Comparison between the finite element method, the localized function method and a novel equivalent averaged index method for modelling photonic crystal fibres

Three numerical approaches for the analysis of photonic crystal fibres are presented and compared. A full-vector finite element method based on the resolution of the Maxwell equations is found to be a very efficient and reliable tool for accurately modelling these optical guiding structures. The localized function method in the scalar form applies as long as the air-filling fraction is not too large. We present a very simplified novel model based on an equivalent averaged refractive index profile that is in good accordance with the finite element method as long as the optical wavelength is not too enlarged. Finally, comparisons between numerical results and measurements are taken into account in order to discuss the reliability of the three models.