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Vortex dynamics within arrays of square ferromagnetic nanoelements have been studied by time-resolved scanning Kerr microscopy (TRSKM), while x-ray photoemission electron microscopy has been used to investigate the equilibrium magnetic state of the arrays. An alternating field demagnetization process was found to initialize a distribution of equilibrium states within the individual elements of the array, including quasiuniform states and vortex states of different chirality and core polarization. Repeated initialization revealed some evidence of stochastic behavior during the formation of the equilibrium state. TRSKM with a spatial resolution of ~300 nm was used to detect vortex gyration within arrays of square nanoelements of 250-nm lateral size. Two arrays were studied consisting of a 9 × 9 and 5 × 5 arrangement of nanoelements with 50- and 500-nm element edge-to-edge separation to encourage strong and negligible dipolar interactions, respectively. In the 5 × 5 element array, TRSKM images, acquired at a fixed phase of the driving microwave magnetic field, revealed differences in the gyrotropic phase within individual elements. While some phase variation is attributed to the dispersion in the size and shape of elements, the vortex chirality and core polarization are also shown to influence the phase. In the 9 × 9 array, strong magneto-optical response due to vortex gyration was observed across regions with length equal to either one or two elements. Micromagnetic simulations performed for 2 × 2 arrays of elements suggest that particular combinations of vortex chirality and polarization in neighboring elements are required to generate the observed magneto-optical contrast. [ABSTRACT FROM AUTHOR]