Optical constants

Refractive index of BeAl₂O₄ (Beryllium aluminate, chrysoberyl)

Walling et al. 1980: n(β) 0.25–2.6 µm

Data: formula 4
Range: 0.25–2.6 µm
Optical axis: beta
Licence: CC0-1.0

Biaxial crystal, axes: beta

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.74845
Extinction coefficient k: 0

Permittivity ε₁: 3.05708
Permittivity ε₂: 0

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

Abbe number V_d: 72.84
Chromatic dispersion dn/dλ: -0.0535092 µm⁻¹

Group index n_g: 1.77989
Group velocity dispersion: 87.5171 fs²/mm

Dispersion parameter D: -477.452 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

# BeAl2O4 (Beryllium aluminate, chrysoberyl): Walling et al. 1980: n(β) 0.25–2.6 µm
beal2o4 = ls.fetch_refractiveindex("main", "BeAl2O4", "Walling-β", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(beal2o4.range_nm)  # (250, 2600) nm
eps = beal2o4.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_67602b5acb4b/lightsmith"
beal2o4 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(beal2o4.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (beal2o4/walling-1980-2).

# ... load beal2o4 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=beal2o4)],
    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"]).

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

RefractiveIndex.INFO (formula 4), λ in µm

n^{2} = 1.58829 + \frac{1.42711 λ^{2.0}}{λ^{2} - {0.01113}^{1.0}} - 0.01696 λ^{2.0}

Valid from 0.25 to 2.6 µm.

Coefficients as stored

C_i	Value
C1	1.58829
C2	1.42711
C3	2.0
C4	0.01113
C5	1.0
C6	0.0
C7	0.0
C8	0.0
C9	0.0
C10	-0.01696
C11	2.0

Comments and conditions

n_β; Room temperature.

Conditions

direction: beta

References

1) J. Walling, O. Peterson, H. Jenssen, R. Morris, E. O'Dell. Tunable alexandrite lasers. IEEE J. Quantum Electron., 16, 1302–1315 (1980)
2) P. Loiko, A. Major. Dispersive properties of alexandrite and beryllium hexaaluminate crystals. Opt. Mater. Express, 6, 2177–2183 (2016)
* Ref. 2 provides a dispersion formula based on the experimental data from Ref. 1

doi:10.1109/jqe.1980.1070430 Tunable alexandrite lasers, IEEE Journal of Quantum Electronics (1980)
doi:10.1364/ome.6.002177 Dispersive properties of alexandrite and beryllium hexaaluminate crystals, Optical Materials Express (2016)

Cite

J. Walling, O. Peterson, H. Jenssen, R. Morris and E. O'Dell. Tunable alexandrite lasers. IEEE Journal of Quantum Electronics, 16, 1302-1315 (1980), doi:10.1109/jqe.1980.1070430; Pavel Loiko and Arkady Major. Dispersive properties of alexandrite and beryllium hexaaluminate crystals. Optical Materials Express, 6, 2177 (2016), doi:10.1364/ome.6.002177; 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

