Ross C. McPhedran

Multipole method for microstructured optical fibers. I. Formulation

We describe a multipole method for calculating the modes of microstructured optical fibers. The method uses a multipole expansion centered on each hole to enforce boundary conditions accurately and matches expansions with different origins by use of addition theorems. We also validate the method and give representative results.

Microstructured polymer optical fibre

The first microstructured polymer optical fibre is described. Both experimental and theoretical evidence is presented to establish that the fibre is effectively single moded at optical wavelengths. Polymer-based microstructured optical fibres offer key advantages over both conventional polymer optical fibres and glass microstructured fibres. The low-cost manufacturability and the chemical flexibility of the polymers provide great potential for applications in data communication networks and for the development of a range of new polymer-based fibre-optic components.

The Dielectric Lamellar Diffraction Grating

A rigorous modal theory describing the diffraction properties of a dielectric lamellar grating is presented. The numerical implementation is shown to be suited to modelling the behaviour of high refractive index gratings. This suggests that an approach of this type may be successfully applied to the problem of lossy metallic lamellar gratings.

Confinement losses in microstructured optical fibers

We describe a multipole formulation that can be used for high-accuracy calculations of the full complex propagation constant of a microstructured optical fiber with a finite number of holes. We show how the imaginary part of the microstructure, which describes confinement losses not associated with absorption, varies with hole size, the number of rings of holes, and wavelength, and give the minimum number of rings of holes required for a specific loss for given parameters.

Symmetry and degeneracy in microstructured optical fibers

The symmetry of an optical waveguide determines its modal degeneracies. A fiber with rotational symmetry of order higher than 2 has modes that either are nondegenerate and support the complete fiber symmetry or are twofold degenerate pairs of lower symmetry. The latter case applies to the fundamental modes of perfect microstructured optical fibers, guaranteeing that such fibers are not birefringent. We explore two numerical methods and demonstrate their agreement with these symmetry constraints.

Aphrodite's iridescence

The most intense colours displayed in nature result from either multilayer reflectors or linear diffraction gratings1,2,3. Here we investigate the spectacular iridescence of a spine (notoseta) from the sea mouse Aphrodita sp. (Polychaeta: Aphroditidae). The spine normally appears to be deep red in colour, but when light is incident perpendicular to the axis of the spine, different colours are seen as stripes running parallel to the axis of the spine; over a range of smaller incident angles, the complete visible spectrum is reflected with a reflectivity of 100% to the human eye. The simple structure responsible for this effect is a remarkable example of photonic engineering by a living organism.

The conductivity of lattices of spheres II. The body centred and face centred cubic lattices

The conductivities of body-centred (b. c. c.) and face-centred (f. c. c.) cubic lattices of spheres of a conducting material in a conducting matrix are calculated by using a method originally devised by Lord Rayleigh. Measurements of the conductivity of the b. c. c. lattice of perfectly conducting spheres are presented. Good agreement between theory and experiment is obtained. Our results are shown to be in agreement with asymptotic equations derived by other authors. A formula is given for the case of a disordered array.

The Finitely Conducting Lamellar Diffraction Grating

A rigorous modal theory describing the diffraction properties of a finitely conducting lamellar grating is presented. The method used is the generalization to lossy structures of an earlier formalism for the dielectric lamellar grating. Sample results of the method are given, demonstrating its accuracy and its ability to deal with problems intractable by the widely used integral-equation formalisms of diffraction grating theory.

Modal cutoff in microstructured optical fibers

We analyze the nature of modal cutoff in microstructured optical fibers of finite cross section. In doing so, we reconcile the striking endlessly single-mode behavior with the fact that in such fibers all propagation constants are complex. We show that the second mode undergoes a strong change of behavior that is reflected in the losses, effective area, and multipolar structure. We establish the parameter subspace in which the fibers are single mode and an accurate value for the limit of the endlessly single-mode regime.

Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance

Discrete systems of infinitely long polarizable line dipoles are considered in the quasistatic limit, interacting with a two-dimensional cloaking system consisting of a hollow plasmonic cylindrical shell. A numerical procedure is described for accurately calculating electromagnetic fields arising in the quasistatic limit, for the case when the relative permittivity of the cloaking shell has a very small imaginary part. Animations are given which illustrate cloaking of discrete systems, both for the case of induced dipoles and induced quadrupoles on the interacting particles. The simulations clarify the physical mechanism for the cloaking.