Abstract
We used the finite-difference time-domain method to solve Maxwell equations. More specifically, we applied the non-dissipative Yees algorithm with a duality relation between the spatial representations of the electric and magnetic fields that represents both the differential and integral forms of Maxwell equations. Ref. 1 and 2. To shorten the computational run time a parallel code was developed and run on a Pentium III linux cluster (the results are obtained from runs with 31 processors). The computational domain consists of 19 photonic lattice cells in the periodic structure for e in the x and y direction and 8 mesh cells in the z direction. Each photonic lattice cell has been divided into 40 × 40 computational mesh cells, but due to duality of the discretization mesh (see1), effectively we determined each field on only 20 × 20 points inside a photonic lattice cell. Periodic boundary conditions were used in all three directions. Each period of oscillation was divided into 90 time steps for the numerical integration. A typical 50-period run (about 4500 time steps) took 50 minutes.
© 2001 Optical Society of America
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