Birefringence & Retardation
Phase retardation from crystal birefringence, thickness, and wavelength.
Δn = ne − no, Γ = 2πΔn·d/λ
Full-wave wavelengths: |Δn(λ)|·d/λ = m (m = 1, 2, …): dark between crossed polarizers
Sellmeier fit: G. Ghosh, Opt. Commun. 163, 95 (1999), doi:10.1016/S0030-4018(99)00091-7; 198–2053 nm, room temperature.
Results
nₒ / nₑ1.54595 / 1.55511
Birefringence Δn = nₑ − nₒ0.00916
Crystal signpositive (optic axis slow)
Phase retardation Γ104.6410 rad
Retardation (waves)16.6541
Retardation (degrees)5995.49°
Order / fraction of a wave16 + 0.6541
Acts asno standard plate (not ¼, ½ or 1 wave)
Full-wave wavelengths in the chart range
29 wavelengths (nm):
301.6308.5315.9323.7332.1341.2351.0361.5372.9385.2398.7413.4429.5447.2466.8488.5512.7539.8570.5605.2645.1691.1744.7808.1883.9976.01090.31235.11424.2
Retardation against wavelength
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
Γ = 2πΔn·d/λ at normal incidence on a plate with its optic axis in the faces; Δn(λ) from published Sellmeier fits, or constant. Not modelled: tilt, temperature, reflections.
- Hecht E. (2002). Optics, 4th ed., §8.4 Birefringence and §8.7 Retarders. Addison-Wesley.
- 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
- 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