BeAl2O4 (Beryllium aluminate, chrysoberyl), Walling et al. 1980: n(β) 0.25–2.6 µm: n and k versus wavelength
λ (µm)	n
0.25	1.823059
0.251472	1.821854
0.252952	1.820668
0.254441	1.819501
0.255939	1.818353
0.257445	1.817222
0.258961	1.816109
0.260485	1.815014
0.262018	1.813935
0.263561	1.812873
0.265112	1.811828
0.266673	1.810799
0.268242	1.809785
0.269821	1.808787
0.27141	1.807804
0.273007	1.806836
0.274614	1.805882
0.276231	1.804943
0.277857	1.804018
0.279493	1.803107
0.281138	1.802209
0.282793	1.801325
0.284457	1.800454
0.286132	1.799596
0.287816	1.79875
0.28951	1.797916
0.291214	1.797095
0.292929	1.796286
0.294653	1.795489
0.296387	1.794703
0.298132	1.793928
0.299887	1.793165
0.301652	1.792412
0.303428	1.79167
0.305214	1.790939
0.307011	1.790219
0.308818	1.789508
0.310636	1.788808
0.312464	1.788117
0.314304	1.787436
0.316154	1.786765
0.318015	1.786103
0.319887	1.78545
0.32177	1.784807
0.323664	1.784172
0.325569	1.783546
0.327485	1.782929
0.329413	1.78232
0.331352	1.78172
0.333303	1.781128
0.335265	1.780544
0.337238	1.779967
0.339223	1.779399
0.34122	1.778838
0.343229	1.778285
0.345249	1.77774
0.347281	1.777202
0.349326	1.776671
0.351382	1.776147
0.35345	1.77563
0.355531	1.77512
0.357624	1.774616
0.359729	1.77412
0.361846	1.77363
0.363976	1.773146
0.366119	1.772669
0.368274	1.772198
0.370442	1.771733
0.372622	1.771274
0.374816	1.770821
0.377022	1.770374
0.379242	1.769933
0.381474	1.769497
0.383719	1.769068
0.385978	1.768643
0.38825	1.768224
0.390536	1.767811
0.392834	1.767402
0.395147	1.766999
0.397473	1.766601
0.399813	1.766208
0.402166	1.76582
0.404533	1.765437
0.406915	1.765059
0.40931	1.764685
0.411719	1.764316
0.414143	1.763952
0.416581	1.763592
0.419033	1.763237
0.4215	1.762886
0.423981	1.762539
0.426476	1.762197
0.428987	1.761859
0.431512	1.761524
0.434052	1.761194
0.436607	1.760868
0.439177	1.760546
0.441762	1.760228
0.444363	1.759914
0.446978	1.759603
0.44961	1.759297
0.452256	1.758993
0.454918	1.758694
0.457596	1.758398
0.46029	1.758105
0.462999	1.757816
0.465725	1.75753
0.468466	1.757248
0.471224	1.756969
0.473998	1.756693
0.476788	1.756421
0.479594	1.756151
0.482417	1.755885
0.485257	1.755622
0.488114	1.755361
0.490987	1.755104
0.493877	1.75485
0.496784	1.754598
0.499709	1.754349
0.50265	1.754103
0.505609	1.75386
0.508585	1.75362
0.511579	1.753382
0.51459	1.753147
0.517619	1.752914
0.520666	1.752684
0.523731	1.752457
0.526814	1.752232
0.529915	1.752009
0.533034	1.751789
0.536172	1.751571
0.539328	1.751356
0.542503	1.751142
0.545696	1.750931
0.548909	1.750722
0.55214	1.750516
0.55539	1.750311
0.558659	1.750109
0.561948	1.749909
0.565256	1.749711
0.568583	1.749514
0.57193	1.74932
0.575296	1.749128
0.578683	1.748938
0.582089	1.748749
0.585516	1.748563
0.588962	1.748378
0.592429	1.748195
0.595917	1.748014
0.599424	1.747835
0.602953	1.747657
0.606502	1.747481
0.610072	1.747306
0.613663	1.747134
0.617276	1.746963
0.620909	1.746793
0.624564	1.746625
0.628241	1.746459
0.631939	1.746294
0.635659	1.74613
0.6394	1.745968
0.643164	1.745808
0.64695	1.745648
0.650758	1.745491
0.654589	1.745334
0.658442	1.745179
0.662318	1.745025
0.666217	1.744872
0.670139	1.744721
0.674083	1.744571
0.678051	1.744422
0.682043	1.744274
0.686057	1.744128
0.690096	1.743982
0.694158	1.743838
0.698244	1.743695
0.702354	1.743553
0.706489	1.743412
0.710647	1.743271
0.714831	1.743132
0.719038	1.742994
0.723271	1.742857
0.727528	1.742721
0.731811	1.742586
0.736119	1.742452
0.740452	1.742318
0.74481	1.742186
0.749195	1.742054
0.753605	1.741923
0.758041	1.741793
0.762503	1.741663
0.766992	1.741535
0.771506	1.741407
0.776048	1.74128
0.780616	1.741154
0.785211	1.741028
0.789833	1.740903
0.794482	1.740779
0.799159	1.740655
0.803863	1.740532
0.808595	1.74041
0.813355	1.740288
0.818143	1.740166
0.822959	1.740046
0.827803	1.739925
0.832676	1.739806
0.837577	1.739686
0.842508	1.739568
0.847467	1.739449
0.852456	1.739331
0.857474	1.739214
0.862521	1.739097
0.867598	1.73898
0.872705	1.738864
0.877842	1.738748
0.88301	1.738632
0.888208	1.738517
0.893436	1.738402
0.898695	1.738288
0.903985	1.738173
0.909306	1.738059
0.914659	1.737945
0.920043	1.737831
0.925459	1.737718
0.930907	1.737605
0.936386	1.737492
0.941898	1.737379
0.947443	1.737266
0.95302	1.737153
0.95863	1.737041
0.964273	1.736928
