Poincaré Rotator for Vortexed Photons

Abstract

A Poincaré sphere is a powerful prescription to describe a polarized state of coherent photons, oscillating along certain directions. The polarized state is described by a vector in the sphere, and various passive optical components, such as polarization plates and quartz rotators are able to rotate the vectorial state by changing the phase and the amplitude among two orthogonal basis states. The polarization 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-Poincaré sphere. Here, we propose a compact Poincaré 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 evanescently coupled to two silicon photonic waveguides, which convert optical momentum to OAM with both left and right vortexed states. By controlling the relative phase and the amplitude of two traveling waves in input ports, we can control the vortexed states in the hyper-Poincaré 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.