Spin–orbit coupling in photonic graphene

Zhaoyang Zhang,Yiming Li,Min Xiao,Yanpeng Zhang,Dmitry Solnyshkov,Shaohuan Ning,Guillaume Malpuech,Shun Liang,Feng Li

doi:10.1364/optica.390386

Abstract

Spin–orbit coupling of electromagnetic waves is one of the most important effects in topological photonics, but so far it has not been studied in photonic graphene implementations based on paraxial configuration, in particular, in atomic vapor cells. We generate experimentally a honeycomb refractive index pattern in such a cell using electromagnetically induced transparency. We demonstrate that an effective spin–orbit coupling appears as a correction to the paraxial beam equations because of the strong spatial gradients of the permittivity. It leads to the coupling of spin and angular momentum at the Dirac points of the graphene lattice. Our results suggest that the polarization degree of freedom plays an important role in many configurations where it has been previously neglected.

Highlights

Topological photonics [1, 2] is a rapidly growing field, combining fundamental physics and applied optics
We experimentally study photonic graphene in a configuration established by coherently-prepared multilevel atomic systems, where this spin-orbit coupling (SOC) plays a dominant role in the observations
We show that SOC couples the spin and angular momentum at the Dirac points, modifying the angular momentum of the probe beam depending on its polarization

Summary

INTRODUCTION

Topological photonics [1, 2] is a rapidly growing field, combining fundamental physics and applied optics. The evolution of a photonic beam in a spatially varying medium is a important fundamental and applied problem It is often described in the paraxial approximation of the Helmholtz equation [32], especially in the field of nonlinear optics, where it allows to determine the spatial mode profiles. The intrinsic coupling of polarizations is neglected in the paraxial approximation [33] Taking it into account in the calculations of the beam trajectory and properties often leads to spectacular effects, such as the spin Hall effect of light [3, 37, 38]. If the ray trajectory becomes three-dimensional (e.g. helix trajectory), the linear polarization starts to rotate This effect gives an important contribution to the depolarization of light beams in turbulent atmosphere [40, 41]. We show that SOC couples the spin and angular momentum at the Dirac points, modifying the angular momentum of the probe beam depending on its polarization

THE MODEL

EXPERIMENTAL IMPLEMENTATION OF PHOTONIC

RESULTS AND DISCUSSION

FUNDING INFORMATION