Single-shot measurement of the photonic band structure in a fiber-based Floquet-Bloch lattice

Corentin Lechevalier,Pierre Suret,Clément Evain,Stéphane Randoux,François Copie,Alberto Amo

doi:10.1038/s42005-021-00750-w

Abstract

Floquet-Bloch lattices are systems in which wave packets are subjet to periodic modulations both in time and space, showing rich dynamics. While this type of lattice is difficult to implement in solid-state physics, optical systems have provided excellent platforms to probe their physics: among other effects, they have revealed genuine phenomena such as the anomalous Floquet topological insulator and the funnelling of light into localised interface modes. Despite the crucial importance of the band dispersion in the photon dynamics and the topological properties of the lattice, the direct experimental measurement of the Floquet-Bloch bands has remained elusive. Here we report the direct measurement of the Floquet-Bloch bands of a photonic lattice with a single shot method. We use a system of two coupled fibre rings that implements a time-multiplexed Floquet-Bloch lattice. By Fourier transforming the impulse response of the lattice we obtain the band structure together with an accurate characterization of the lattice eigenmodes, i. e. the amplitudes and the phases of the Floquet-Bloch eigenvectors over the entire Brillouin zone. Our results open promising perspectives for the observation of topological effects in the linear and nonlinear regime in Floquet systems.

Highlights

Floquet-Bloch lattices are systems in which wave packets are subjet to periodic modulations both in time and space, showing rich dynamics
We report the experimental implementation of a method that allows the single-shot recording of the photonic band structure characterizing a Floquet–Bloch lattice realized with two coupled fiber loops
To the best of our knowledge, this idea has never been implemented in practice and the fact that the full eigenmode structure of the photonic mesh lattice can be determined from the measurement of its impulse response has not been considered before our work

Summary

Introduction

Floquet-Bloch lattices are systems in which wave packets are subjet to periodic modulations both in time and space, showing rich dynamics. Time-multiplexed photonic mesh lattices are often implemented by connecting two appropriately designed fiber loops with a directional 50/50 fiber coupler[23,24,25] In these systems, the phenomenon of discrete diffraction created at the fiber coupler results in the spreading of light wavepackets across the whole array as Floquet–Bloch waves[26,27]. Beyond the only measurement of the band structure, the direct measurement of the amplitude and phase of the Floquet–Bloch eigenvectors would open the possibility of extracting experimentally fundamental properties such as winding and Chern numbers, of great importance to characterize the topological properties of a lattice. To the best of our knowledge, this idea has never been implemented in practice and the fact that the full eigenmode structure of the photonic mesh lattice can be determined from the measurement of its impulse response has not been considered before our work

Methods

Results

Conclusion