  We study the optimal diffusive transmission and absorption of broadband or
polychromatic light in a disordered medium. By introducing matrices describing
broadband transmission and reflection, we formulate an extremal eigenvalue
problem where the optimal input wavefront is given by the corresponding
eigenvector. We show analytically that a single wavefront can exhibit strongly
enhanced total transmission or total absorption across a bandwidth that is
orders of magnitude broader than the spectral correlation width of the medium,
due to long-range correlations in coherent diffusion. We find excellent
agreement between the analytic theory and numerical simulations.
