Lindsay C. Botten

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.

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 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.

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.

Properties and structure of amorphous hydrogenated carbon films

Abstract Results are presented of a study of physical and optical properties of amorphous hydrogenated carbon films (a-CH x ) prepared by d.c. magnetron glow-discharge decomposition of acetylene in argon, both as prepared and after heat treatment in vacuum. The dependences of density, deposition rate and hardness on the partial pressure of acetylene used in film preparation are examined. A description of the investigations of material produced by distillation from the films is given and the optical constants of both the films and the distilled material in the energy range 0·5 to 6·5 eV are determined; these constants are used both to deduce optical gaps and ascertain the number of π-bonded electrons per carbon atom. It is shown that the average carbon—carbon coordination number of the annealed films is very close to three. Measurements of the temperature dependence of electrical conductivity indicate variable-range hopping. The results of infrared spectroscopy show that heat treatment increases the aromat...

Random Lasing in Weakly Scattering Systems

We present detailed experimental and numerical studies of random lasing in weakly scattering systems. The interference of scattered light, which is weak in the passive systems, is greatly enhanced in the presence of high gain, providing coherent and resonant feedback for lasing. The lasing modes are confined in the vicinity of the pumped volume due to absorption of emitted light outside it. In the ballistic regime where the size of the gain volume is less than the scattering mean free path, lasing oscillation occurs along the direction in which the gain volume is most extended, producing directional laser output. The feedback for lasing originates mainly from backscattering of particles near the boundaries of the pumped region. It results in nearly constant frequency spacing of lasing modes, which scales inversely with the maximum dimension of the gain volume.

Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method

We present a formulation for wave propagation and scattering through stacked gratings comprising metallic and dielectric cylinders. By modeling a photonic crystal as a grating stack of this type, we thus formulate an efficient and accurate method for photonic crystal calculations that allows us to calculate reflection and transmission matrices. The stack may contain an arbitrary number of gratings, provided that each has a common period. The formulation uses a Greens function approach based on lattice sums to obtain the scattering matrices of each layer, and it couples these layers through recurrence relations. In a companion paper [J. Opt Soc. Am. A 17, 2177 (2000)] we discuss the numerical implementation of the method and give a comprehensive treatment of its conservation properties.

Highly conducting lamellar diffraction gratings

We outline an improved root-finding algorithm necessary for the solution of the eigenvalue equation associated with the diffraction formalism for lossy lamellar gratings. A numerical example is presented, demonstrating the adequacy of this technique for a highly-conducting aluminium grating.