THIERRY
Abstract. A time harmonic far field model for closed electromagnetic time reversal mirrors is
proposed. Then, a limit model corresponding to small perfectly conducting scatterers is derived. This
asymptotic model is used to prove the selective focusing properties of the time reversal operator. In
particular, a mathematical justification of the decomposition of the time reversal operator (DORT)
method is given for axially symmetric scatterers.
Key words. electromagnetic scattering, time reversal, far field, small obstacles
AMS subject classifications. 35B40, 35P25, 45A05, 74J20, 78M35
DOI. 10.1137/080715779
1. Introduction. In the last decade, acoustic time reversal has definitely demon
strated its efficiency in target characterization by wave focusing in complex media (see
the review papers [13, 15]). In particular, it has been shown that selective focusing
can be achieved using the eigenvectors (resp., eigenfunctions) of the socalled time
reversal matrix (resp., operator). Known as the DORT method (French acronym for
