No abstract

Optical waveguides are the basis of the optoelectronics and telecommunications industry. These comprise optical fibres and the integrated optical components which manipulate, filter and dispatch incoming optical signals. A taper is a generic kind of optical waveguide with a cross section that varies continuously along its length z. Tapers are used to couple light from a waveguide into another with different cross sectional profile. It is well known that the power lost through the taper side walls decreases for increasing taper lengths. For practical reasons however, it is desirable to keep the taper length as short as possible. The aim of this study is to develop a formulation to minimize the power loss by varying the taper profile of a given fixed length. It turns out that this shape optimization problem exhibits ill-posed behaviour which would slow down the convergence of traditional optimization routines. We show how these problems can be overcome by reformulating the shape optimization problem as a nonlinear inverse problem, which can then be solved using established inverse problem regularization techniques. Numerical results presented here show that this new approach can lead to robust optimization algorithms less sensitive to large discretization refinements.

In a process involving electromagnetic shaping, a high-frequency electromagnetic field is used to deform a liquid conductor into a required shape. This is particularly relevant to processes such as levitation melting. In this paper the stability of such configurations are investigated. The second variation of an appropriate energy functional is derived whose minimum states correspond to stable configurations, thus providing a stability criterion. As an example, this is applied to the shaping of a levitated cylinder of circular cross-section and to an almost spherical axisymmetric shape. In both cases we find that these shapes are unstable. We then consider enclosing the entire shaping device in a metal shield, thus preventing the escape of the magnetic field. It is then shown that in general the shield has a stabilizing effect, whose exact nature depends on the topology of the liquid shape and on the field structure on its surface. This differing behaviour is discussed for two-dimensional spherical and toroidal shapes.

We present a tool for the simulation of active and passive photonic integrated circuits (PIC) based on EME (eigenmode expansion) for modelling the details of circuit elements plus the travelling wave time domain (TWTD) technique for connecting the circuit together and modelling non-linear elements such as SOAs. We show how the two algorithms can be linked together using FIR filters to create a highly efficient PIC simulator. We discuss the strengths and weaknesses of the approach and illustrate it with the simulation of a variety of active and passive examples.

We present structures obtained with numerical optimization techniques capable of efficiently channeling light at a fraction of the length of a conventional taper. These results could open the way to novel designs in ultra-short light injection devices. We also consider the rather different problem of how to optimise the transmission through a photonic crystal bend. We show how, using a deterministic global optimisation algorithm, novel optimal geometries can be obtained leading to considerable performance improvements.