Optical constants

Refractive index of MgAl₂O₄ (Magnesium aluminate, spinel)

Tropf and Thomas 1991: n 0.35–5.5 µm

Data: formula 1
Range: 0.35–5.5 µm
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.71621
Extinction coefficient k: 0

Permittivity ε₁: 2.94537
Permittivity ε₂: 0

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

Abbe number V_d: 60.667
Chromatic dispersion dn/dλ: -0.0611922 µm⁻¹

Group index n_g: 1.75216
Group velocity dispersion: 105.241 fs²/mm

Dispersion parameter D: -574.146 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

# MgAl2O4 (Magnesium aluminate, spinel): Tropf and Thomas 1991: n 0.35–5.5 µm
mgal2o4 = ls.fetch_refractiveindex("main", "MgAl2O4", "Tropf", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(mgal2o4.range_nm)  # (350, 5500) nm
eps = mgal2o4.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_8b18cffcf24f/lightsmith"
mgal2o4 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(mgal2o4.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (mgal2o4/tropf-thomas-1991).

# ... load mgal2o4 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=mgal2o4)],
    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_8b18cffcf24f/lightsmith?model=drude_lorentz"
mgal2o4_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{1.8938 λ^{2}}{λ^{2} - {0.09942}^{2}} + \frac{3.0755 λ^{2}}{λ^{2} - {15.826}^{2}}

Valid from 0.35 to 5.5 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	1.8938
C3	0.09942
C4	3.0755
C5	15.826

Comments and conditions

Room temperature

Notes on the source data (kept exactly as published):

no primary reference in the source file

References

1) W. J. Tropf and M. E. Thomas, Magnesium aluminum spinel (MgAlO₄), in E. D. Palik (ed.), Handbook of Optical Constants of Solids II, Academic Press, Orlando, 1991, pp. 881-895
2) Handbook of Optics, 3rd edition, Vol. 4. McGraw-Hill 2009
* Ref. 2 provides improved Sellmeier equation based on data from Ref. 1

