This thesis describes theoretically the evanescent coupling of a D-fibre, with the aim of calculating the propagation constants of the transverse modes. Both analytical and numerical methods are considered for the study of coupling situations involving a fibre. The first analytical method, Coupled Mode Theory (CMT), provides an understanding of the coupling phenomenon which occurs between two similar guides. In this situation, for example, for two fibres/guides with a similar range of propagation constants, coupling does not occur between a guided mode of the first guide and a radiation mode of the second. However, plane wave analysis is preferred to CMT for its simplicity and adequacy in prism coupling application. Secondly, the GF method is selected as the appropriate numerical method for the case of a D-fibre coupled to a semi-infinite dielectric medium, in preference to the point matching and finite elements methods. The GF method (a semi-numerical method) leads to an eigenvalue problem, with the propagation constant as the only unknown. The behaviour of the GF is dependent on the refractive index of the medium surrounding the fibre, the distance from the core to the flat surface of the cladding, and the possible effective refractive indices of the guided modes. A program is developed to calculate the GF as a function of these variables. By defining these parameters, it enables the testing of several routines which could be later introduced into a final program calculating the different propagation constants of the guiding structure. Finally, the analytical study has been extended to allow direct application in the final program
