Theory of Electromagnetic Time-Reversal Mirrors

The theory of monochromatic time-reversal mirrors (TRM) or equivalently phase conjugate mirrors is developed for electromagnetic waves. We start from the fundamental time-symmetry of the Maxwell's equations. From this symmetry, a differential expression similar to the Lorentz reciprocity theorem is deduced. The radiating conditions on TRM are expressed in terms of 6-dimension Green's functions. To predict the time reversal focusing on antenna arrays, a formalism that involves impedance matrix is developed. We show that antenna coupling can dramatically modify the focal spot. Especially, we observe, that in some circumstances, sub-wavelength focusing on a bi-dimensional array may arise.