Cite

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

MgAl2O4 (Magnesium aluminate, spinel), Tropf and Thomas 1991: n 0.35–5.5 µm: n and k versus wavelength
λ (µm)	n
0.35	1.748861
0.352425	1.748147
0.354866	1.747444
0.357324	1.746751
0.3598	1.74607
0.362292	1.745399
0.364802	1.744738
0.367329	1.744087
0.369874	1.743446
0.372436	1.742814
0.375016	1.742193
0.377614	1.74158
0.38023	1.740977
0.382864	1.740383
0.385517	1.739798
0.388187	1.739221
0.390877	1.738653
0.393585	1.738094
0.396311	1.737543
0.399057	1.737
0.401821	1.736465
0.404605	1.735938
0.407408	1.735419
0.41023	1.734908
0.413072	1.734403
0.415933	1.733907
0.418815	1.733417
0.421716	1.732935
0.424638	1.73246
0.427579	1.731991
0.430541	1.731529
0.433524	1.731074
0.436527	1.730626
0.439551	1.730184
0.442596	1.729748
0.445663	1.729319
0.44875	1.728895
0.451859	1.728478
0.454989	1.728066
0.458141	1.727661
0.461315	1.727261
0.464511	1.726866
0.467728	1.726478
0.470969	1.726094
0.474231	1.725716
0.477517	1.725343
0.480825	1.724976
0.484156	1.724613
0.48751	1.724256
0.490887	1.723903
0.494288	1.723556
0.497712	1.723213
0.50116	1.722874
0.504631	1.722541
0.508127	1.722211
0.511647	1.721887
0.515192	1.721566
0.518761	1.72125
0.522355	1.720938
0.525973	1.720631
0.529617	1.720327
0.533286	1.720027
0.53698	1.719732
0.5407	1.71944
0.544446	1.719152
0.548218	1.718868
0.552016	1.718587
0.55584	1.718311
0.55969	1.718037
0.563568	1.717768
0.567472	1.717501
0.571403	1.717238
0.575361	1.716979
0.579347	1.716722
0.583361	1.716469
0.587402	1.716219
0.591471	1.715972
0.595569	1.715729
0.599695	1.715488
0.603849	1.71525
0.608032	1.715015
0.612244	1.714783
0.616486	1.714554
0.620757	1.714327
0.625057	1.714103
0.629387	1.713882
0.633747	1.713664
0.638137	1.713448
0.642558	1.713234
0.64701	1.713023
0.651492	1.712814
0.656005	1.712608
0.66055	1.712404
0.665126	1.712203
0.669733	1.712003
0.674373	1.711806
0.679045	1.711611
0.683749	1.711418
0.688486	1.711228
0.693255	1.711039
0.698058	1.710852
0.702893	1.710667
0.707763	1.710485
0.712666	1.710304
0.717603	1.710125
0.722574	1.709947
0.72758	1.709772
0.73262	1.709598
0.737695	1.709426
0.742806	1.709256
0.747952	1.709087
0.753133	1.70892
0.758351	1.708754
0.763604	1.70859
0.768894	1.708427
0.774221	1.708266
0.779584	1.708107
0.784985	1.707948
0.790423	1.707792
0.795898	1.707636
0.801412	1.707482
0.806964	1.707329
0.812554	1.707177
0.818183	1.707027
0.823851	1.706877
0.829559	1.706729
0.835305	1.706582
0.841092	1.706436
0.846919	1.706291
0.852786	1.706147
0.858694	1.706004
0.864642	1.705862
0.870632	1.705721
0.876664	1.705581
0.882737	1.705442
0.888852	1.705304
0.895009	1.705166
0.90121	1.70503
0.907453	1.704894
0.913739	1.704759
0.920069	1.704624
0.926443	1.704491
0.932861	1.704357
0.939324	1.704225
0.945831	1.704093
0.952383	1.703962
0.958981	1.703831
0.965624	1.703701
0.972314	1.703572
0.979049	1.703443
0.985832	1.703314
0.992661	1.703186
0.999538	1.703058
1.00646	1.702931
1.01343	1.702803
1.02046	1.702677
1.02752	1.70255
1.03464	1.702424
1.04181	1.702298
1.04903	1.702173
1.05629	1.702047
1.06361	1.701922
1.07098	1.701797
1.0784	1.701672
1.08587	1.701547
1.09339	1.701422
1.10097	1.701298
1.10859	1.701173
1.11627	1.701048
1.12401	1.700924
1.13179	1.700799
1.13963	1.700674
1.14753	1.700549
1.15548	1.700424
1.16348	1.700299
1.17154	1.700174
1.17966	1.700048
1.18783	1.699923
1.19606	1.699797
1.20435	1.699671
1.21269	1.699544
1.22109	1.699417
1.22955	1.69929
1.23807	1.699163
1.24664	1.699035
1.25528	1.698906
1.26398	1.698778
1.27273	1.698649
1.28155	1.698519
1.29043	1.698389
1.29937	1.698258
1.30837	1.698127
1.31743	1.697995
1.32656	1.697862
1.33575	1.697729
1.345	1.697595
1.35432	1.697461
1.3637	1.697325
1.37315	1.697189
1.38266	1.697052
1.39224	1.696915
1.40189	1.696776
1.4116	1.696637
1.42138	1.696497
1.43122	1.696356
1.44114	1.696214
1.45112	1.69607
1.46117	1.695926
1.4713	1.695781
1.48149	1.695635
1.49175	1.695488
1.50209	1.695339
1.51249	1.69519
1.52297	1.695039
1.53352	1.694887
1.54414	1.694734
1.55484	1.69458
1.56561	1.694424
1.57646	1.694267
1.58738	1.694108
1.59838	1.693948
1.60945	1.693787
1.6206	1.693624
