Showing papers by "John B. Pendry published in 1994"

Photonic Band Structures

Abstract: Building complex materials with structures on a scale comparable to the wavelength of light offers possibilities for radically changing the way light moves around such materials, in the same way that we engineer atomic structure to vary electronic properties of semiconductors. In this paper we describe in detail how to make numerical calculations of the dispersion relations (the band structure) of these complex objects, and how to calculate transmission through, and reflection from them. Finally these methodologies are applied to a colloidal dispersion of metallic particles at 12% volume filling fraction to reproduce the well known characteristics of strong optical absorption.

Symmetry and transport of waves in one-dimensional disordered systems

Abstract: The transfer matrix approach to transport in one-dimensional systems is reviewed in detail with emphasis on the role of symmetrized products. First, the concept of a transfer matrix is introduced, and then generalized through the introduction of symmetrized products. The resulting formalism is successively applied to the problem of averaging: resistance, density of states, conductance (i.e. transmission coefficient), phases of transmission and reflection, and frequency response. Finally the problem of 1/f noise in disordered systems is addressed in the language of symmetrized transfer matrices.

Interaction of surface states with rows of adsorbed atoms and other one-dimensional scatterers

Abstract: This paper investigates the interaction of a surface state with a one-dimensional scattering object on the surface of a metal. Examples are straight rows of regularly spaced adsorbed atoms, and straight step edges. The layer--Korringa-Kohn-Rostoker method is employed to investigate the electronic structure of periodic arrays of rows of adatoms on the Cu(111) surface in a 6\ifmmode\times\else\texttimes\fi{}2 geometry, as well as periodic arrays of missing rows to simulate step edges. From these band structures, the behavior of one individual scatterer is extracted by means of a one-dimensional model. Thus we obtain the rates of reflection, transmission, and scattering into the substrate. Rows of adsorbed Cu, Fe, S, and C are considered as well as single and double missing rows. It is found that none of these scatterers comes close to total reflectivity (R=1). Most cases lead to R around 0.3--0.4. The rest of the incoming electrons are mainly transmitted into the surface state on the other side, if the scatterer is a row of Cu or Fe atoms, while they are mainly scattered into the bulk by S and C. The behavior of missing rows is found to lie in between. By counting the number of outgoing states that a surface state can scatter into, qualitative information is obtained for two important situations. First, it is shown that for less than close-packed rows of adsorbed atoms, the ratio of the scattering rate into the bulk to that into the surface state is enhanced because of Bragg scattering. On Cu(111), this enhancement starts at an adatom spacing of M\ensuremath{\ge}2. Second, it is argued that replacing the semi-infinite substrate by a thin film is unlikely to reduce the loss of electrons into the bulk. While it is found that surface states interact strongly with most adsorbates, our results suggest that the total confinement of surface states within artificially made structures may not be feasible.

Energy loss by charged particles in complex media.

Abstract: The introduction of geometrical complexity into a dielectric structure radically alters the pattern of losses from a passing charged particle. Here we introduce an approach to the problem which is ideally suited to numerical work and to the treatment of complex geometry. We apply the method to losses in colloidal metallic systems where the local juxtaposition of surfaces produces a host of modes and consequent changes in the loss spectrum. We also calculate the ``Smith-Purcell effect,'' in which a particle passing over a grating may radiate energy into the vacuum. This method is powerful and flexible and will, we trust, open a class of materials to quantitative study.

A Polarized Transfer Matrix for Electromagnetic Waves in Structured Media

Abstract: The study of electromagnetic systems with dielectric or magnetic properties that vary spatially on or below the scale set by the wavelength of the radiation considered is of interest both in the field of photonic band gap materials and in that of random multiple scattering media. A key calculation technique in both areas is the transfer matrix. We derive a new transfer matrix, written in the language of scattering between transverse polarized wave states. This could be used in either photonic band calculations or in disordered media calculations. We demonstrate the use of the new transfer matrix to describe transport through a layered random dielectric in the Rayleigh scattering regime. This problem has considerable similarities to that of non-interacting electrons in a one-dimensional random potential. A complete solution for one polarization can be given by the use of group theoretical results. The other polarization exhibits pronounced dipole effects which can easily be calculated to lowest order.