N. A. Nicorovici

On the cloaking effects associated with anomalous localized resonance

Regions of anomalous localized resonance, such as occurring near superlenses, are shown to lead to cloaking effects. This occurs when the resonant field generated by a polarizable line or point dipole acts back on the polarizable line or point dipole and effectively cancels the field acting on it from outside sources. Cloaking is proved in the quasistatic limit for finite collections of polarizable line dipoles that all lie within a specific distance from a coated cylinder having a shell permittivity where is the permittivity of the surrounding matrix, and is the core permittivity. Cloaking is also shown to extend to the Veselago superlens outside the quasistatic regime: a polarizable line dipole located less than a distance d/2 from the lens, where d is the thickness of the lens, will be cloaked due to the presence of a resonant field in front of the lens. Also a polarizable point dipole near a slab lens will be cloaked in the quasistatic limit.

A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance

Enlarging upon work of Nicorovici, McPhedran & Milton (Nicorovici et al. 1994 Phys. Rev. B 49(12), 8479–8482), a rigorous proof is given that in the quasistatic regime a cylindrical superlens can successfully image a dipole line source in the limit as the loss in the lens tends to zero. In this limit it is proved that the field magnitude diverges to infinity in two sometimes overlapping annular anomalously locally resonant regions, one of which extends inside the lens and the other of which extends outside the lens. The wavelength of the oscillations in the locally resonant regimes is set by the geometry and the loss, and goes to zero as the loss goes to zero. If the object or source being imaged responds to an applied field it is argued that it must lie outside the resonant regions to be successfully imaged. If the image is being probed it is argued that the resonant regions created by the probe should not surround the tip of the probe. These conditions taken together make it difficult to directly probe the potential in the near vicinity of the image of a source or object having small extent. The corresponding quasistatic results for the slab lens are also derived. If the source is too close to the slab lens, i.e. lying within the resonant region, then the power dissipation in the lens tends to infinity as the loss goes to zero, which makes the lens impractical for imaging such quasistatic sources. Perfect imaging in a cylindrical superlens is shown to extend to the static equations of magnetoelectricity or thermoelectricity, provided they have a special structure which makes these equations equivalent to the quasistatic equations.

Solutions in folded geometries and associated cloaking due to anomalous resonance

Solutions for the fields in a coated cylinder where the core radius is bigger than the shell radius are seemingly unphysical, but can be given a physical meaning if one transforms to an equivalent problem by unfolding the geometry. In particular, the unfolded material can act as an impedance matched hyperlens, and as the loss in the lens goes to zero finite collections of polarizable line dipoles lying within a critical region surrounding the hyperlens are shown to be cloaked having vanishingly small dipole moments. This cloaking, which occurs both in the folded geometry and the equivalent unfolded one, is due to anomalous resonance, where the collection of dipoles generates an anomalously resonant field, which acts back on the dipoles to essentially cancel the external fields acting on them.

Eigenvalue problems for doubly periodic elastic structures and phononic band gaps

We consider the problem of elastic waves propagating in a two–dimensional array of circular cavities, taking rigorous account of coupling between shear and dilational waves. A technique, originally due to Rayleigh, is derived that involves an elegant identity between the singular and non–singular components of the stress fields in the array. This leads to an infinite linear system which can be truncated and solved in order to determine the complete structure of the propagating modes. Of particular interest is the possibility of exhibiting phononic band gaps, i.e. domains of frequency for which all propagating vibration in the material is suppressed.

Transport Properties of a Three-Phase Composite Material: The Square Array of Coated Cylinders

The analytic properties of the effective dielectric constant of a class of three-phase composite materials are studied. Specifically, we investigate the effective dielectric constant of a periodic array of coated cylinders, as a function of the core dielectric constant (ϵc) and the shell dielectric constant (ϵs), while keeping the matrix dielectric constant (ϵb) fixed. We show that when ϵs = – ϵc, the composite has exactly the same effective dielectric constant as a periodic array of solid cylinders with dielectric constant ϵc and radius equal to the outer radius of the original coated cylinder. We also show that when ϵs = – 1, the composite has exactly the same effective dielectric constant as a periodic array of solid cylinders with dielectric constant ϵc, and radius exceeding the shell radius. We explore the location of poles and zeros of the three-phase effective dielectric constant in the (ϵs,ϵc) plane. The lines ϵs = – 1 and ϵs + ϵc = 0 are loci of essential singularities. We also comment on the behaviour of the effective dielectric constant in the neighbourhood of the two special points (ϵs,ϵc) = (0,0) and (ϵs,ϵc) = ( - 1 , + 1 ).

Structural colours through photonic crystals

We discuss two examples of living creatures using photonic crystals to achieve iridescent colouration. The first is the sea mouse (Aphroditidae, Polychaeta), which has a hexagonal close packed structure of holes in its spines and lower-body felt, while the second is the jelly fish Bolinopsis infundibulum, which has an oblique array of high index inclusions in its antennae. We show by measurements and optical calculations that both creatures can achieve strong colours despite having access only to weak refractive index contrast.

Low Frequency Corrections to the Static Effective Dielectric Constant of a Two-Dimensional Composite Material

We derive the first dynamic correction to the effective refractive index for a square array of cylinders (of finite or infinite refractive index), subject to a low frequency incident radiation. This correction also imposes constraints on the wavenumber region for which the Lorentz-Lorenz formula in two dimensions is accurate.

Lattice sums for gratings and arrays

Lattice sums arising in quasiperiodic Green’s functions for the Helmholtz equation, over general two-dimensional arrays are investigated. The array sums are related to those over a single quasiperiodic line of sources, and their difference is be expressed in terms of exponentially convergent series. It is shown that our expressions can be used to generate the sums pertaining to the case of photonic gap states, associated with complex quasiperiodicity (Bloch) vectors. The accuracy and computational speed of our expressions are illustrated.

Optical resonances of three-phase composites and anomalies in transmission

Abstract Composite media prepared by coevaporation of two constituents are modelled, in this work, as three-phase composites to take account of the presence of void spaces, which are inevitably formed during growth. Previous work on the effective dielectric constant of regular arrays of coated cylinders revealed the unexpected phenomenon of the extension of core properties to and beyond the coating (or shell), at certain ‘resonance wavelengths’. We extend this treatment first to the case of regular arrays of coated spheres and then to the case of disordered arrangements of cylinders and spheres. Our model uses the quasistatic approximation and is applicable to composite media when the size of the inclusions is much smaller than the wavelength of the incident radiation. The model is intended to predict if a three-phase composite exhibits resonances and, if so, what are the wavelengths of the incident radiation producing this effect. The results of the model are compared with experimental measurements on AgMgF2 cermets by treating the cermets as three-phase composites containing voids. The resonance wavelengths are identified with features in the transmission, reflectance and absorption spectra of the cermets.

The Sea Mouse and the Photonic Crystal

Sea mice (Aphroditidae, Polychaeta) are furry-looking marine worms that forage on, or in, the sea-bed. They are distinguished by an amazing iridescence along the lower sides of the body, associated with both hairs and spines known as chaetae. We show by electron microscopic and optical analysis that the iridescence of spines is caused by a highly regular, sub-micron scale structure resembling that being developed for photonic crystals, and that in fact the sea mouse exploits a partial photonic band gap to achieve its remarkable coloration effects. Manuscript received: 27 October 2000. Final version: 24 July 2001.