# 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
$n = \left(1 + \frac{5.79211 \times 10^{-2}}{238.019 - \lambda^{-2}} + \frac{1.67917 \times 10^{-3}}{57.3620 - \lambda^{-2}}\right)$

Wavelength range: 200 nm to 2000 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”.
AlN
$n = \left(1 + \frac{2.80729}{1 - \left(0.147012/\lambda\right)^2} + \frac{0.231236}{1 - \left(1.58561 \times 10^{-4}/\lambda\right)^2} + \frac{1.56250 \times 10^{-2}}{1 - \left(1139.06/\lambda\right)^2}\right)^{0.5}$

Wavelength range: 210 nm to 1690 nm

(1) L. Y. Beliaev, E. Shkondin, A. V. Lavrinenko, and O. Takayama, “Thickness-dependent optical properties of aluminum nitride films for mid-infrared wavelengths,” J. Vac. Sci. Technol. A 39, 043408 (2021).
(2) L. Y. Beliaev, E. Shkondin, A. V. Lavrinenko, and O. Takayama, “Erratum: Thickness-dependent optical properties of aluminum nitride films for mid-infrared wavelengths,” J. Vac. Sci. Technol. A 40, 027001 (2022).
Al2O3
$n = \left( 1 + \frac{1.43135}{1 - (7.26631 \times 10^{-2}/ \lambda)^2} + \frac{0.650547}{1 - (0.119324/ \lambda)^2} + \frac{5.34140}{1 - (18.0283/ \lambda)^2} \right)^{0.5}$

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.
BBO
$\begin{split}n_\mathrm{o} &= \left( 1 + \frac{0.90291}{1 - 3.926 \times 10^{-3} / \lambda^2} + \frac{0.83155}{1 - 1.8786 \times 10^{-2}/ \lambda^2} + \frac{0.76536}{1 - 60.01/ \lambda^2} \right)^{0.5} \\ n_\mathrm{e} &= \left( 1 + \frac{1.151075}{1 - 7.142 \times 10^{-3} / \lambda^2} + \frac{0.21803}{1 - 2.259 \times 10^{-2}/ \lambda^2} + \frac{0.656}{1 - 263/ \lambda^2} \right)^{0.5}\end{split}$

Wavelength range: 188 nm to 6220 nm

(1) G. Tamošauskas, G. Beresnevičius, D. Gadonas, and A. Dubietis, “Transmittance and phase matching of BBO crystal in the 3−5 μm range and its application for the characterization of mid-infrared laser pulses,” Opt. Mater. Express 8, 1410 (2018).
(2) G. Tamošauskas, “β-barium borate (BBO) absorption in the 0.188-6.22 μm range,” arXiv:2111.01212 [physics.optics] (2021).
Notes: The n_e is the y-direction and n_o is the x- and z-direction.
GaAs
$n = \left( 1 + 4.37251 + \frac{5.46674}{1 - (0.443131/ \lambda)^2} + \frac{2.42996 \times 10^{-2}}{1 - (0.874645/ \lambda)^2} + \frac{1.95752}{1 - (36.9166/ \lambda)^2} \right)^{0.5}$

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
GaP

See citation for refractive index equation.

Wavelength range: 207 nm to 12400 nm

S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlxGa1−xAs, and In1−xGaxAsyP1−y,” J. Appl. Phys. 66, 6030 (1989).
GaSb

See citation for refractive index equation.

Wavelength range: 207 nm to 12400 nm

A. B. Djurišić, E. H. Li, D. Rakić, and M. L. Majewski, “Modeling the optical properties of AlSb, GaSb, and InSb,” Appl Phys A 70, 29 (2000).
Ge
$n = \left( 1 + \frac{0.488633}{1 - (1.39396/ \lambda)^2} + \frac{14.5143}{1 - (0.162643/ \lambda)^2} + \frac{9.12240 \times 10^{-3}}{1 - (752.190/ \lambda)^2} \right)^{0.5}$

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).
GGG
$n = \left( 1 + \frac{1.7727\lambda^2}{\lambda^2 - 0.1567^2} + \frac{0.9767\lambda^2}{\lambda^2 - 0.01375^2} + \frac{4.9668\lambda^2}{\lambda^2 - 22.715^2} \right)^{0.5}$

Wavelength range: 360 nm to 6000 nm

D. L. Wood and K. Nassau, “Optical properties of gadolinium gallium garnet,” Appl. Opt. 29, 3704 (1990).
H2O
$n = \left(1 + \frac{0.760520}{1 - \left(8.59042 \times 10^{-2}/\lambda\right)^2} + \frac{3.99325 \times 10^{-2}}{1 - \left(2.83879/\lambda\right)^2} + \frac{1.56214 \times 10^{-2}}{1 - \left(2.83887/\lambda\right)^2}\right)^{0.5}$

Wavelength range: 200 nm to 2400 nm

G. M. Hale and M. R. Querry, “Optical constants of water in the 200-nm to 200-µm wavelength region,” Appl. Opt. 12, 555 (1973).
HfO2
$n = \left(1.875 + \frac{6.28 \times 10^{-3}}{ \lambda^{2}} + \frac{5.80 \times 10^{-4}}{ \lambda^{4}}\right)$

Wavelength range: 200 nm to 2000 nm

M. F. Al-Kuhaili, “Optical properties of hafnium oxide thin films and their application in energy-efficient windows,” Opt. Mat. 27, 383 (2004).
InAs

See citation for refractive index equation.

