Spin wave excitations in dipolarly coupled nanodisks from permalloy are investigated. We address, both, onedimensional (1D) chains and two-dimensional (2D) arrays consisting of nanodisks of different diameter. An out-of-plane magnetic field allows us to initialize the so-called vortex state in each of them. Our micromagnetic simulations show that in such 1D and 2D periodic devices the low-frequency excitations of the individual disks couple and form allowed frequency bands for spin-wave propagation. The devices operate as magnonic wave guides and magnonic crystals. The diameter is found to allow one to control both the center frequency and bandwidth of the allowed miniband in the few GHz frequency regime. We discuss a hybrid nanodisk device which might allow one to control and slow down the spin waves, i.e., the transmitted GHz signal. © 2011 SPIE.