  We study the dispersion relations in slow-light waveguide structures
consisting of coupled microdisk resonators. A group theoretical analysis of the
symmetry properties of the propagating modes reveals an interesting phenomenon:
The degeneracy of the CW and CCW rotating modes is removed, giving rise to two
distinct transmission bands. This effect induces symmetry-based dispersion
which may limit usable bandwidth of such structures. The properties of this
band splitting and its impact on CROW performance for optical communications
are studied in detail.
