  This paper proposes an efficient FDTD technique for determining
electromagnetic fields interacting with a finite-sized 2D and 3D periodic
structures. The technique combines periodic boundary conditions---modelling
fields away from the edges of the structure---with independent simulations of
fields near the edges of the structure. It is shown that this algorithm
efficiently determines the size of a periodic structure necessary for fields to
converge to the infinitely-periodic case. Numerical validations of the
technique illustrate the savings concomitant with the algorithm.
