# Material Database

Descriptions of all materials available in built-in material database. This information is also accessible from refractive_index and material_explorer. Unless specified otherwise, all materials have $$\mu = 1.0$$. Each equation for the refractive index assumes that the wavelength $$\lambda$$ has units of $$\mu\mathrm{m}$$.

Air
$n = 1 + \frac{0.05792105}{238.0185 - \lambda^{-2}} + \frac{0.00167917}{57.362 - \lambda^{-2}}$

Wavelength range: 230 nm to 1690 nm

P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566 (1996).
AlGaAs
$\begin{split}\mathrm{Al}_x &\mathrm{Ga}_{1-x}\mathrm{As} \\\ \\ E_0 &= 3.65 + 0.871 x + 0.179 x^2 \\ E_\mathrm{d} &= 36.1 - 2.45 x \\ E_\Gamma &= 1.424 + 1.266 x + 0.26 x^2 \\ E_\mathrm{f} &= (2 E_0^2 - E_\Gamma^2)^{0.5} \\ \eta &= \pi E_\mathrm{d}/(2 E_0^3 (E_0^2 - E_\Gamma^2)) \\ M_1 &= \frac{\eta}{2 \pi} (E_\mathrm{f}^4 - E_\Gamma^4) \\ M_3 &= \frac{\eta}{\pi} (E_\mathrm{f}^2 - E_\Gamma^2) \\ E &= h c/ \lambda ,\\ &\mathrm{where}\:h\:\mathrm{is\:Planck's\:constant\:and}\:c\:\mathrm{is\:the\:speed\:of\:light\:in\:vacuum.} \\ \chi &= M_1 + M_3 E^2 + \frac{\eta}{\pi} E^4 \mathrm{ln}((E_\mathrm{f}^2 - E^2)/(2 E_\Gamma - E^2)) \\ n &= (\chi + 1)^{0.5} \\\end{split}$

Wavelength range: 689 nm to 1033 nm

M. A. Afromowitz, “Refractive index of Ga_{1-x}Al_{x}As,” Solid State Commun. 15, 59 (1974).
Notes: requires Al fraction input (x between 0 and 1), which defaults to x=0: “AlGaAs, x”.
Al2O3
$n = \left( 1 + \frac{1.4313493}{1 - (0.0726631/ \lambda)^2} + \frac{0.65054713}{1 - (0.1193242/ \lambda)^2} + \frac{5.3414021}{1 - (18.028251/ \lambda)^2} \right)^{0.5}$

Wavelength range: 200 nm to 5000 nm

(1) I. H. Malitson and M. J. Dodge, “Refractive Index and Birefringence of Synthetic Sapphire,” J. Opt. Soc. Am. 62, 1405 (1972).
(2) M. J. Dodge, “Refractive Index” in Handbook of Laser Science and Technology, Volume IV, Optical Materials: Part 2, CRC Press, Boca Raton, 1986, p. 30.
GaAs
$n = \left( 1 + 4.372514 + \frac{5.466742}{1 - (0.4431307/ \lambda)^2} + \frac{0.02429960}{1 - (0.8746453/ \lambda)^2} + \frac{1.957522}{1 - (36.9166/ \lambda)^2} \right)^{0.5}$

Wavelength range: 970 nm to 17000 nm

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys., 94, 6447 (2003).
Notes: 22 deg C
Ge
$n = \left( 1 + \frac{0.4886331}{1 - (1.393959/ \lambda)^2} + \frac{14.5142535}{1 - (0.1626427/ \lambda)^2} + \frac{0.0091224}{1 - (752.190/ \lambda)^2} \right)^{0.5}$

Wavelength range: 2000 nm to 14000 nm

J. H. Burnett, S. G. Kaplan, E. Stover, and A. Phenis, “Refractive index measurements of Ge,” Proc. SPIE 9974, 99740X (2016).
LN_MgO_z
$\begin{split}n_\mathrm{o} &= \left( 5.653 + \frac{0.1185}{\lambda^2 - 0.2091^2} + \frac{89.61}{\lambda^2 - 10.85^2} - 0.0197 \lambda^2 \right)^{0.5} \\ n_\mathrm{e} &= \left( 5.756 + \frac{0.0983}{\lambda^2 - 0.2020^2} + \frac{189.32}{\lambda^2 - 12.52**2} - 0.0132 \lambda^2 \right)^{0.5}\end{split}$

