Luis Alberto Razo López

Date:  November 7th, 2022.  At 5:00 pm (Mexico time).

Título: Energy confinement in microwave aperiodic lattices and localization landscape in 2D discrete systems.

Abstract: 

This talk is divided into two different parts, each one presenting a different problem related with wave localization. In the first part, we study transport properties in 2D microwave lattices embedded in a quasi 2D cavity. A regular lattice, an aperiodic lattice (Vogel spiral), and a disordered lattice were constructed using a set of dielectric cylinders. Our experimental platform allows us to extract the decay of the energy in time, the density of states, the Thouless conductance as well as the spatial shape of the eigenstates. We found that frequency windows where the Thouless conductance is small contain eigenstates that look spatially confined inside the lattice then the radial behavior of those states is analyzed. Gaussian and exponential radial behaviors are experimentally found for the different localized states in Vogel spirals, while localized states in disordered systems always decay in a exponential way. In the second part, we show how the recent localization landscape (LL) theory can be extended to almost all known 2D lattices, and propose a systematic way of designing LL even for higher dimension. The localization landscape approach has brought many tools and theoretical results to understand such localization phenomena in the continuous setting, but with very few extensions so far to the discrete realm or to tight-binding Hamiltonians. We demonstrate in detail how this LL theory works and predicts accurately not only the location, but also the energies of localized eigenfunctions in the low and high energy regimes for the honeycomb and hexagonal lattices, making it a highly promising tool for investigating the role of disorder in these materials.