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.

Quantum field theory for coherent photons: isomorphism between Stokes parameters and spin expectation values

“…As applications of our formalism, we consider several typical optical components to control the polarisation states [1,2,5,[20][21][22]28,[45][46][47][64][65][66][67][68][69][70][71][72]. Practically, this is nothing new compared with well-established Jones matrix formulation, but the purpose of this consideration is to establish a fundamental basis to justify the calculation of polarisation states using Jones matrices based on a many-body quantum physics and an SU(2) group theory.…”

Symmetry and Quantum Features in Optical Vortices

“…Although beyond the scope of the present analysis, it will be interesting to develop and further explore counterpart principles for vector-vortex modes whose polarization varies within the beam cross-section [147][148][149]-including Poincaré states whose profiles may include a distribution of polarizations spanning the whole surface in a Poincaré sphere representation [105,[150][151][152]. The generation and properties of such modes commonly involve an intricate interplay of OAM and polarization features [153,154]; for such modes, further aspects of symmetry arise, such as the Poincaré-Hopf indices for interference singularities producing a distribution of intensity nulls [155]. However, the fully-fledged quantum field theory for the nanoscale light-matter interactions of such beams has yet to be developed; that level of analysis represents the next edge of ongoing research.…”

SU(2) symmetry of coherent photons and application to Poincaré rotator

“…A Poincaré rotator is also useful to control the orbital angular momentum of photons [54]. The left and right vortexed states are orthogonal each other, such that they form SU(2) states [54][55][56][57][58][59][60][61][62][63].…”

“…A Poincaré rotator is also useful to control the orbital angular momentum of photons [54]. The left and right vortexed states are orthogonal each other, such that they form SU(2) states [54][55][56][57][58][59][60][61][62][63]. A superposition states with these vortices can be controlled by a Poincaré rotator by adjusting the phase and amplitudes [54].…”