Optical constants

Refractive index of Al₂O₃ (Aluminium sesquioxide, Sapphire, Alumina)

Hagemann et al. 1974: n,k 0.000775–0.207 µm

Data: tabulated nk
Range: 0.0007749–0.2066 µm
Points: 100
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 0.96937
Extinction coefficient k: 0.0345074

Permittivity ε₁: 0.938488
Permittivity ε₂: 0.0669009

Absorption coefficient α: 341443 cm⁻¹
Penetration depth δ = λ/(2πk): 58.5749 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: 7.40741 µm⁻¹

Group index n_g: 0.875296
Group velocity dispersion: — fs²/mm

Dispersion parameter D: — ps/(nm·km)
Photon energy: 97.6254 eV

ε = (n + ik)², α = 4πk/λ, n_g = n − λ dn/dλ, GVD = λ³/(2πc²) d²n/dλ², D = −(λ/c) d²n/dλ². Group-velocity dispersion is given for formula data only.

Use it in Lightsmith

Load this data in Python, simulate in one more line

pip install lightsmith

import lightsmith as ls

# Al2O3 (Aluminium sesquioxide, Sapphire, Alumina): Hagemann et al. 1974: n,k 0.000775–0.207 µm
al2o3 = ls.fetch_refractiveindex("main", "Al2O3", "Hagemann", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(al2o3.range_nm)  # (0.7749, 206.6) nm
eps = al2o3.eps([12.7])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

import json, urllib.request
import lightsmith as ls

url = "https://materials.lightsmith.dev/v1/datasets/ds_db79fbbe66b5/lightsmith"
al2o3 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(al2o3.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (al2o3/hagemann-1974).

# ... load al2o3 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=al2o3)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=1, stop_nm=206, num=81),
)
res = ls.solve(sim)  # exact Mie for a sphere
print(res.q_ext)     # extinction efficiency at each wavelength

Same spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).

Materials guide Open a sphere of it in Studio Quick start Ask the community

Lightsmith is open source (MIT): Mie, T-matrix, BEM, DDA, FDTD, RCWA, TMM, mode solvers and inverse design behind one spec, on CPU or GPU. GitHub.

References

1) H.-J. Hagemann, W. Gudat, C. Kunz. Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al₂O₃. J. Opt. Soc. Am. 65, 742-744 (1975)
2) H.-J. Hagemann, W. Gudat, C. Kunz. DESY report SR-74/7 (1974)

doi:10.1364/josa.65.000742 Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al_2O_3, Journal of the Optical Society of America (1975)

Cite

H.-J. Hagemann, W. Gudat and C. Kunz. Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al_2O_3. Journal of the Optical Society of America, 65, 742 (1975), doi:10.1364/josa.65.000742; H.-J. Hagemann, W. Gudat, C. Kunz. DESY report SR-74/7 (1974); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

