Symmetry, topology and localisation of waves

Charlista: Prof. Vassos Achilleos, Université du Maine (LAUM) - UMR, CNRS

Resumen: For a long time, there have been persistent efforts to find novel ways to manipulate waves in many different fields including condensed matter, electromagnetism, elasticity and acoustics. It was recently understood that beyond the usual control of intrinsic wave properties, such as the frequency, polarization, amplitude and phase, another means to manipulate waves relies purely on symmetries.

Lending ideas from topological insulators, under certain conditions, periodic structures may host localised waves that are symmetry protected, which makes them robust against disorder and defects. In this presentation I will discuss one of the milestone examples of such lattices  the Su-Schrieffer-Heeger (SSH) chain and also how it can be implemented in classical wave systems as well as the importance of boundary conditions. A relevant subject will also be discussed which is how to construct families of setups whose unit cell features neither mirror nor chiral symmetry, but share the same properties as the SSH chain.  

Finally note that, one of the hallmarks of topology and waves is to exhibit  perfect transmission (with no backscattering) in the presence of defects. Although this immunity to backscattering  is usually argued heuristically it has not been quantitatively understood. In this presentation, i will present recent results on how to obtain not only perfect transmission but also invisibility of topological edge waves by exploiting the combination of chiral and mirror symmetry. The underlying symmetries guarantee a unit transmission with a zero phase shift for scattering across symmetry preserving defects.