Polarizing beam splitter

A polarizing beam splitter sends two orthogonal linear polarizations to different output paths. Acting coherently on $\alpha |H⟩+\beta |V⟩$, it correlates path with photon polarization instead of measuring photon polarization unless a path is actually detected or discarded.

For an ideal polarizing beam splitter with one input, choose orthogonal unit electromagnetic polarization vectors ${\mathbf{e}}_H,{\mathbf{e}}_V$ and an incident power-normalized field $a_H{\mathbf{e}}_H+a_V{\mathbf{e}}_V$. If $H$ is transmitted and $V$ reflected, the output powers are $P_{\mathrm{transmitted}}=|a_H{|}^2$ and $P_{\mathrm{reflected}}=|a_V{|}^2$. The associated complex amplitudes can acquire different wave phases; the routing is not an equal-power split for every incident electromagnetic polarization. For linear polarization at angle $\theta$ to $H$, input power $P$ gives $P{\cos }^2\theta$ and $P{\sin }^2\theta$, respectively. At $\theta =30^{\circ }$, a stipulated $4\mathrm{mW}$ input gives $3\mathrm{mW}$ transmitted and $1\mathrm{mW}$ reflected. A $45^{\circ }$ input gives equal powers even though an $H$ input goes entirely into the transmitted output.^[ref]

Real polarizing beam splitters have leakage into the unwanted output and losses. Each linear polarization has its own field transformation and power coefficients. To make an ordinary power wave interference term between the two output contributions, first bring them into the same path with overlapping transverse profiles and a common electromagnetic polarization, for example using a polarizer. Merely placing two orthogonal linear polarizations on a polarization-insensitive photodetector adds their powers. Coherent routing can be reversed by suitable optics before detection; discarding a path loses access to that part of the field but supplies no recorded measurement outcome by itself.

// Target: optics.bigb