We calculate the average transmission for s-and p-polarized electromagnetic ͑EM͒ waves and consequently the localization length of two-dimensional ͑2D͒ disordered systems which are periodic on the average; the periodic systems form a square lattice consisting of infinitely long cylinders parallel to each other and embedded in a different dielectric medium. In particular, we study the dependence of the localization length on the frequency, the dielectric function ratio between the scatterer and the background, and the filling ratio of the scatterer. We find that the gaps of the s-polarized waves can sustain a higher amount of disorder than those of the p-polarized waves, due to the fact that the gaps of the s-polarized waves are wider than those of the p-polarized waves. For high frequencies, the gaps of both types of waves easily disappear, the localization length is constant and it can take very small values. The optimum conditions for obtaining localization of EM waves in 2D systems will be discussed.

No abstract

We present a careful study of the energetics of vacancy and substitutional impurities in aluminum in both the bulk and small cluster environments. The calculations are done within the framework of the local-densityfunctional formalism and are based on the pseudopotential method with plane-wave expansion and periodic boundary conditions. Both the ionic and electronic degrees of freedom are fully relaxed. The electronic structure problem is treated with a preconditioned conjugate-gradient method that applies equally well to insulators and metals, and is suitable for parallel computing. We have considered up to 216 atoms in the supercell, and we show that reliable results can be obtained with 108-atom cells with proper k-point sampling. Vacancy-formation energy, heats of solution of the impurities and the relaxations near the defects are in good agreement with available experimental data. The energetics of substitution in small clusters was found to be rather different from bulk. ͓S0163-1829͑97͒07320-7͔