Calculating photonic Green's functions using a non-orthogonal finite difference time domain method

In this paper we shall propose a simple scheme for calculating Green's functions for photons propagating in complex structured dielectrics or other photonic systems. The method is based on an extension of the finite difference time domain (FDTD) method, originally proposed by Yee, also known as the Order-N method, which has recently become a popular way of calculating photonic band structures. We give a new, transparent derivation of the Order-N method which, in turn, enables us to give a simple yet rigorous derivation of the criterion for numerical stability as well as statements of charge and energy conservation which are exact even on the discrete lattice. We implement this using a general, non-orthogonal co-ordinate system without incurring the computational overheads normally associated with non-orthogonal FDTD. We present results for local densities of states calculated using this method for a number of systems. Firstly, we consider a simple one dimensional dielectric multilayer, identifying the suppression in the state density caused by the photonic band gap and then observing the effect of introducing a defect layer into the periodic structure. Secondly, we tackle a more realistic example by treating a defect in a crystal of dielectric spheres on a diamond lattice. This could have application to the design of super-efficient laser devices utilising defects in photonic crystals as laser cavities.Comment: RevTex file. 10 pages with 8 postscript figures. Submitted to Phys Rev

Order N photonic band structures for metals and other dispersive materials

We show, for the first time, how to calculate photonic band structures for metals and other dispersive systems using an efficient Order N scheme. The method is applied to two simple periodic metallic systems where it gives results in close agreement with calculations made with other techniques. Further, the approach demonstrates excellent numerical stablity within the limits we give. Our new method opens the way for efficient calculations on complex structures containing a whole new class of material.Comment: Four pages, plus seven postscript figures. Submitted to Physical Review Letter

Homogenization of nonlocal wire metamaterial via a renormalization approach

It is well known that defining a local refractive index for a metamaterial requires that the wavelength be large with respect to the scale of its microscopic structure (generally the period). However, the converse does not hold. There are simple structures, such as the infinite, perfectly conducting wire medium, which remain non-local for arbitrarily large wavelength-to-period ratios. In this work we extend these results to the more realistic and relevant case of finite wire media with finite conductivity. In the quasi-static regime the metamaterial is described by a non-local permittivity which is obtained analytically using a two-scale renormalization approach. Its accuracy is tested and confirmed numerically via full vector 3D finite element calculations. Moreover, finite wire media exhibit large absorption with small reflection, while their low fill factor allows considerable freedom to control other characteristics of the metamaterial such as its mechanical, thermal or chemical robustness.Comment: 8 pages on two columns, 7 figures, submitted to Phys. Rev.

Effective calculation of LEED intensities using symmetry-adapted functions

The calculation of LEED intensities in a spherical-wave representation can be substantially simplified by symmetry relations. The wave field around each atom is expanded in symmetry-adapted functions where the local point symmetry of the atomic site applies. For overlayer systems with more than one atom per unit cell symmetry-adapted functions can be used when the division of the crystal into monoatomic subplanes is replaced by division into subplanes containing all symmetrically equivalent atomic positions

Determination of Effective Permittivity and Permeability of Metamaterials from Reflection and Transmission Coefficients

We analyze the reflection and transmission coefficients calculated from transfer matrix simulations on finite lenghts of electromagnetic metamaterials, to determine the effective permittivity and permeability. We perform this analysis on structures composed of periodic arrangements of wires, split ring resonators (SRRs) and both wires and SRRs. We find the recovered frequency-dependent permittivity and permeability are entirely consistent with analytic expressions predicted by effective medium arguments. Of particular relevance are that a wire medium exhibits a frequency region in which the real part of permittivity is negative, and SRRs produce a frequency region in which the real part of permeability is negative. In the combination structure, at frequencies where both the recovered real part of permittivity and permeability are simultaneously negative, the real part of the index-of-refraction is found also to be unambigously negative.Comment: *.pdf file, 5 figure

Strong Resonance of Light in a Cantor Set

The propagation of an electromagnetic wave in a one-dimensional fractal object, the Cantor set, is studied. The transfer matrix of the wave amplitude is formulated and its renormalization transformation is analyzed. The focus is on resonant states in the Cantor set. In Cantor sets of higher generations, some of the resonant states closely approach the real axis of the wave number, leaving between them a wide region free of resonant states. As a result, wide regions of nearly total reflection appear with sharp peaks of the transmission coefficient beside them. It is also revealed that the electromagnetic wave is strongly enhanced and localized in the cavity of the Cantor set near the resonant frequency. The enhancement factor of the wave amplitude at the resonant frequency is approximately $6/|\eta_\mathrm{r}|$, where $\eta_\mathrm{r}$ is the imaginary part of the corresponding resonant eigenvalue. For example, a resonant state of the lifetime $\tau_\mathrm{r}=4.3$ms and of the enhancement factor $M=7.8\times10^7$ is found at the resonant frequency $\omega_\mathrm{r}=367$GHz for the Cantor set of the fourth generation of length L=10cm made of a medium of the dielectric constant $\epsilon=10$.Comment: 20 pages, 11 figures, to be published in Journal of the Physical Society of Japa

Plasmon-assisted electron-electron collisions at metallic surfaces

We present a theoretical treatment for the ejection of a secondary electron from a clean metallic surface induced by the impact of a fast primary electron. Assuming a direct scattering between the incident, primary electron and the electron in a metal, we calculate the electron-pair energy distributions at the surfaces of Al and Be. Different models for the screening of the electron-electron interaction are examined and the footprints of the surface and the bulk plasmon modes are determined and analyzed. The formulated theoretical approach is compared with the available experimental data on the electron-pair emission from Al.Comment: 30 pages, 9 figure

Effective electronic response of a system of metallic cylinders

The electronic response of a composite consisting of aligned metallic cylinders in vacuum is investigated, on the basis of photonic band structure calculations. The effective long-wavelength dielectric response function is computed, as a function of the filling fraction. A spectral representation of the effective response is considered, and the surface mode strengths and positions are analyzed. The range of validity of a Maxwell-Garnett-like approach is discussed, and the impact of our results on absorption spectra and electron energy-loss phenomena is addressed.Comment: 15 pages, 6 figures, to appear in Phys. Rev.

Transformation-optics description of nonlocal effects in plasmonic nanostructures

We develop an insightful transformation-optics approach to investigate the impact that nonlocality has on the optical properties of plasmonic nanostructures. The light-harvesting performance of a dimer of touching nanowires is studied by using the hydrodynamical Drude model, which reveals nonlocal resonances not predicted by previous local calculations. Our method clarifies the interplay between radiative and nonlocal effects in this nanoparticle configuration, which enables us to elucidate the optimum size that maximizes its absorption and field enhancement capabilitiesThis work was supported by the ESF plasmonbionanosense program, the Leverhulme Trust, and the Engineering and Physical Sciences Research Council (EPSRC