Indicadores del Análisis Coste-Beneficio

A GA has been applied, for the first time to the best of my knowledge, to the inverse design of HFs with a large number of free-parameters (up to 6) and for which the manual optimisation approach becomes unreliable and cumbersome.

The chosen design goal was a holey fibre with flat and nearly zero dispersion character- istics over a 100 nm range centred at 1.55 µm, and our approach has proved effective in finding various optimised solutions with D = 0 ± 0.1 ps/nm/km over the full wave- length range of interest. Despite possessing similar dispersion characteristics, the fibres analysed present different nonlinear parameters, ranging from 2.2 W−1_km−1 _{for fibre}

F4 to 10.4 W−1_km−1 _{for fibre F2. Fibre F3, representing a structural compromise be-}

tween holes with the same size throughout the cladding and different hole sizes for each ring, offers an intermediate nonlinear parameter (γ= 3.9 W−1_km−1_{). Similar values of}

dispersion slope and nonlinear parameter to those provided by the 4 NL-DFHF anal- ysed here have also recently been achieved in conventional doped fibres [189] although it is to be appreciated that the fabrication tolerances are extremely demanding. How- ever, it is well known that the higher index contrast of HF can lead to the realisation of fibres with a larger nonlinear parameter than is achievable with conventional fibres. Silica NL-DFHF with a nonlinear parameter as high as 44 W−1_km−1 _{and slightly com-}

promised slope have already been identified and simulated [192], and can be targeted more systematically in the future by extending the generic approach demonstrated in this section. Through the definition of different fitness functions, future work could also address the maximisation of the nonlinear parameter of NL-DFHF, or of their recently proposed figure-of-merit [29, 181]. Other useful design goals can also be targeted such

as flattened dispersion at wavelengths around 1µm, or a dispersion characteristic with two specifically positioned zero-dispersion wavelengths (see Section 3.3).

Fabrication guidelines for the structures established in this section have also been pro- posed, indicating that the dimension of the first ring of holes is particularly important in controlling the dispersion flatness. It is also important to accurately define the pitch, the dimension of the holes in the second ring of holes, and the position of the first two rings of holes. During the work it was found that some geometries, like F3, beside presenting an easier fabrication target than fibres F1 and F2, are also nearly twice less sensitive to fabrication errors - albeit with reduced fibre nonlinearity. From the analysis presented, we can roughly estimate that an accuracy of order 1-2% will be required for most of the critical structural parameters in order to control the overall dispersion with reasonable accuracy. Measurements on some of our recently fabricated fibres indicate that such a level of accuracy is well within sight and should be achievable with realistic improvements in the preform fabrication and fibre drawing processes.

4.4

Conclusion

In this chapter two different, general methods for the optimisation of complex functions have been presented, implemented and applied to practical inverse designs. Using this approach nonlinear fibres with optimised dispersion characteristics have been designed and, in some cases, fabricated and characterised, showing a good agreement between simulated and measured values. Although the two methods presented are rather general and could have been used in conjunction with any of the other methods for the modal simulation of HFs (see Chapter 2), the efficiency of the method chosen for the solution of each direct problem – the FEM – allows these computationally intensive simulations to be carried out overnight, making this design approach suitable and appealing to a vast range of other design tasks. The combination of GA and FEM proposed in this chapter has been subsequently used, for example, by other groups to design broadband dispersion compensating fibres [198] or holey fibres optimised for gain-flattened discrete Raman amplifications [199].

Although these inverse approaches have quite a large applicability in the structural inverse design of fibres, they both require a parametrisation of the structures to be optimised. For example, in the previous examples the holes were assumed to be circular, and their radius was a free parameter. Since the parametrisation must be chosen a-priori, the existence of potentially better solutions cannot be excluded. Alternative methods able to modify the structure and topology of the fibre’s cross section in a way free of any pre-fixed rules would represent a further improvement and are currently under examination. An example of such a method is the Level-Set method, which can be employed to move arbitrarily the interface between two media [200]. If this algorithm is

driven by the generalised gradient of the function to optimise, a very powerful topology optimisation method is constructed, as the work by Kaoet al.[201] for the maximisation of photonic bandgaps for in-plane propagation demonstrates.

Other fibre designs

5.1

Introduction

This section presents additional modelling work and fibre designs carried out during my PhD using the modal solver based on the finite element method. These studies have been conducted in collaboration with a number of colleagues, in order to complement and reinforce their fabrication and/or experimental work. Every time a comparison between a measured and simulated value was possible it showed a good agreement, indicating the reliability and accuracy of the implemented full-vector method, and also that simulation results can be employed to reliably design new fibres and to predict optical properties where actual measurements are not possible.

A particularly useful feature is the possibility of simulating an exact representation of a real, fabricated fibre, through the processing of an SEM image of its cross-section. This method is used, in the first part of the chapter, to study the performance of a fabricated suspended-core fibre and to foresee some of its possible applications.

In the second part of the chapter, my contribution to a larger project, aiming at the production of fibre sources for efficient white light generation, is presented. A fibre with a suitable core shape and dimension for optimised supercontinuum generation in the visible is designed. Some modelling is conducted in order to support experimental observations of parametric processes in the visible region of the spectrum, taking place in the cladding of microstructured fibres.