Generalized Poincaré sphere

Abstract

We present a generalized Poincaré sphere (G sphere) and generalized Stokes parameters (G parameters), as a geometric representation, which unifies the descriptors of a variety of vector fields. Unlike the standard Poincaré sphere, the radial dimension in the G sphere is not used to describe the partially polarized field. The G sphere is constructed by extending the basic Jones vector bases to the general vector bases with the continuously changeable ellipticity (spin angular momentum, SAM) and the higher dimensional orbital angular momentum (OAM). The north and south poles of different spherical shells in the G sphere represent the pair of different orthogonal vector basis with different ellipticity (SAM) and the opposite OAM. The higher-order Poincaré spheres are just the two special spherical shells of the G sphere. We present a quite flexible scheme, which can generate all the vector fields described in the G sphere.

Geometric-phase-based shearing interferometry for broadband vortex state decoding

“…We choose δ = π/2 in this work and an arbitrary vector vortex state can be described by where and with and . Referencing the definition of the Stokes parameters of regular Poincaré sphere, the higher-order Stokes parameters are extended to with Re() and Im() representing the real and imaginary parts 29 . Here and to satisfy the normalized higher-order Stokes parameters , and .…”

Optical Singularity Built on Tiny Holes

“…Recently, the expressions of HPVB with φ 0 = π and PLVB with φ 0 = π and θ = π are also suggested to be unified by one superposition form of two vortex beams, and these two vortex beams have the forms of cos θ exp( jmφ )[exp(− jR π) e x + j exp( jR π) e y ] and sin θ exp(− jnφ )[exp(− jR π) e x exp( jR π) e y ]. [ 142 ] These works show us more possibility to definite and generate new singular beams. Though we have not found the related studies based on the metasurface consisting of nanoholes till now, we believe the new singular beams including PLVBs built on nanoholes will take on soon.…”

10 nm SiO2 TM Slot Mode in Laterally Mismatched Asymmetric Fin-Waveguides

“…One also expects some degree of diagonal polarization. The degree of linear, diagonal and circular polarization can be determined by calculating the Stokes parameters S 1 , S 2 and S 3 , respectively, for each polarization field profile [22,46]. The Stokes parameters at each x, y point can be calculated using the following equations: approach each other at the BZE, coupling and forming a degenerate mode when m = 0.5, and closing the PBG.…”