Second-order accurate FDTD space and time grid refinement method in three space dimensions

We present an algorithm based on the finite-difference time-domain method for local refinement of a three-dimensional computational grid in space and time. The method has second-order accuracy in space and time as verified in the numerical examples. A number of test cases with material traverse normal to the grid interfaces were used to assess the long integration time stability of the algorithm. Resulting improvements in the computation time are discussed for a photonic crystal microcavity design that exhibits a sensitive dependence of the quality factor on subwavelength geometrical features.