  We study electromagnetic properties of periodic composite structures, such as
photonic crystals, involving lossy components. We show that in many cases a
properly designed periodic structure can dramatically suppress the losses
associated with the absorptive component, while preserving or even enhancing
its useful functionality. As an example, we consider magnetic photonic
crystals, in which the lossy magnetic component provides nonreciprocal Faraday
rotation. We show that the electromagnetic losses in the composite structure
can be reduced by up to two orders of magnitude, compared to those of the
uniform magnetic sample made of the same lossy magnetic material. Importantly,
the dramatic absorption reduction is not a resonance effect and occurs over a
broad frequency range covering a significant portion of photonic frequency
band.
