1 Department of Photonics Engineering, Technical University of Denmark2 National Space Institute, Technical University of Denmark3 Rector’s office, Administration, Technical University of Denmark
In the presenta ph.d. work a theoretical study of aspects of modelling photonic crystal fibres was carried out. Photonic crystal fibres form a class of optical waveguides where guidance is no longer provided by a difference in refractive index between core and cladding. Instead, guidance is provided by an arrangement of air-holes running along the length of the fibre. Depending on the geometry of the fibre, the guiding mechanism may be either arising from the formation of a photonic bandgap in the cladding structure (photonic bandgap fibre), or by an effect resembling total internal reflection, which may described by an effective refractive index which is lower in the cladding than in the core (index guiding fibre). By solving Maxwell's equations, under the conditions defined by the geometry of the fibre structure, we may predict the properties of the fibre. In all but rare cases, this is done via an approximative numerical modelling scheme. In this thesis, we describe some of the modelling procedures that have been proposed, with strong emphasis on the localised function method, and propose a novel variant of the former, which may overcome some of the shortcomings of the standard method. WE give a detailed description of the new variant - the Hermite-Gaussian method, and evaluate the results in view of the limitations inherent in the modelling procedure. WE present modelling results for triangular and square lattice fibres, a novel pentagonal symmetric index guiding fibre, as well as a honeycomb bandgap fibre and the first analysis of semi-periodic layered air-hole fibres. Using the modelling framework established as a basis, we provide an analysis of microbend loss, by regarding displacement of a fibre core as a stationary stochastic process, inducing mismatch between modes in contiguous fibre segments curved at different radii. Overall microbend loss is expressed as a statistical mean of mismatch losses. Extending a well proven, established formula for macrobending losses in stop index fibres, we provide an estimate of macrobend losses in an air-guiding photonic bandgap fibre, based on effective refractive index arguments.