The electromagnetic wave propagation in a complex plasma containing macroparticle inclusions (dust) is reviewed. We focus on two classes of phenomena due to the presence of dust:(1), collection of plasma electrons and ions by macroparticle inclusions and related modification of dielectric properties, and (2), surface plasmon resonances on the macroparticle surfaces and their effect on electromagnetic wave propagation. It is demonstrated that the presence of these phenomena can significantly modify plasma electromagnetic properties by introducing additional (charging) damping, modifying field distributions near macroparticles, and leading to resonances and cut-offs in the effective permittivity. The conditions to observe such phenomena in laboratory dusty plasma and/or space (cosmic) dusty plasmas are discussed.
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