No abstract

We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a viable alternative to the plane-wave method to analyze the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we reproduce the main features of the spectrum obtained by the plane wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eights and ninth bands if the dielectric constant ε s of spheres is lower than the dielectric constant ε b of the background medium. If ε s > ε b , no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast ε b /ε s for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of an fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.

We present a generalization of the transition state technique introduced by Slater for the calculation of many-electron relaxation effects accompanying electronic excitations in molecules and molecular simulations of solids. By making use of ground state information (which is generally available but not used in the Slater formulation) and transition states which are computationally cheaper (due to being closer to the ground state), the generalization permits the evaluation of excitation energies to be improved in any of three ways: (1) comparable accuracy for less computation; (2) improved accuracy for comparable computation; and (3) full Δ-SCF accuracy can be approximated with arbitrary precision with additional computation. In particular, we show that excitation energies of somewhat greater accuracy are obtained from self-consistent calculations performed for transition states corresponding to 2/3 of the transition rather than 1/2 of the transition as in the original formulation by Slater.