A Memory-efficient Strategy for the FDTD Implementation Applied to the Photonic Crystals Problems

The Finite Difierence Time Domain (FDTD) method is well suited for the com- putation of the photonic crystals problems. However, this technique has the drawback of high computer memory requirements, when involving complex structures. In this paper, a modifled array implementation for the FDTD algorithm, with increased memory e-ciency, is presented and applied to studies on the abnormal refraction phenomena of the electromagnetic propagat- ing in the photonic crystals. The novel approach is based on memory-mapped flles, which is a mechanism of manipulating memory in Windows or Linux operating system. By using this mechanism, we make use of memory space more availably in allocating and implementing mul- tidimensional arrays for FDTD algorithm. The computed examples are given in the paper to prove the feasibility and accuracy of this strategy. A detailed discussion is presented for the case of the electromagnetic propagating in two-dimensional photonic crystals, formed by parallel air cylinders in a dielectric medium. The results show that some interesting relations can be obtained between the incident and the refraction angles with the group velocity (Vg) and the energy velocity (Ve).