Wavelength range: 207 nm to 12400 nm

S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlxGa1−xAs, and In1−xGaxAsyP1−y,” J. Appl. Phys. 66, 6030 (1989).
InGaAs
$\begin{split}&\mathrm{In}_x\mathrm{Ga}_{1-x}\mathrm{As} \\\ \\ &E_\mathrm{g,GaAs} = 1.424 \\ &E_\mathrm{g,InGaAs} = E_\mathrm{g,GaAs} - 1.501 x + 0.436 x^2 \\\ \\ &n = \left( 1 + 4.37251 + \frac{5.46674}{1 - \left( \frac{E_\mathrm{g,GaAs}}{E_\mathrm{g,InGaAs}}\frac{0.443131}{\lambda} \right)^2} + \frac{0.0242996}{1 - \left( \frac{E_\mathrm{g,GaAs}}{E_\mathrm{g,InGaAs}}\frac{0.874645}{\lambda} \right)^2} + \frac{1.95752}{1 - \left( \frac{36.9166}{\lambda} \right)^2} \right)^{0.5} \\\end{split}$

Wavelength range: 970 nm to 17000 nm

Index calculated by shifting the bandgap relative to the refractive index of GaAs. The bandgap of InGaAs is reference from:
R. E. Nahory, M. A. Pollack, W. D. Johnston Jr., R. L. Barns, “Band gap versus composition and demonstration of Vegard’s law for In1−xGaxAsyP1−y lattice matched to InP,” Appl. Phys. Lett. 33, 659 (1978).
Notes: requires In fraction input (x between 0 and 1), which defaults to x=0: “InGaAs, x”.
InGaP
$n = \left(6.74340 + \frac{2.61641}{1 - \left(0.498744/\lambda\right)^2} + \frac{6.07490 \times 10^{-3}}{1 - \left(0.685707/\lambda\right)^2} + \frac{0.489381}{1 - \left(224.998/\lambda\right)^2}\right)^{0.5}$

Wavelength range: 700 nm to 1550 nm

M. Schubert, V. Gottschalch, C. M. Herzinger, H. Yao, P. G. Snyder, and J. A. Woollam, “Optical constants of GaxIn1−xP lattice matched to GaAs,” J. Appl. Phys. 77, 3416 (1995)
InP
$n = \left(1 + 6.255 + \frac{2.316}{{1 - \left(0.6263/\lambda\right)^2}} + \frac{2.765}{{1 - \left(32.935/\lambda\right)^2}}\right)^{0.5}$

Wavelength range: 950 nm to 10000 nm

G. D. Pettit and W. J. Turner, “Refractive Index of InP,” J. Appl. Phys. 36, 2081 (1965).
InSb

See citation for refractive index equation.

Wavelength range: 207 nm to 12400 nm

S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlxGa1−xAs, and In1−xGaxAsyP1−y,” J. Appl. Phys. 66, 6030 (1989).
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.
PMMA_495
$n = \left(1.491 + \frac{3.427 \times 10^{-3}}{\lambda^{2}} + \frac{1.819 \times 10^{-4}}{\lambda^{4}}\right)$

Wavelength range: 200 nm to 1100 nm

PMMA_950
$n = \left(1.488 + \frac{2.898 \times 10^{-3}}{\lambda^{2}} + \frac{1.579 \times 10^{-4}}{\lambda^{4}}\right)$

Wavelength range: 200 nm to 1100 nm

Si
$n = \left( 1 + \frac{10.6684}{1 - (0.301516/ \lambda)^2} + \frac{3.04347 \times 10^{-3}}{1 - (1.13475/ \lambda)^2} + \frac{1.54133}{1 - (1104/ \lambda)^2} \right)^{0.5}$

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
$n = \left( 1 + \frac{3.0249}{1 - (0.135341/ \lambda)^2} + \frac{40314}{1 - (1239.84/ \lambda)^2} \right)^{0.5}$

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
$n = \left( 1 + \frac{0.696166}{1 - (6.84043 \times 10^{-2}/ \lambda)^2} + \frac{0.407943}{1 - (0.116241/ \lambda)^2} + \frac{0.897479}{1 - (9.89616/ \lambda)^2} \right)^{0.5}$

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).
SU8_2000
$n = \left(1.566 + \frac{7.96 \times 10^{-3}}{\lambda^{2}} + \frac{1.4 \times 10^{-4}}{\lambda^{4}}\right)$

Wavelength range: 200 nm to 1100 nm

SU8_3000
$n = \left(1.5525 + \frac{6.29 \times 10^{-3}}{\lambda^{2}} + \frac{4.0 \times 10^{-4}}{\lambda^{4}}\right)$

Wavelength range: 320 nm to 1700 nm

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.
TiO2_rutile
$\begin{split}n_\mathrm{o} &= \left(3.2089 + \frac{3.4000 \times 10^{-5}}{1.2270 \times 10^{-5} - \lambda^{-2}} - 3.2545\times 10^{-8}\lambda^2 \right)^{0.5} \\ n_\mathrm{e} &= \left(2.9713 + \frac{5.1891 \times 10^{-5}}{1.2280 \times 10^{-5} - \lambda^{-2}} - 4.2950 \times 10^{-8}\lambda^2 \right)^{0.5}\end{split}$

Wavelength range: 612 nm to 4449 nm

A. Borne, P. Segonds, B. Boulanger, C. Félix, and J. Debray, “Refractive indices, phase-matching directions and third order nonlinear coefficients of rutile TiO2 from third harmonic generation,” Opt. Mater. Express 2, 1797 (2012).
Notes: The n_e is the y-direction and n_o is the x- and z-direction. Equation takes wavelength in nanometers.