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.
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