1.63183	1.69346
1.64313	1.693294
1.65451	1.693127
1.66598	1.692958
1.67752	1.692787
1.68914	1.692615
1.70084	1.692441
1.71262	1.692265
1.72449	1.692087
1.73643	1.691908
1.74846	1.691727
1.76057	1.691544
1.77277	1.691359
1.78505	1.691172
1.79742	1.690983
1.80987	1.690792
1.82241	1.690599
1.83503	1.690403
1.84774	1.690206
1.86055	1.690006
1.87343	1.689804
1.88641	1.6896
1.89948	1.689394
1.91264	1.689185
1.92589	1.688973
1.93923	1.68876
1.95267	1.688543
1.96619	1.688324
1.97981	1.688103
1.99353	1.687879
2.00734	1.687652
2.02125	1.687423
2.03525	1.68719
2.04935	1.686955
2.06354	1.686717
2.07784	1.686476
2.09223	1.686232
2.10673	1.685985
2.12132	1.685735
2.13602	1.685481
2.15082	1.685225
2.16572	1.684965
2.18072	1.684702
2.19583	1.684435
2.21104	1.684165
2.22635	1.683892
2.24178	1.683615
2.25731	1.683334
2.27295	1.68305
2.28869	1.682761
2.30455	1.68247
2.32051	1.682174
2.33659	1.681874
2.35277	1.68157
2.36907	1.681263
2.38548	1.680951
2.40201	1.680634
2.41865	1.680314
2.43541	1.679989
2.45228	1.67966
2.46927	1.679326
2.48637	1.678988
2.5036	1.678645
2.52094	1.678297
2.5384	1.677945
2.55599	1.677587
2.5737	1.677225
2.59152	1.676858
2.60948	1.676485
2.62756	1.676107
2.64576	1.675724
2.66409	1.675335
2.68254	1.674941
2.70113	1.674542
2.71984	1.674136
2.73868	1.673725
2.75765	1.673308
2.77676	1.672885
2.79599	1.672456
2.81536	1.672021
2.83487	1.67158
2.8545	1.671132
2.87428	1.670677
2.89419	1.670216
2.91424	1.669749
2.93443	1.669274
2.95476	1.668793
2.97523	1.668304
2.99584	1.667808
3.01659	1.667305
3.03749	1.666795
3.05853	1.666277
3.07972	1.665751
3.10105	1.665217
3.12254	1.664676
3.14417	1.664126
3.16595	1.663569
3.18788	1.663002
3.20997	1.662428
3.2322	1.661844
3.2546	1.661252
3.27714	1.660651
3.29984	1.66004
3.3227	1.659421
3.34572	1.658792
3.3689	1.658153
3.39224	1.657505
3.41574	1.656846
3.4394	1.656178
3.46323	1.655499
3.48722	1.65481
3.51138	1.65411
3.5357	1.653399
3.5602	1.652677
3.58486	1.651944
3.6097	1.651199
3.6347	1.650443
3.65988	1.649675
3.68524	1.648895
3.71077	1.648102
3.73647	1.647297
3.76236	1.646479
3.78842	1.645648
3.81466	1.644804
3.84109	1.643947
3.8677	1.643076
3.89449	1.64219
3.92147	1.641291
3.94864	1.640377
3.97599	1.639448
4.00354	1.638504
4.03127	1.637545
4.0592	1.63657
4.08732	1.635579
4.11564	1.634572
4.14415	1.633549
4.17286	1.632508
4.20176	1.631451
4.23087	1.630376
4.26018	1.629283
4.28969	1.628172
4.31941	1.627042
4.34933	1.625893
4.37946	1.624725
4.4098	1.623538
4.44035	1.62233
4.47111	1.621102
4.50209	1.619853
4.53328	1.618582
4.56468	1.61729
4.5963	1.615976
4.62814	1.614639
4.66021	1.613279
4.69249	1.611895
4.725	1.610487
4.75773	1.609055
4.79069	1.607597
4.82388	1.606114
4.8573	1.604605
4.89094	1.603069
4.92483	1.601505
4.95894	1.599914
4.9933	1.598294
5.02789	1.596645
5.06272	1.594967
5.09779	1.593257
5.13311	1.591517
5.16867	1.589745
5.20447	1.587941
5.24053	1.586103
5.27683	1.584231
5.31339	1.582325
5.3502	1.580383
5.38726	1.578404
5.42458	1.576389
5.46216	1.574335
5.5	1.572242

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: —

MgAl₂O₄ (Magnesium aluminate, spinel): all datasets

About MgAl2O4 (Magnesium aluminate, spinel)

Magnesium aluminium oxide, commonly known as spinel (MgAl₂O₄), is a transparent ceramic material with a cubic crystal structure. Spinel possesses excellent optical transparency from the ultraviolet to the mid-infrared range, making it valuable for various optical applications. This material is notably durable, resistant to attack from harsh environments, and can withstand high temperatures. These characteristics make it ideal for protective windows in specific high-stress applications. Moreover, due to its favorable mechanical properties and refractive index, spinel is being considered for anti-reflective coatings and other advanced optical devices. Additionally, its non-birefringent nature is a plus in certain optical scenarios. Mineral: Spinel

Spinel - Wikipedia

More about MgAl2O4 (Magnesium aluminate, spinel) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/MgAl2O4/nk/Tropf.yml
ID: ds_8b18cffcf24f
API: /v1/datasets/ds_8b18cffcf24f

Plot