Optical constants

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

Malitson and Dodge 1972: α-Al2O3 (Sapphire); n(e) 0.20–5.0 µm

Data: formula 1
Range: 0.2–5 µm
Temperature: 293 K
Optical axis: e
State: crystalline
Licence: CC0-1.0

Uniaxial crystal, axes: oe

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.76009
Extinction coefficient k: 0

Permittivity ε₁: 3.09793
Permittivity ε₂: 0

Absorption coefficient α: 0 cm⁻¹
Penetration depth δ = λ/(2πk): — nm

Abbe number V_d: 72.988
Chromatic dispersion dn/dλ: -0.054217 µm⁻¹

Group index n_g: 1.79195
Group velocity dispersion: 89.1223 fs²/mm

Dispersion parameter D: -486.21 ps/(nm·km)
Photon energy: 2.11001 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): Malitson and Dodge 1972: α-Al2O3 (Sapphire); n(e) 0.20–5.0 µm
al2o3 = ls.fetch_refractiveindex("main", "Al2O3", "Malitson-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(al2o3.range_nm)  # (200, 5000) nm
eps = al2o3.eps([633])  # 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_4e92800c3cf8/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/malitson-dodge-1972-e).

# ... 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=400, stop_nm=1000, 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"]).

import json, urllib.request
import lightsmith as ls

url = "https://materials.lightsmith.dev/v1/datasets/ds_4e92800c3cf8/lightsmith?model=drude_lorentz"
al2o3_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))

A dispersive Drude–Lorentz model for time-domain solvers.

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.

Dispersion formula

Sellmeier (formula 1), λ in µm

n^{2} - 1 = \frac{1.5039759 λ^{2}}{λ^{2} - {0.0740288}^{2}} + \frac{0.55069141 λ^{2}}{λ^{2} - {0.1216529}^{2}} + \frac{6.5927379 λ^{2}}{λ^{2} - {20.072248}^{2}}

Valid from 0.2 to 5.0 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	1.5039759
C3	0.0740288
C4	0.55069141
C5	0.1216529
C6	6.5927379
C7	20.072248

Comments and conditions

Synthetic sapphire, Extraordinary ray (e), 20 °C

Conditions

temperature: 293 K
direction: e

References

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
* Ref. 1 is a talk abstract in a conference program; Ref. 2 provides a dispersion formula

Cite

I. H. Malitson and M. J. Dodge. Refractive index and birefringence of synthetic sapphire. J. Opt. Soc. Am. 62, 1405 (1972); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 400 wavelengths, the same grid as the API and the library

