  Optical vortex and vector field are two important types of structured optical
fields. Due to their wide applications and unique features in many scientific
realms, the generation, manipulation and measurement of such fields have
attracted significant interest and become very important topics. However, most
ways to generate vector fields have a trade-off among flexibility, efficiency,
stability, and simplicity. Meanwhile, an easy and direct way to measure the
topological charges, especially for high order optical vortex, is still a
challenge. Here we design and manufacture a prism: polarization interferometric
prism (PIP) as a single-element interferometer, which can conveniently convert
an optical vortex to vector fields with high efficiency and be utilized to
precisely measure the topological charge (both absolute value and sign) of an
arbitrary optical vortex, even with a high order. Experimentally we generate a
variety of vector fields with global fidelity ranging from 0.963 to 0.993 and
measure the topological charge of an optical vortex by counting the number of
petals uniformly distributed over a ring on the output intensity patterns. As a
versatile tool to generate, manipulate and detect the spin-orbital state of
single photons, PIP can also work in single-photon regime for quantum
information processing. In experiment, the PIP is utilized as a spin-orbit
Controlled-Not gate on the generated 28 two-qubit states, achieving the state
fidelities ranging from 0.966 to 0.995 and demonstrating the feasibility of the
PIP for single photons.
