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Periodic structures in plasmas form unique dispersions of electromagnetic waves, which are examined in numerical calculation. Above electron plasma frequency, where waves equivalently propagate in dielectric media, plasma arrays with 2-D periodicity produce frequency regions of forbidden propagation, like band gaps in a photonic crystal. Below electron plasma frequency, where waves are usually forbidden to propagate due to cutoff phenomenon, bulk plasmas with periodic holes can become wave-propagating media in which localized surface modes play an important role. Such features give rise to concepts of dynamic wave controllers that change their inner electron density in time.