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

Al2O3 (Aluminium sesquioxide, Sapphire, Alumina), Malitson and Dodge 1972: α-Al2O3 (Sapphire); n(e) 0.20–5.0 µm: n and k versus wavelength
λ (µm)	n
0.2	1.901626
0.20162	1.898319
0.203253	1.895103
0.204899	1.891976
0.206559	1.888933
0.208232	1.885972
0.209919	1.883089
0.211619	1.880282
0.213333	1.877548
0.215061	1.874884
0.216803	1.872288
0.21856	1.869757
0.22033	1.86729
0.222115	1.864884
0.223914	1.862536
0.225727	1.860246
0.227556	1.858011
0.229399	1.85583
0.231257	1.8537
0.23313	1.851621
0.235019	1.84959
0.236922	1.847606
0.238841	1.845668
0.240776	1.843775
0.242726	1.841924
0.244692	1.840115
0.246674	1.838347
0.248672	1.836617
0.250687	1.834927
0.252717	1.833273
0.254764	1.831655
0.256828	1.830073
0.258908	1.828524
0.261005	1.827009
0.263119	1.825526
0.265251	1.824075
0.267399	1.822654
0.269565	1.821263
0.271748	1.819901
0.27395	1.818567
0.276169	1.817261
0.278406	1.815981
0.280661	1.814728
0.282934	1.8135
0.285226	1.812297
0.287536	1.811119
0.289865	1.809964
0.292213	1.808831
0.29458	1.807722
0.296966	1.806634
0.299371	1.805568
0.301796	1.804523
0.304241	1.803498
0.306705	1.802493
0.30919	1.801508
0.311694	1.800541
0.314219	1.799593
0.316764	1.798663
0.31933	1.797751
0.321916	1.796857
0.324524	1.795979
0.327152	1.795117
0.329802	1.794272
0.332474	1.793443
0.335167	1.792629
0.337882	1.79183
0.340618	1.791046
0.343377	1.790277
0.346159	1.789521
0.348963	1.78878
0.351789	1.788051
0.354639	1.787337
0.357511	1.786635
0.360407	1.785945
0.363326	1.785268
0.366269	1.784604
0.369236	1.783951
0.372227	1.78331
0.375242	1.78268
0.378282	1.782061
0.381346	1.781453
0.384434	1.780856
0.387548	1.780269
0.390688	1.779693
0.393852	1.779126
0.397042	1.778569
0.400258	1.778022
0.4035	1.777485
0.406769	1.776956
0.410064	1.776437
0.413385	1.775926
0.416734	1.775424
0.420109	1.774931
0.423512	1.774445
0.426942	1.773968
0.430401	1.773499
0.433887	1.773038
0.437401	1.772585
0.440944	1.772138
0.444516	1.7717
0.448116	1.771268
0.451746	1.770844
0.455405	1.770426
0.459094	1.770015
0.462813	1.769611
0.466562	1.769213
0.470341	1.768822
0.47415	1.768437
0.477991	1.768058
0.481863	1.767685
0.485766	1.767318
0.489701	1.766957
0.493667	1.766601
0.497666	1.766251
0.501697	1.765906
0.505761	1.765566
0.509857	1.765232
0.513987	1.764903
0.51815	1.764578
0.522347	1.764259
0.526578	1.763944
0.530844	1.763634
0.535144	1.763329
0.539478	1.763028
0.543848	1.762732
0.548253	1.76244
0.552694	1.762152
0.557171	1.761868
0.561684	1.761588
0.566234	1.761312
0.57082	1.76104
0.575444	1.760772
0.580105	1.760507
0.584804	1.760246
0.58954	1.759989
0.594316	1.759735
0.59913	1.759485
0.603983	1.759238
0.608875	1.758994
0.613807	1.758753
0.618779	1.758515
0.623791	1.758281
0.628843	1.758049
0.633937	1.75782
0.639072	1.757594
0.644248	1.757371
0.649467	1.757151
0.654727	1.756933
0.660031	1.756718
0.665377	1.756505
0.670766	1.756295
0.6762	1.756087
0.681677	1.755881
0.687198	1.755678
0.692765	1.755477
0.698376	1.755278
0.704033	1.755081
0.709736	1.754886
0.715484	1.754693
0.72128	1.754503
0.727122	1.754313
0.733012	1.754126
0.738949	1.753941
0.744935	1.753757
0.750969	1.753575
0.757052	1.753395
0.763184	1.753216
0.769365	1.753038
0.775597	1.752862
0.78188	1.752688
0.788213	1.752515
0.794597	1.752343
0.801034	1.752172
0.807522	1.752003
0.814063	1.751835
0.820657	1.751668
0.827304	1.751502
0.834005	1.751337
0.840761	1.751173
0.847571	1.75101
0.854436	1.750848
0.861357	1.750687
0.868334	1.750526
0.875368	1.750367
0.882458	1.750208
0.889606	1.75005
0.896812	1.749892
0.904076	1.749735
0.911399	1.749579
0.918781	1.749423
0.926223	1.749267
0.933726	1.749112
