Focusing through random media in space and time: a transmission matrix approach.

We exploit the evolution in time of the transmission matrix following pulse excitation of a random medium to focus radiation at a selected time delay t' and position r. The temporal profile of a focused microwave pulse is the same as the incident Gaussian pulse. The contrast in space at time t' of the focused wave is determined by the participation number of transmission eigenvalues M' and the size N' of the measured transmission matrix. The initial rise and subsequent decay of the contrast observed reflect the distribution of decay rates of the quasi-normal modes within the sample.