Wollaston prism
= Wollaston prism
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A <Wollaston prism>, named for <William Hyde Wollaston>, is a <polarizing beam splitter> formed from two <birefringent> <optical prisms> with crossed crystal-axis orientations. The two <linear polarization> components encounter different effective <refractive indices> and leave in different directions. Both output beams are retained, with orthogonal <linear polarizations>. A manufacturer describes approximately equal and opposite deviations and explicitly defines its splitting angle as the full angle between the emerging beams.<Wollaston Polarizers by B. Halle Nachfl. GmbH>[Opening technical description and full-angle convention]{ref}
<Calcite> and <quartz> implementations illustrate why material matters. The manufacturer uses cemented <calcite> elements and optically contacted <quartz> elements; its <quartz> designs provide smaller splitting angles because the <birefringence> is smaller. A prism's material, wavelength and cut therefore belong with a stated angular separation, rather than treating that separation as a universal property of the name.<Wollaston Polarizers by B. Halle Nachfl. GmbH>[Opening material discussion and General specifications]{ref}
The ideal intensity division follows projection onto the prism's polarization axes. For incident <linear polarization> at angle $\theta$ to one axis and total <optical power> $P$, a lossless model gives
$$
P_1=P\cos^2\theta,\qquad P_2=P\sin^2\theta.
$$
For an original2milliwatt beam at $\theta=30^\circ$, the outputs carry1.5and0.5milliwatts. Equal powers occur at45degrees; they are not guaranteed for every input. Unpolarized <light> gives equal average powers in this ideal model. Real transmission loss and unequal detector responses require separate characterization.
For an original geometric example, suppose a particular prism produces a symmetric full separation $\Delta=1^\circ$. At distance $L=0.50\,\mathrm m$ from a common effective exit point, the separation of beam centres is
$$
s=2L\tan(\Delta/2)\approx8.73\,\mathrm{mm}.
$$
Using $\tan\Delta$ for each beam would mistakenly treat the full splitting angle as a one-sided deviation. Finite beam diameters and any exit-face displacement also affect detector placement.
A bench demonstration rotates a <polarizer> before the <Wollaston prism> while recording both output powers. Their complementary variation tests the polarization decomposition. An analyzing <polarizer> after each exit can check the two output directions independently. Unlike the virtual copies produced by an <optical biprism>, orthogonally polarized beams have no mutual intensity cross term on a polarization-insensitive screen. Projecting coherent beams onto a common polarization can permit interference after suitable spatial overlap; changing direction alone does not supply that projection.