Waveplate Thickness Calculator
Calculate required crystal thickness for waveplates of any retardance order.
d = (m + f)·λ / |ne − no|
f = fraction of a wave (¼ for a quarter-wave plate), m = order (0 for a zero-order plate), Δn at the design wavelength.
Sellmeier fit: G. Ghosh, Opt. Commun. 163, 95 (1999), doi:10.1016/S0030-4018(99)00091-7; 198–2053 nm, room temperature.
|Δn| at the design λ
0.00916
positive crystal: optic axis slow
Zero-order thickness
15.011 µm
Order-10 thickness
615.46 µm
10.25 waves
Compound zero order
615.46 − 600.45 µm
two plates, axes crossed; same retardance as the zero-order plate
Retardance against wavelength, folded to one wave (both plates designed at λ)
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
d = (m + f)λ/|Δn| for a plate with its optic axis in the faces at normal incidence; Δn(λ) from published Sellmeier fits. Compound plates: axes crossed, d₁ − d₂. Not modelled: tilt, temperature.
- Hecht E. (2002). Optics, 4th ed., §8.4 Birefringence and §8.7 Retarders. Addison-Wesley.
- 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