What is the relation between grid step and simulation period?
there is not really any relation. One is the about the distance between 2 grid lines, the other is the duration of the simulation (in physical units, not the time it will take for the simulation to run).
However, the time step is determined by the size of the smallest grid cell (a stability requirement of the FDTD method) and the number of time steps needed is determined by the size and number of simulation periods. So effectively, the total runtime depends simultaneously (and linearly) on both the grid step and the number of simulation periods.