Semi-analytical design of antireflection gratings for photonic crystals

This article concerns the design of antireflection structures which, placed on a photonic crystal surface, significantly diminish the fraction of energy lost to reflected waves. After a review of the classes of these structures proposed to date, a new method is presented in detail for the design of antireflection gratings operating in a wide range of angles of incidence. The proposed algorithm is illustrated by means of several examples, showing the advantages and limitations.Comment: Submitted to Phys. Rev.

Photonic crystal carpet: Manipulating wave fronts in the near field at 1550 nm

Ground-plane cloaks, which transform a curved mirror into a flat one, and recently reported at wavelengths ranging from the optical to the visible spectrum, bring the realm of optical illusion a step closer to reality. However, all carpet-cloaking experiments have thus far been carried out in the far-field. Here, we demonstrate numerically and experimentally that a dielectric photonic crystal (PC) of a complex shape made of a honeycomb array of air holes can scatter waves in the near field like a PC with a at boundary at stop band frequencies. This mirage effect relies upon a specific arrangement of dielectric pillars placed at the nodes of a quasi-conformal grid dressing the PC. Our carpet is shown to work throughout the range of wavelengths 1500nm to 1650nm within the stop band extending from 1280 to 1940 nm. The device has been fabricated using a single- mask advanced nanoelectronics technique on III-V semiconductors and the near field measurements have been carried out in order to image the wave fronts's curvatures around the telecommunication wavelength 1550 nm.Comment: 6 page

Product algebras for galerkin discretisations of boundary integral operators and their applications

Operator products occur naturally in a range of regularised boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp, we have implemented a complete operator algebra that depends on knowledge of the domain, range, and test space. The aim was to develop a way of working with Galerkin operators in boundary element software that is as close to working with the strong form on paper as possible, while hiding the complexities of Galerkin discretisations. In this article, we demonstrate the implementation of this operator algebra and show, using various Laplace and Helmholtz example problems, how it significantly simplifies the definition and solution of a wide range of typical boundary integral equation problems

Software frameworks for integral equations in electromagnetic scattering based on Calderón identities

In recent years there have been tremendous advances in the theoretical understanding of boundary integral equations for Maxwell problems. In particular, stable dual pairings of discretisation spaces have been developed that allow robust formulations of the preconditioned electric field, magnetic field and combined field integral equations. Within the BEM++ boundary element library we have developed implementations of these frameworks that allow an intuitive formulation of the typical Maxwell boundary integral formulations within a few lines of code. The basis for these developments is an efficient and robust implementation of Calderón identities together with a product algebra that hides and automates most technicalities involved in assembling Galerkin boundary integral equations. In this paper we demonstrate this framework and use it to derive very simple and robust software formulations of the standard preconditioned electric field, magnetic field and regularised combined field integral equations for Maxwell