Birefringent Polarizer Design
Compare Glan-Taylor, Wollaston, Rochon and Sénarmont prism polarizers: exact beam deviations and the Glan field of view from crystal dispersion data.
Each face conserves the tangential wave vector; in a uniaxial crystal the wave takes the normal component its index surface allows.
Wollaston: n₁ sin α = n₂ sin β, sin ε = n₂ sin(β − α); split ≈ 2|Δn| tan α
Glan: the higher-index ray is totally reflected when kt ≥ 1 at the gap
Sellmeier fit: G. Ghosh, Opt. Commun. 163, 95 (1999), doi:10.1016/S0030-4018(99)00091-7; 204–2172 nm, room temperature.
Optic axes along x then y (both across the beam): the two polarizations leave on either side of the axis. Normal incidence on the entrance face; s is polarized along y (across the plane of the drawing), p in it.
no / ne
1.65836 / 1.48614
Δn = -0.17222
Exit angles in air
s: 3.622°
p: -3.569°
Angle between the beams
7.191°
first-order estimate 7.183° (-0.12 %)
Beam separation against the wedge angle
|Δn| of the listed crystals at 589 nm
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Normal incidence on two-wedge splitters: tangential wave vector kept at each face, e waves on the index ellipsoid; Glan field from total reflection at the gap. Not modelled: off-axis rays in splitters, losses.
- Born M., Wolf E. (1999). Principles of Optics, 7th ed., ch. 15 Optics of crystals, pp. 790–852. Cambridge University Press. doi:10.1017/CBO9781139644181.024
- Shurcliff W. A. (1962). Polarized Light: Production and Use, ch. 5 Birefringence polarizers, pp. 65–77. Harvard University Press. doi:10.4159/harvard.9780674424135.c6
- Archard J. F., Taylor A. M. (1948). Improved Glan-Foucault prism. J. Sci. Instrum. 25, 407–409: the Glan-Taylor design, optic axis in the plane of incidence. doi:10.1088/0950-7671/25/12/304
- Ghosh G. (1999). Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals. Opt. Commun. 163, 95–102. doi:10.1016/S0030-4018(99)00091-7
- Dodge M. J. (1984). Refractive properties of magnesium fluoride. Appl. Opt. 23, 1980–1985. doi:10.1364/AO.23.001980
- Malitson I. H., Dodge M. J. (1972). Refractive index and birefringence of synthetic sapphire. J. Opt. Soc. Am. 62, 1405 (abstract); formula in Dodge M. J. (1986), Handbook of Laser Science and Technology vol. IV, part 2, p. 30, CRC Press.
- Lomheim T. S., DeShazer L. G. (1978). Optical-absorption intensities of trivalent neodymium in the uniaxial crystal yttrium orthovanadate. J. Appl. Phys. 49, 5517–5522: YVO₄ dispersion formula. doi:10.1063/1.324471
- Zelmon D. E., Small D. L., Jundt D. (1997). Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol% magnesium oxide-doped lithium niobate. J. Opt. Soc. Am. B 14, 3319–3322. doi:10.1364/JOSAB.14.003319
- DeVore J. R. (1951). Refractive indices of rutile and sphalerite. J. Opt. Soc. Am. 41, 416–419. doi:10.1364/JOSA.41.000416