  Shaping the wavefront of an incident wave to a complex scattering medium has
demonstrated interesting possibilities, such as sub-diffraction wave focusing
and enhancing light energy delivery. However, wavefront shaping has mainly been
based on the control of transmitted waves that are inaccessible in most
realistic applications. Here, we investigate the effect of maximizing the
backscattered waves at a specific flight time on wave propagation dynamics and
energy transport. We find both experimentally and numerically that the
maximization at a short flight time focuses waves on the particles constituting
the scattering medium, leading to the attenuation of the wave transport. On the
contrary, maximization at a long flight time induces constructive wave
interference inside the medium and thus enhances wave transport. We provide a
theoretical model explaining this interesting transition behavior based on wave
correlation. Our study provides a fundamental understanding of the effect of
wave control on internal wave dynamics.
