Modelización de dispositivos optoelectrónicos microestructuradosmétodos modales

Abstract

In this doctoral thesis a novel modal method has been formulated to analyse three dimensional dielectric systems. The vector wave equation which determines the resonant frequencies and fields is written in terms of a linear operator, whose eigenvectors satisfy a orthonormality relation. The key of the method is to obtain a matrix representation of the wave equation in a basis that is defined by the modes of an auxiliary system. The method has been applied to study optical devices (photonic crystal waveguides) and microwave cavities. The accuracy of the method is demonstrated by comparing the obtained results with other results available in the literature. In a second part, the technique has been particularised to analyse translation invariant systems reobtaining the biorthogonal-basis method. This method has been used to model the complex wave propagation in inhomogeneously filled waveguides and the group velocity dispersion properties of a novel type of Bragg fibres. Finally, a computationally efficient technique has been developed for the full-wave characterisation of inhomogeneously dielectric-filled cavities connected to inhomogeneously dielectric loaded waveguides. The multimode scattering matrix of the cavity is computed throughout an efficient implementation of the orthonormal-basis method for the calculation of the cavity modes. Moreover, the biorthogonal-basis method is employed for the analysis of the waveguides connected to the cavity. Non-radiative dielectric guide components and microstructured optoelectronic devices generated with photonic crystal waveguides have been analysed using the present technique.