= Polarizing beam splitter
= Polarising beam splitter
{synonym}
A <polarizing beam splitter> sends two orthogonal <linear polarizations> to different output paths. Acting coherently on $\alpha|H\rangle+\beta|V\rangle$, 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 $P_{\rm transmitted}=|a_H|^2$ and $P_{\rm reflected}=|a_V|^2$. 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.<Photon quantum mechanics and beam splitters by Charles H. Holbrow and others>[Photon quantum mechanics and beam splitters, §IV.D, printed p. 264, figure 5: polarization routed into different detected paths]{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
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