  Transmission through disordered samples can be controlled by illuminating a
sample with waveforms corresponding to the eigenchannels of the transmission
matrix. But can the TM be exploited to selectively excite quasi-normal modes
and so control the spatial profile and dwell time inside the medium? We show in
microwave and numerical studies that spectra of the TM can be analyzed into
modal transmission matrices of rank unity. This makes it possible to enhance
the energy within a sample by a factor equal to the number of channels. Limits
to modal selectivity arise, however, from correlation in the speckle patterns
of neighboring modes. In accord with an effective Hamiltonian model, the degree
of modal speckle correlation grows with increasing modal spectral overlap and
non-orthogonality of the modes of non-Hermitian systems. This is observed when
the coupling of a sample to its surroundings increases, as in the crossover
from localized to diffusive waves.