100 rows as published

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

Al2O3 (Aluminium sesquioxide, Sapphire, Alumina), Hagemann et al. 1974: n,k 0.000775–0.207 µm: n and k versus wavelength
λ (µm)	n	k
0.0007749	1.0	9.14e-05
0.0007999	1.0	2.97e-05
0.0008266	1.0	3.4e-05
0.0008856	1.0	4.5e-05
0.001033	1.0	8.1e-05
0.00124	0.999	0.000161
0.00155	0.999	0.000349
0.002066	0.999	0.000977
0.002254	0.999	0.000809
0.00248	0.998	0.000402
0.0031	0.997	0.000729
0.003542	0.995	0.00124
0.004133	0.994	0.00181
0.004959	0.991	0.00326
0.006199	0.987	0.00533
0.006888	0.985	0.00709
0.007749	0.982	0.00977
0.008266	0.98	0.0113
0.008856	0.978	0.0133
0.008984	0.978	0.0135
0.009116	0.977	0.0139
0.009253	0.976	0.0143
0.009537	0.975	0.0156
0.00984	0.974	0.0171
0.009999	0.974	0.0181
0.01016	0.973	0.0183
0.01033	0.973	0.0185
0.01078	0.97	0.0204
0.01127	0.968	0.0233
0.01181	0.966	0.0275
0.0124	0.966	0.0332
0.01265	0.969	0.0346
0.01292	0.971	0.0341
0.01319	0.972	0.0314
0.01348	0.97	0.0291
0.01362	0.968	0.0284
0.01378	0.966	0.0286
0.01393	0.964	0.0295
0.01409	0.963	0.0307
0.01425	0.962	0.032
0.01442	0.962	0.033
0.01459	0.961	0.0337
0.01476	0.96	0.0343
0.01494	0.959	0.035
0.01512	0.957	0.0365
0.01531	0.956	0.0404
0.0154	0.958	0.0431
0.0155	0.961	0.0445
0.0156	0.965	0.043
0.01569	0.966	0.0398
0.01579	0.965	0.0372
0.0159	0.963	0.0363
0.016	0.963	0.0392
0.0161	0.967	0.0372
0.01621	0.966	0.0305
0.01631	0.961	0.0298
0.01642	0.958	0.0302
0.01653	0.957	0.0306
0.01664	0.955	0.0311
0.01675	0.953	0.0317
0.01698	0.951	0.0329
0.01722	0.948	0.0341
0.01771	0.944	0.0365
0.01907	0.933	0.0438
0.02066	0.92	0.0541
0.02254	0.907	0.0686
0.0248	0.892	0.0864
0.02755	0.872	0.111
0.031	0.848	0.148
0.03542	0.823	0.203
0.04133	0.794	0.282
0.04428	0.774	0.327
0.04769	0.748	0.393
0.05166	0.722	0.502
0.05636	0.765	0.651
0.05904	0.812	0.723
0.06048	0.841	0.747
0.06199	0.862	0.769
0.06358	0.88	0.794
0.06525	0.896	0.825
0.06888	0.947	0.912
0.07293	1.035	0.997
0.07749	1.148	1.07
0.08266	1.293	1.14
0.08551	1.379	1.16
0.08856	1.471	1.16
0.09184	1.555	1.17
0.09537	1.649	1.17
0.09919	1.753	1.17
0.1033	1.868	1.17
0.1078	2.017	1.16
0.1127	2.218	1.11
0.1181	2.484	0.951
0.124	2.582	0.597
0.1305	2.524	0.253
0.1378	2.297	0.0895
0.1459	2.153	0.0478
0.155	2.058	0.028
0.1771	1.924	0.00824
0.2066	1.774	0.0022

Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

Al₂O₃ (Aluminium sesquioxide, Sapphire, Alumina): all datasets

Crystal

Thin film

About Al2O3 (Aluminium sesquioxide, Sapphire, Alumina)

Al₂O₃, commonly known as alumina or aluminum oxide, is a ceramic material that has a wide range of applications due to its excellent mechanical and optical properties. This compound crystallizes in various phases, the most stable and common of which is the corundum structure. Alumina is transparent in the ultraviolet to the infrared range, making it a versatile material for a variety of optical applications such as protective windows and lenses. It has a high refractive index and is also known for its strong dielectric properties. One of the key attributes of Al₂O₃ is its remarkable thermal stability and resistance to chemical attack, which makes it suitable for harsh environment applications. Furthermore, the material has been investigated for its nonlinear optical characteristics, although it is generally less efficient in this regard compared to other nonlinear optical materials. Alumina can also serve as a substrate material for thin-film optical coatings. In summary, Al₂O₃ is a robust and multifunctional material that is extensively studied for its enduring relevance in both traditional and advanced optical systems. Mineral: Corundum Gemstones: Sapphire, Ruby

More about Al2O3 (Aluminium sesquioxide, Sapphire, Alumina) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Al2O3/nk/Hagemann.yml
ID: ds_db79fbbe66b5
API: /v1/datasets/ds_db79fbbe66b5

Plot