ABSTRACT
Wannier functions derived from Bloch functions have been identified as an efficient means of analyzing the properties of photonic crystals in which localized functions have now opened the door for 2D and 3D structures containing defects to be investigated. In this paper, based on the Maxwell equations in diagonalized form and utilizing Bloch waves we have obtained an equivalent system of algebraic equations in eigenform. By establishing and exploiting several distinct properties of the resulting eigenpairs, we demonstrate an ability to construct Wannier functions associated with the simplest one-dimensional photonic structure. More importantly, the numerical investigation of the inner- and intra-band orthonormality conditions as well as Hilbert space partitioning features shows a capability for multi-resolution analysis that will make all-optical signal processing devices with photonic crystal structures feasible.
ABSTRACT
In modern electronic devices the finite size of the substrates requires three-dimensional analysis. To this end, the boundary element method (BEM) may be utilized. The BEM involves problem-specific Green's functions (GFs), which are to be constructed first. This work has derived a GF which is the electric potential response to an isolated point charge in an unbounded anisotropic dielectric.
ABSTRACT
An easy-to-implement, accurate, and fast method to calculate 2-D quasi-static capacitance and inductance of electrodes in SAW devices is presented. The method is outlined by considering electrodes with any cross-section geometries in dielectric environment, consisting of two anisotropic materials with a plane interface. The analysis allows the inclusion of arbitrarily shaped metallic packages. A significant shift of charges on enclosures, due to the substrate anisotropy, is observed.
ABSTRACT
An accurate simulation tool to meet the stringent requirements for broadband surface-acoustic-wave (SAW) filters is described. The primary goal was to develop a modular software tool in which first- and second-order effects can be easily modeled as separate modules providing an overall high-precision model for SAW devices. The model takes into account surface wave diffraction and refraction, quasi-two-dimensional static charge distribution, metal resistance and external load impedances. The angular spectrum of waves formalism is interpreted in such a way as to render possible the simultaneous description of all effects mentioned. A sample of the results is given for the potential distribution.