0.941289	1.748957
0.948913	1.748803
0.9566	1.748649
0.964348	1.748495
0.972159	1.748342
0.980034	1.748188
0.987972	1.748035
0.995974	1.747882
1.00404	1.747729
1.01217	1.747576
1.02037	1.747422
1.02864	1.747269
1.03697	1.747116
1.04537	1.746962
1.05384	1.746809
1.06237	1.746655
1.07098	1.7465
1.07965	1.746346
1.0884	1.746191
1.09721	1.746036
1.1061	1.74588
1.11506	1.745724
1.12409	1.745567
1.1332	1.745409
1.14238	1.745251
1.15163	1.745093
1.16096	1.744933
1.17036	1.744773
1.17984	1.744612
1.1894	1.744451
1.19903	1.744288
1.20875	1.744124
1.21854	1.74396
1.22841	1.743794
1.23836	1.743628
1.24839	1.74346
1.2585	1.743291
1.26869	1.743121
1.27897	1.74295
1.28933	1.742778
1.29977	1.742604
1.3103	1.742429
1.32091	1.742252
1.33161	1.742074
1.3424	1.741894
1.35327	1.741713
1.36423	1.74153
1.37528	1.741346
1.38642	1.741159
1.39765	1.740972
1.40898	1.740782
1.42039	1.74059
1.43189	1.740397
1.44349	1.740201
1.45518	1.740003
1.46697	1.739804
1.47885	1.739602
1.49083	1.739398
1.50291	1.739192
1.51508	1.738983
1.52735	1.738772
1.53972	1.738559
1.5522	1.738343
1.56477	1.738125
1.57744	1.737904
1.59022	1.737681
1.6031	1.737454
1.61609	1.737225
1.62918	1.736994
1.64237	1.736759
1.65568	1.736521
1.66909	1.73628
1.68261	1.736036
1.69624	1.735789
1.70998	1.735539
1.72383	1.735286
1.73779	1.735029
1.75187	1.734768
1.76606	1.734504
1.78036	1.734237
1.79478	1.733966
1.80932	1.733691
1.82397	1.733412
1.83875	1.733129
1.85364	1.732843
1.86866	1.732552
1.88379	1.732257
1.89905	1.731958
1.91443	1.731655
1.92994	1.731347
1.94557	1.731035
1.96133	1.730718
1.97722	1.730397
1.99324	1.730071
2.00938	1.72974
2.02566	1.729404
2.04206	1.729063
2.0586	1.728717
2.07528	1.728365
2.09209	1.728009
2.10904	1.727647
2.12612	1.727279
2.14334	1.726906
2.1607	1.726527
2.1782	1.726142
2.19585	1.725752
2.21363	1.725355
2.23156	1.724952
2.24964	1.724542
2.26786	1.724127
2.28623	1.723704
2.30475	1.723275
2.32342	1.722839
2.34224	1.722397
2.36121	1.721947
2.38033	1.72149
2.39962	1.721026
2.41905	1.720554
2.43865	1.720075
2.4584	1.719588
2.47831	1.719093
2.49839	1.71859
2.51862	1.718079
2.53902	1.717559
2.55959	1.717031
2.58032	1.716495
2.60122	1.715949
2.62229	1.715395
2.64353	1.714831
2.66495	1.714258
2.68653	1.713676
2.70829	1.713084
2.73023	1.712482
2.75235	1.71187
2.77464	1.711248
2.79711	1.710615
2.81977	1.709972
2.84261	1.709318
2.86564	1.708653
2.88885	1.707977
2.91225	1.707289
2.93584	1.70659
2.95962	1.705879
2.98359	1.705156
3.00776	1.70442
3.03212	1.703672
3.05668	1.702911
3.08144	1.702137
3.1064	1.70135
3.13156	1.700549
3.15693	1.699734
3.1825	1.698906
3.20827	1.698063
3.23426	1.697205
3.26046	1.696332
3.28687	1.695445
3.31349	1.694542
3.34033	1.693623
3.36739	1.692688
3.39466	1.691736
3.42216	1.690768
3.44988	1.689783
3.47782	1.68878
3.50599	1.68776
3.53439	1.686721
3.56302	1.685665
3.59188	1.684589
3.62098	1.683494
3.65031	1.68238
3.67987	1.681246
3.70968	1.680091
3.73973	1.678916
3.77002	1.67772
3.80056	1.676501
3.83134	1.675261
3.86238	1.673999
3.89366	1.672713
3.9252	1.671405
3.95699	1.670072
3.98905	1.668715
4.02136	1.667333
4.05393	1.665925
4.08677	1.664492
4.11987	1.663032
4.15324	1.661546
4.18688	1.660031
4.22079	1.658489
4.25498	1.656918
4.28945	1.655317
4.32419	1.653687
4.35922	1.652025
4.39453	1.650333
4.43012	1.648608
4.46601	1.646851
4.50218	1.645061
4.53865	1.643236
4.57541	1.641377
4.61247	1.639482
4.64983	1.63755
4.6875	1.635581
4.72547	1.633575
4.76374	1.631529
4.80233	1.629443
4.84123	1.627317
4.88044	1.625149
4.91997	1.622939
4.95983	1.620685
5	1.618386

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/Malitson-e.yml
ID: ds_4e92800c3cf8
API: /v1/datasets/ds_4e92800c3cf8

Plot