Glan Prism Polarizer Design
Design Glan-Taylor, Glan-Foucault and Glan-Thompson prism polarizers: the field of view from total internal reflection of the o and e rays, with crystal dispersion.
sin φ = kx (air) → o and e waves in the crystal; at the hypotenuse kt = kx cos θh + kz sin θh
total internal reflection when kt ≥ ngap; polarized: the higher-index wave reflected, the other transmitted
length/aperture L/A = tan θh
Sellmeier fit: G. Ghosh, Opt. Commun. 163, 95 (1999), doi:10.1016/S0030-4018(99)00091-7; 204–2172 nm, room temperature.
θhis the axial ray's angle of incidence on the hypotenuse (the angle between hypotenuse and entrance face). φ is the ray's angle in air from the entrance-face normal, in the plane of incidence of the hypotenuse; φ > 0 meets the hypotenuse more steeply. The optic axis is parallel to the entrance face.
no / ne
1.65836 / 1.48614
critical angles 37.09° (o), 42.29° (e, axial); passes the e ray
Polarizing window (external φ)
-2.35° … 5.61°
full width 7.95°
Symmetric half-field
±2.35°
lower edge: the reflected ray starts to leak through; upper: the passed ray starts to be totally reflected
Length / aperture
0.795
per prism pair, L/A = tan θh
Tangential wave vector at the hypotenuse against φ
Window edges against wavelength (this θh)
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
Plane waves in the hypotenuse's plane of incidence; tangential wave vector kept, total reflection when k_t ≥ n_gap; Sellmeier indices. Not modelled: out-of-plane rays, gap interference, 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
- Born M., Wolf E. (1999). Principles of Optics, 7th ed., §1.5.4 Total reflection (Fresnel rhomb). Cambridge University Press. doi:10.1017/CBO9781139644181.010
- 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
- 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
- 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