We are interested in exploring different topological phases by engineering the unit cell of periodic structures. Band-symmetry inversion trough geometry is the key concept to test in these systems. One of the goals here is to apply topological concepts used in the field of topological insulators in condensed matter Physics and apply them to bosonic systems. One main question we have related to this field is how robust are these analogies taken from solid-sate Physics and applied to the electromagnetic field and the mechanical vibrations. We aim to quantify the robustness of this topological materials against disorder.

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We have recently shown how to quantify the robustness of a topological edge state against white noise on its structural parameters. Calculating the backscattering length linked to the group index enables us to do that, as these two parameters are related to each other through the density of optical states. We have made a quantitative analysis of the backscattering mean free path in two waveguides, on topological and one conventional. We conclude that current proposals of topological photonic phases relying on the breaking of different parity symmetries as the valley-Hall effect are quantitatively, by almost  five times, more robust than standard conventional waveguides with small disorder levels, although this protection is lost at higher imperfection amount.