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Periodic waveguides bring a new twist onto the typical waveguiding problems been intermediate case between photonic crystal waveguides and photonic wires or ridge waveguides. We develop an asymptotic theory applicable for a broad class of coupled periodic waveguide structures, and use the analytical expressions to identify the generic types of dispersion in the vicinity of a photonic band-edge, where the group velocity of light is reduced. We show that the dispersion can be controlled by thedoi:10.1364/josab.25.000c65 fatcat:igqoum7izzdorazihlqtar2t24