Efficient Simulation of Driven Finite Periodic Structures using the Finite-difference Time-domain Method

Infinitely-periodic geometries are efficiently modelled in the finite-difference time-domain (FDTD) method using periodic boundary conditions (PBCs). Several PBC implementations operate by maintaining a constant wave vector component in the periodic directions. This work presents the underlying mathematical background for all these methods and demonstrates their usage. However, infinitely-periodic structures modelled by PBCs are unrealizable physically. Therefore, an efficient FDTD technique for determining electromagnetic fields interacting with finite-sized periodic structures is proposed. 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.M.A.S