0.969949	1.736816
0.975658	1.736704
0.981401	1.736591
0.987178	1.736479
0.992989	1.736367
0.998835	1.736255
1.00471	1.736142
1.01063	1.73603
1.01658	1.735918
1.02256	1.735805
1.02858	1.735693
1.03464	1.73558
1.04073	1.735468
1.04685	1.735355
1.05301	1.735242
1.05921	1.735129
1.06545	1.735015
1.07172	1.734902
1.07803	1.734788
1.08437	1.734674
1.09076	1.73456
1.09718	1.734446
1.10364	1.734331
1.11013	1.734216
1.11667	1.734101
1.12324	1.733985
1.12985	1.733869
1.1365	1.733753
1.14319	1.733636
1.14992	1.733519
1.15669	1.733401
1.1635	1.733283
1.17035	1.733165
1.17724	1.733046
1.18417	1.732927
1.19114	1.732807
1.19815	1.732687
1.2052	1.732566
1.2123	1.732445
1.21943	1.732323
1.22661	1.7322
1.23383	1.732077
1.24109	1.731954
1.2484	1.731829
1.25575	1.731704
1.26314	1.731579
1.27058	1.731452
1.27806	1.731326
1.28558	1.731198
1.29315	1.731069
1.30076	1.73094
1.30842	1.73081
1.31612	1.73068
1.32386	1.730548
1.33166	1.730416
1.3395	1.730282
1.34738	1.730148
1.35531	1.730013
1.36329	1.729878
1.37131	1.729741
1.37939	1.729603
1.38751	1.729465
1.39567	1.729325
1.40389	1.729184
1.41215	1.729043
1.42047	1.7289
1.42883	1.728756
1.43724	1.728611
1.4457	1.728466
1.45421	1.728319
1.46277	1.72817
1.47138	1.728021
1.48004	1.727871
1.48875	1.727719
1.49752	1.727566
1.50633	1.727412
1.5152	1.727257
1.52412	1.7271
1.53309	1.726942
1.54211	1.726782
1.55119	1.726622
1.56032	1.72646
1.56951	1.726296
1.57875	1.726131
1.58804	1.725965
1.59739	1.725797
1.60679	1.725628
1.61625	1.725457
1.62576	1.725285
1.63533	1.725111
1.64496	1.724935
1.65464	1.724758
1.66438	1.72458
1.67418	1.724399
1.68403	1.724217
1.69395	1.724033
1.70392	1.723848
1.71395	1.723661
1.72404	1.723471
1.73418	1.723281
1.74439	1.723088
1.75466	1.722893
1.76499	1.722697
1.77538	1.722498
1.78583	1.722298
1.79634	1.722095
1.80692	1.721891
1.81755	1.721684
1.82825	1.721476
1.83901	1.721265
1.84984	1.721052
1.86073	1.720837
1.87168	1.72062
1.8827	1.720401
1.89378	1.720179
1.90493	1.719956
1.91614	1.719729
1.92742	1.719501
1.93877	1.71927
1.95018	1.719036
1.96166	1.718801
1.97321	1.718562
1.98482	1.718322
1.9965	1.718078
2.00826	1.717832
2.02008	1.717584
2.03197	1.717333
2.04393	1.717079
2.05596	1.716822
2.06806	1.716563
2.08024	1.716301
2.09248	1.716035
2.1048	1.715768
2.11719	1.715497
2.12965	1.715223
2.14219	1.714946
2.1548	1.714666
2.16748	1.714384
2.18024	1.714098
2.19308	1.713809
2.20599	1.713516
2.21897	1.713221
2.23203	1.712922
2.24517	1.71262
2.25839	1.712314
2.27168	1.712005
2.28505	1.711693
2.2985	1.711377
2.31203	1.711058
2.32564	1.710735
2.33933	1.710408
2.3531	1.710078
2.36696	1.709743
2.38089	1.709406
2.3949	1.709064
2.409	1.708718
2.42318	1.708369
2.43745	1.708015
2.45179	1.707658
2.46623	1.707296
2.48074	1.706931
2.49535	1.706561
2.51003	1.706187
2.52481	1.705808
2.53967	1.705425
2.55462	1.705038
2.56966	1.704647
2.58478	1.70425
2.6	1.70385

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: —

BeAl₂O₄ (Beryllium aluminate, chrysoberyl): all datasets

About BeAl2O4 (Beryllium aluminate, chrysoberyl)

BeAl₂O₄, commonly known as chrysoberyl, is a beryllium-aluminum oxide mineral that is noteworthy for its excellent hardness and durability. In the field of optics, chrysoberyl is used mainly as a gemstone and is not often encountered in technical applications due to its high cost and relative scarcity. However, its natural form, known as "cat's eye," is a unique gemstone admired for its chatoyancy. While not commonly utilized in high-technology optical applications, the properties of chrysoberyl, such as its excellent thermal stability and high hardness, could theoretically make it valuable in extreme environments where other materials may fail. The crystal structure of BeAl₂O₄ contributes to its remarkable hardness, which is second only to diamond among naturally occurring materials. Overall, while not a mainstream choice for technical optics, chrysoberyl remains an intriguing material whose unique characteristics could inspire future research and applications in specialized optical contexts. Mineral: Chrysoberyl

More about BeAl2O4 (Beryllium aluminate, chrysoberyl) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/BeAl2O4/nk/Walling-beta.yml
ID: ds_67602b5acb4b
API: /v1/datasets/ds_67602b5acb4b

Plot