Scale modelling and Wave Finite Element Method for the analysis of complex waveguides at high frequency

Modelling complex waveguides at high frequency is still a challenge for conventional Finite Element analyses (FEA), limiting the possibility to study and optimise the structure's performance according to the analysis of wave mode propagation. The Wave Finite Elements Method (WFEM) has been widely used to study waveguides: it exploits Bloch-Floquet theory and conventional FE elements, allowing the prediction of the overall behaviour of the complex waveg-uide just by studying one arbitrary small segment of the structure using commercial FE software. Nevertheless, for wave problems where the wavelength is very small compared to the cross-sectional dimensions, such as in the analysis of wave modes in photonic crystal fibres, the number of elements needed to discretise the cross-section becomes enormous. The present work proposes an innovative scale model, based on WFEM, where dispersion relations of a periodic structure with isotropic material are studied and compared with a down-scaled orthotropic solution , aiming to preserve dispersion curves of the isotropic one, but with a substantially smaller number of mesh elements. To this aim, constitutive matrix elements of the orthotropic plate are properly altered with reference to the scale factor used to reduce the periodic cell's section dimensions.