When does passing through a polarizer change phase besides just changing polarization?
Consider three cases:
A polarizing beam splitter (PBS) is a clear case. Horizontally polarized light leaves from one output and vertically polarized light leaves from the other output. As one beam is transmitted and the other beam reflected, they differ in phase because reflection introduced a phase shift.
A linear polarizer oriented horizontally: the horizontally polarized component is transmitted, while the vertical component is absorbed.
The same linear polarizer oriented vertically: the vertically polarized component is now transmitted, while the horizontal component is absorbed.
Would light transmitted in cases #2 (H) and #3 (V) be in phase or out of phase? And how can we measure it experimentally?
A related question: Can we say that light transmitted and light absorbed by a linear polarizer have the same phase? Or is this question meaningless because we don't have information about the absorbed part?