  Dispersion diagrams play a crucial role in examining, analyzing and designing
wave propagation in periodic structures. Despite their ubiquity and current
research interest, introductory papers and reference scripting tailored to
novel researchers in the field are lacking. This paper aims to address this
gap, by presenting a comprehensive educational resource for researchers
starting in the field of periodic structures and more specifically on the study
of dispersion relations captured by dispersion surfaces or curves in dispersion
diagrams. The objective is twofold. A first objective is to give a detailed
explanation of dispersion diagrams, with graphical illustrations. Secondly, a
documented Matlab code is provided to compute dispersion curves of 3D
structures with 2D periodicity using the so-called inverse approach. These
dispersion curves are obtained with numerical simulations using the finite
element method. The code is written for elastic wave propagation and orthogonal
periodicity directions, but can be extended to other types of linear wave
propagation, non-orthogonal periodicity directions or 1D and 3D periodicity.
The aim of this code is to serve as a starting point for novice researchers in
the field, to facilitate their understanding of different aspects of dispersion
diagrams and serve as a stepping stone in their future research.
