AUTHOR=Saito Shinichi 

TITLE=Poincaré Rotator for Vortexed Photons

JOURNAL=Frontiers in Physics

VOLUME=Volume 9 - 2021

YEAR=2021

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.646228

DOI=10.3389/fphy.2021.646228

ISSN=2296-424X

ABSTRACT=A Poincar\'{e} sphere is a powerful prescription to describe a polarised state of coherent photons, oscillating along certain directions. The polarised state is described by a vector in the sphere, and various passive optical componets such as polarisation plates and quartz rotators are able to rotate the vectorial state by changing the phase and the amplitude among two orthogonal basis states.
The polarisation is originated from spin of photons, and recently, significant attentions have been made for optical Orbital Angular Momentum  (OAM) as another fundamental degree of freedom for photons. The beam shape of photons with OAM is a vortex with a topological charge at the core, and the state of vortexed photons can be described by a hyper-Poincar\'{e} sphere. Here, we propose a compact Poincar\'{e} rotator, which controls a vortexed state of photons in a silicon photonic platform, based on Finite-Difference Time-Domain (FDTD) simulations. A ring-shaped gear is evanecentlly coupled to two silicon photonic waveguides, wihch converts optical momentum to OAM with both left and right vortexed states. By controlling the relative phase and the amplitude of two travelling waves in input ports, we can control the vortexed states in the hyper-Poincar\'{e} sphere for photons out of the gear. The impact of the geometrical Pancharatnam-Berry-Guoy's phase and the conservation law of spin and OAM for vortexed photons out of the gear are discussed.