The aim of this introductory chapter was to provide the reader with an overview of the potential of microstructured optical fibres to produce optical properties unreachable with conventional fibres, to exploit novel physical effects and to permit entirely new applications. At the beginning of this project, nearly 7 years after the first fabricated MOF, a wide variety of fibres had been already fabricated and characterised at the ORC, as well as in a few other research facilities worldwide, employing different glasses and fabrication techniques. An example of some of these structures is shown in Figure 1.16.
In order to improve our understanding of these fibres and to design novel fibres for spe- cific applications, adequate modelling tools are also required. The modelling of these fibres however was still a demanding task and a rather unexplored field at that time. This motivated the development and application of novel simulation methods for the study of MOFs, which represents the underlying theme of this research project. As will be further discussed in Chapter 2, analytical models can not be applied to the modelling of MOFs, and numerical models have to be specifically formulated or adapted from other applications. A number of numerical models were already available at the beginning of this project, and the first task was therefore to review the various methods and assess their efficiency, accuracy and suitability to simulate a broad range of ideal and real fi- bres. The outcome of this work, reported in Chapter 2, suggested the finite element method (FEM) as one of the most complete, versatile and efficient methods. Rather
Figure 1.16: Some examples of the wide variety of MOFs and preforms fabricated at the ORC in recent years by employing various glasses and fabrication techniques.
than implementing the FEM ourselves, it was decided to adapt a general commercial FEM package for the specific needs of MOF modelling. A number of scripts were there- fore implemented, allowing us to design a range of new fibres and to complement the experimental characterisation of fabricated fibres in several different projects, as will be reported in the following chapters. Scripts and specific methods for studying both index guiding and photonic bandgap guiding fibres have been developed. In addition, another requisite of the project was to develop inverse design techniques that would help in the search for the best microstructure to provide one or more target optical properties. The outcome of this work is presented in Chapter 3 and 4.
An outline of the main content in each chapter of this thesis is reported in the following. In Chapter 2 an introduction on the electromagnetic modelling of MOFs is presented. This contains an overview of the specific issues to be faced, of the various modelling tools currently available to study MOFs, and of the particular numerical method – the finite element method – that will be employed throughout this work, for which some details of our implementation and an accuracy test will also be presented.
The following three chapters included in Part II of this thesis, Chapter 3, 4 and 5, are devoted to the study of index guiding fibres. Chapter 3 and 4 explore different inverse design methods finalised at finding the structure which possesses some desired optical properties, while Chapter 5 presents additional modelling work carried out to support various experimental results.
In particular, Chapter 3 introduces two dimensional optical property maps, which visu- ally overlap the contour plots of many optical properties of hexagonally arranged HFs, and shows the wide applicability of such maps to many HF design problems. Three different studies are reported: (i) the examination of the applicability of HFs as tele- coms transmission media; (ii) the optimisation of the chromatic dispersion of silica HFs for the generation of supercontinuum light at wavelengths around 1µm; (iii) the design of fibre tapers in a number of different glasses allowing simultaneous reduction of the stimulated Brillouin scattering and control of the overall dispersion properties.
In Chapter 4 the inverse design is taken one step further, to allow the optimisation of fibres with a larger number of free-parameters. Although the inverse methods im- plemented are quite general and suitable for a large variety of fibre optimisations, two specific applications are presented. First the simplex method is employed to obtain dis- persion flattened, highly nonlinear lead silicate fibres for application at telecoms wave- lengths; then a genetic algorithm is applied to the inverse design of dispersion flattened silica fibres with a large number of free-parameters. The tolerance to fabrication inac- curacies for the resulting optimum structures is also analysed.
Chapter 5 contains two additional numerical studies of index guiding MOFs, where the simulations have been used to support experimental measurements and to enhance our understanding of the fibres and of the physical phenomena under observation. A fabricated suspended-core HF is studied in order to explore its potential for applications within evanescent field sensing, as well as a polarisation maintaining highly nonlinear fibre. The efficient generation of light in the visible range of the spectrum is then tackled by both optimising a fibre for the generation of a supercontinuum around those wavelengths and through the exploitation of red and blue sidebands, generated through a Four Wave Mixing (FWM) process when a green light is pumped into the cladding of a particular MOF.
The following two chapters which form Part III of this thesis, Chapter 6 and 7, deal with the modelling of photonic bandgap fibres. Chapter 6 proposes a structural model to represent accurately the cross section of fabricated hollow core PBGFs and it applies the model to the study of the typical properties of these fibres, their dependence on the material properties and to obtain general scaling rules. The chapter also includes a study of real (i.e. unsymmetric) fibres from the simulation of their cross-section, as obtained from scanning electron micrograph (SEM) images. This study is made possible by the unique capability of the FEM to describe accurately structural details over a length scale ranging over three orders of magnitude. The necessity of using high resolution scanning electron micrographs is advocated and the influence of the gold coating layer employed in the SEM acquisition is also discussed.
Finally, Chapter 7 is devoted to the study of the surface modes in PBGFs and presents two separate analyses. The first one observes how these modes are extremely dependent
upon the shape of the glass core boundary, and it shows how small asymmetric variations in this boundary can lead to the high birefringence and polarisation dependent loss experimentally observed at some wavelength within the bandgap. The second study tackles the problem of maximising the operational bandwidth of realistic PBGFs by eliminating anticrossings with surface modes. For a particular thickness of the core boundary, a regime is found for which the fibres are surface mode-free. This finding is then confirmed by experimental measurements.
NOTE: The work reported in this thesis has been deeply affected by the fire which, on 30 October 2005, destroyed the ORC clean rooms and a number of offices, including the author’s. Besides the loss of all codes and simulation results produced in the period between December 2004 and the fire, this event has negatively affected most of the experimental projects I was collaborating with. As a result, some of the works presented here could not be completed as originally intended. This is the case, for example, of the works reported in Section 3.3 and Section 4.2, which required the fabrication of silica fibres (which was only recently resumed) and of soft glass fibres (which has not yet been resumed). In all cases however, the theoretical or numerical part representing my contribution to the project, has been either recovered or completely regenerated, and it is thus presented in a consistent form. Please note that a limited number of images reported in the thesis have been recovered from previously generated bitmaps, and therefore they present a lower resolution.
Modelling microstructured
optical fibres
2.1
Introduction
After the general introduction to the history, main properties and applications of mi- crostructured optical fibres presented in the previous chapter, this chapter provides the background information necessary to understand the modelling work conducted in this thesis. The chapter starts with an overview of the differential mathematical problem that needs to be solved in order to study light propagation in a MOF; then the principal simulation methods so far developed for the study of MOFs will be presented. The choice of the finite element method (FEM) as the preferred method for the studies in this thesis is then supported. A final section is then devoted to the introduction of the FEM, to the presentation of the implementation used throughout the thesis and to an analysis of the accuracy achievable with the method.