How are polarized waves of light studied?
The same way as any other electromagnetic radiation - appropriate detectors and/or energy sensors.
Light is just one part of the entire electromagnetic spectrum of energy. Any part of it is studied by detecting and measuring them with instruments that are built to respond to their particular energy.
"Polarized" just means that its vibrations or oscillations are restricted to a particular direction or plane instead of freely moving about. Electromagnetic radiation is often intentionally polarized for particular investigations. The polarization of light itself is studied with various filters that can identify the particular direction of polarization.