# Polarized Photons In Classic Beam Splitter

Given two polarized photons whose quantum states are: $$|{\psi}_A\rangle = \alpha_A|{V}_A\rangle+\beta e^{i\theta_A}|{H}_A\rangle$$ $$|{\psi}_B \rangle= \alpha_B|{V}_B\rangle+\beta_B e^{i\theta_B}|{H}_B\rangle$$ How to describe their crossing through a classic beam splitter? I know how random polarized light crossing a classic beam splitter like the 50/50 will behave, it behaves like described here (https://galileo-unbound.blog/2022/05/08/the-many-worlds-of-the-quantum-beam-splitter/), but does polarized photons behave differently? How to describe this case?

• In general no ..... BUT the typical beam splitter works by reflection (ex. 50% from thin gold coating on glass) and reflection is highly dependent on angle of incidence as well as polarization .... so at higher angles we could expect to see some anomalies. May 17 at 2:13
• @PhysicsDave A typical cube beam splitter has a dielectric coating on one of the prisms before bonding into a cube. Some BSs reflect s-polarization and transmit p-polarization. Some split s-pol 50/50 and p-pol 50/50, but do not preserve polarization. Some split 50/50 and preserve polarization. Metal film beam splitters are uncommon, used in special situations. I've seen articles like the one you've found. I look for a description of the BS; it's never given. I assume the input pol is either s or p, then things may make sense. But the OP's question is a good one. May 17 at 2:37
• Here is the link to Thor labs page thorlabs.com/navigation.cfm?guide_id=18 Yes there are the plate types and the cube types and others ..... yes for all the interference types polarization can play a big role. May 17 at 13:54