(a) Representation in Poincare sphere of Spin-Orbit-Conversion (SOC) via q-plates. A state of circular polarization located in the poles of the Poincare sphere is mapped into its opposite state of circular polarization, while imprinting a fixed azimuthal phase ±2qϕ. (b) Representation in Poincare sphere of spin-orbit conversion (SOC) via J-plates. Arbitrary states of elliptic polarization |λ±〉 are mapped into its opposite state of elliptic polarization, while imprinting a tunable azimuthal phase (n, m)ϕ.