Detecting the polarization and spatial modes using vector vortex beams
We calculate the projection of the vector vortex beam onto either the polarization or spatial modes to detect the other mode. A vector vortex beam is one classical system that utilizes the concept of entanglement that has recently come to light. These beams are states of light where its polarization and spatial modes are described to be non-separable. In this study, we provide the calculations for the spatial mode projection and the polarization mode projection, highlighting the discernible non-separable feature of vector vortex beams. The projection of the vector vortex beam onto either the polarization or spatial mode results in the detection of the other mode, establishing a connection between the two modes, akin to entanglement. Utilizing this property of vector vortex beams finds applications in fields where the determination of chirality in certain media is vital, such as in spectroscopy or biophotonics. This study can be extended such that the vector vortex beam can be projected onto a chiral solution to determine the ratio of the chirality.