Wavelength range: 500 nm to 4000 nm

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys.B 91, 343 (2008).
Notes: z-cut congruent lithium niobate, 5 % MgO-doped. Temperature is 24.5 C. The n_e is the x-direction and n_o is the y- and z-direction.
LN_z
$\begin{split}n_\mathrm{o} &= \left( 1 + \frac{2.6734}{1 - (0.01764/ \lambda)^2} + \frac{1.2290}{1 - (0.05914/ \lambda)^2} + \frac{8.9543}{1 - (416.08/ \lambda)^2} \right)^{0.5} \\ n_\mathrm{e} &= \left( 1 + \frac{2.9804}{1 - (0.02047/ \lambda)^2} + \frac{0.5981}{1 - (0.0666/ \lambda)^2} + \frac{8.9543}{1 - (416.08/ \lambda)^2} \right)^{0.5}\end{split}$

Wavelength range: 400 nm to 5000 nm

D. E. Zelmon, D. L. Small, and D. Jundt, “Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol. % magnesium oxide-doped lithium niobate,” J. Opt. Soc. Am. B 14, 3319 (1997).
Notes: z-cut lithium niobate. The n_e is the x-direction and n_o is the y- and z-direction.
Si
$n = \left( 1 + \frac{10.6684293}{1 - (0.301516485/ \lambda)^2} + \frac{0.0030434748}{1 - (1.13475115/ \lambda)^2} + \frac{1.54133408}{1 - (1104/ \lambda)^2} \right)^{0.5}$

Wavelength range: 1357 nm to 11040 nm

B. Tatian, “Fitting refractive-index data with the Sellmeier dispersion formula,” Appl. Opt. 23, 4477 (1984).
Notes: 26 deg C
SiN
$n = \left( 1 + \frac{3.0249}{1 - (0.1353406/ \lambda)^2} + \frac{40314}{1 - (1239.842/ \lambda)^2} \right)^{0.5}$

Wavelength range: 310 nm to 5504 nm

K. Luke, Y. Okawachi, M. R. E. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si3N4 microresonator,” Opt. Lett. 40, 4823 (2015).
SiO2
$n = \left( 1 + \frac{0.6961663}{1 - (0.0684043/ \lambda)^2} + \frac{0.4079426}{1 - (0.1162414/ \lambda)^2} + \frac{0.8974794}{1 - (9.896161/ \lambda)^2} \right)^{0.5}$

Wavelength range: 210 nm to 6700 nm

(1) I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205 (1965).
(2) C. Z. Tan, “Determination of refractive index of silica glass for infrared wavelengths by IR spectroscopy,” J. Non-Cryst. Solids 223, 158 (1998).
Ta2O5
$n = \left(1 + \frac{0.033 \lambda^2}{\lambda^2 - 0.368^2} + \frac{3.212 \lambda^2}{\lambda^2 - 0.1639^2} + \frac{3.747 \lambda^2}{\lambda^2 - 14.5^2} \right)^{0.5}$

Wavelength range: 500 nm to 5000 nm

J. A. Black, R. Streater, K. F. Lamee, D. R. Carlson, Su-Peng Yu, and S. B. Papp, “Group-velocity-dispersion engineering of tantala integrated photonics,” Opt. Lett. 46, 817 (2021).
TiO2
$n = \left( 5.913 + \frac{0.2441}{1 - (0.0803/ \lambda)^2} \right)^{0.5}$

Wavelength range: 430 nm to 1530 nm

J. R. Devore, “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am. 41, 416 (1951).
Notes: crystalline n(o), thin films (sputtered, evaporated, or by atomic layer deposition) generally have a lower refractive index and it varies significantly depending on the exact deposition technique.