In this article, by using the method of finite difference time domain (FDTD) and PML boundary conditions, we have studied the photonic band gaps for TE and TM modes in square and triangular lattices consisting of air holes in dielectric medium and compared the results. In addition, the effect of nonlinearity of the photonic crystal background on the photonic band gaps and comparison with the re...

This paper discusses the efficient, non-redundant evaluation of a Discrete Fourier Transform on the three dimensional Body-Centered and Face-Centered Cubic lattices. The key idea is to use an axis aligned window to truncate and periodize the sampled function which leads to separable transforms. We exploit the geometry of these lattices and show that by choosing a suitable non-redundant rectangu...

Root lattices are efficient sampling lattices for reconstructing isotropic signals in arbitrary dimensions, due to their highly symmetric structure. One root lattice, the Cartesian grid, is almost exclusively used since it matches the coordinate grid; but it is less efficient than other root lattices. Box-splines, on the other hand, generalize tensor-product B-splines by allowing non-Cartesian ...

In this report, we show the decidability and NP-completeness of the satisfiability problem for non-structural subtyping constraints in quasi-lattices. This problem, first introduced by Smolka in 1989, is important for the typing of logic and functional languages. The decidability result is obtained by generalizing Trifonov and Smith’s algorithm over lattices, to the case of quasi-lattices. Simi...