PhD Defense of Mr. Rabih EL SOKHEN

EL SOKHEN Rabih, PhLAM Laboratory - UMR8523 - Team DYSCO

Title: Two-dimensional topological properties of photonic mesh lattices subject to discrete step walks

Jury: A. AMO GARCIA (PhLAM, supervisor), S. RANDOUX (PhLAM, supervisor), V. COUDERC (Université de Limoges, XLIM, Referee), T. OZAWA (University of Tohoku, Referee), G. Lévêque (Université de Lille, member)

Abstract:

This thesis presents experimental and numerical investigations into bulk and edge invariants within a 2D synthetic photonic lattice subjected to discrete step walks. The lattice is engineered by time-multiplexing light pulses in two unequal length optical fiber rings coupled with a variable beam splitter (VBS). In this configuration, one dimension exhibits real-space dynamics, while the other is governed an external phase modulator (PM). Employing heterodyne detection, we access spectral information and measure eigenvalues and eigenvectors, enabling the extraction of bulk invariants, such as the Chern number, from the Berry curvature associated with the photonic bands. Furthermore, we derive an expression for the winding number and demonstrate that the emergence of edge states is tied to specific geometric boundaries. Finally, we highlight the   of edge topology on the overall system topology, which can either suppress or induce the presence of edge states.