  We demonstrate theoretically that a strong high-frequency circularly
polarized electromagnetic field can turn a two-dimensional periodic array of
interconnected quantum rings into a topological insulator. The elaborated
approach is applicable to calculate and analyze the electron energy spectrum of
the array, the energy spectrum of the edge states and the corresponding
electronic densities. As a result, the present theory paves the way to optical
control of the topological phases in ring-based mesoscopic structures.
