A conceptually simple method for incorporating periodic boundary conditions into the FDTD method

The incorporation of periodic boundary conditions into the FDTD method has been extensively studied for over a decade. For a two-dimensional structure that is periodic in the y direction, the electromagnetic field is the same in every unit cell of the structure except for a time shift. For a marching-in-time procedure, such as the FDTD method, this kind of boundary condition can present a problem, because it may require time-advanced values of the field that have not yet been computed. We present a straightforward method to eliminate the need for the time-advanced field. The technique is conceptually similar to the sliding unit-cell approach presented by H. Holter and H. Steyskal (see Electronics Letters, vol.35, no.10, p.758-9, 1999), but unlike that approach, is not restricted to a finite number of angles.