The Harper-Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

TL;DR

This paper presents a method to create tunable synthetic magnetic fields in photonic lattices using grating assisted tunneling, leading to observable conical diffraction patterns and realizing the Harper-Hofstadter Hamiltonian.

Contribution

It introduces a novel grating assisted tunneling scheme for synthetic magnetic fields in photonic lattices at optical frequencies, enabling experimental exploration of topological effects.

Findings

Observation of conical diffraction patterns indicating Dirac points

Implementation of the Harper-Hofstadter Hamiltonian in photonic lattices

Demonstration of tunable synthetic magnetic fields in optical frequencies

Abstract

We introduce a grating assisted tunneling scheme for tunable synthetic magnetic fields in photonic lattices, which can be implemented at optical frequencies in optically induced one- and two-dimensional dielectric photonic lattices. We demonstrate a conical diffraction pattern in particular realization of these lattices which possess Dirac points in $k$-space, as a signature of the synthetic magnetic fields. The two-dimensional photonic lattice with grating assisted tunneling constitutes the realization of the Harper-Hofstadter Hamiltonian.