According to Huygens' superposition principle, light beams traveling in a linear medium will pass though one another without mutual disturbance. Indeed, it is widely held that controlling light signals with light requires intense laser fields to facilitate beam interactions in nonlinear media, where the superposition principle can be broken. We demonstrate here that two coherent beams of light of arbitrarily low intensity can interact on a metamaterial layer of nanoscale thickness in such a way that one beam modulates the intensity of the other. We show that the interference of beams can eliminate the plasmonic Joule losses of light energy in the metamaterial or, in contrast, can lead to almost total absorbtion of light. Applications of this phenomenon may lie in ultrafast all-optical pulse-recovery devices, coherence filters and THz-bandwidth light-by-light modulators.