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Abstract

This thesis integrates ideas from the fields of computational science and applied mathematics into a simulation-based optimization environment. The proposed computational and mathematical tools are synergistically combined to produce globally optimized specialty fibres for high power fibre lasers.

The main contributions to new knowledge made by this work are outlined below:

• A photonics simulation method for the calculation of the absorption efficiency of large area
double-clad fibres.
• A three-dimensional ray tracing method which is upgraded to a coarse photonics simulator
when combined with a ray caustics model.
• The fair benchmarking of several optimization algorithms in high dimensions.
• The pattern-based, unified description of the modem Nelder-Mead algorithm as well as its Monte Carlo forms that are also proposed here.
• Many globally optimized double-clad, holey fibres based on all-solid-state topologies.

A surrogate model for the simulation of the pump laser light absorption inside large area waveguides is constructed on the basis of a coarse model which computes the pump photons transverse density. The computational backbone of the coarse model is a three-dimensional ray tracing algorithm owing its speed and computational efficiency to an adaptive intersection algorithm that avoids cross product calculations, as well as the evaluation of large point set populations, without loss of accuracy.

The coarse model is augmented to the physically meaningful surrogate model by means of an absorption cross sections based computational link that allows the calculation of the absorption levels inside the active core finite volume elements.

Validation results of the surrogate model have shown that it achieves satisfactory virtual experiment accuracy, rendering it suitable for the optimization of specialty fibre geometries and refractive index profiles. The corresponding objective function maps a fibre’s design parameters and sampled arbitrary geometry to a single point in a tailored multidimensional space. The objective values are satisfactorily accurate, post-processed simulation results obtained from within the geometrical optics domain. No restrictions are imposed to the direction of propagation or to the range of transmission angle values of the simulated rays.

Benchmarking of several zeroth-order optimization algorithms has shown that the golden ratio solution between global convergence and computational efficiency is well approximated by a simplex-based stochastic method. The proposed algorithm combines synergistically the elements of implicitly constrained optimization via pattern imprinted constraints, adaptive pattern search, stochastic search, Monte Carlo optimization and smooth perturbations of an initially proposed coordinate set representing a point in the objective function domain.

By the combination of intuitive virtual photonics experiments and numerical optimization, globally optimized fibre designs are produced showing that simulation-based optimization processes can accelerate, as well as reduce the cost of, the continuous wave fibre lasers power up-scaling. Such an achievement is most foreseeable via the creation of optimized on-chip, rod- type high power fibre lasers arranged in matrix formats for coherent beam combining. Alloy- glass, large-hole, all-solid-state double-clad fibres optimized here have served the above objective and so has the rod-type photonic bandgap fibre proposed for further work.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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