Optical constants

Refractive index of Lu₃Al₅O₁₂ (Lutetium aluminium garnet, LuAG)

Hrabovský et al. 2021: n 0.193–1.69 µm

Data: formula 4
Range: 0.193–1.69 µm
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.83907
Extinction coefficient k: 0

Permittivity ε₁: 3.38218
Permittivity ε₂: 0

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

Abbe number V_d: 58.457
Chromatic dispersion dn/dλ: -0.0735896 µm⁻¹

Group index n_g: 1.88231
Group velocity dispersion: 135.769 fs²/mm

Dispersion parameter D: -740.692 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

# Lu3Al5O12 (Lutetium aluminium garnet, LuAG): Hrabovský et al. 2021: n 0.193–1.69 µm
lu3al5o12 = ls.fetch_refractiveindex("main", "Lu3Al5O12", "Hrabovsky", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(lu3al5o12.range_nm)  # (193, 1690) nm
eps = lu3al5o12.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_5cac97d6ae04/lightsmith"
lu3al5o12 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(lu3al5o12.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (lu3al5o12/hrabovsky-2021).

# ... load lu3al5o12 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=lu3al5o12)],
    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} = 2.077 + \frac{1.237 λ^{2.0}}{λ^{2} - {0.1376}^{2.0}} - 0.0104 λ^{2.0}

Valid from 0.193 to 1.69 µm.

Coefficients as stored

C_i	Value
C1	2.077
C2	1.237
C3	2.0
C4	0.1376
C5	2.0
C6	0.0
C7	0.0
C8	0.0
C9	0.0
C10	-0.0104
C11	2.0

References

J. Hrabovský, M. Kučera, L. Paloušová, L. Bi, M. Veis. Optical characterization of Y₃Al₅O₁₂ and Lu₃Al₅O₁₂ single crystals. Opt. Mater. Express 11, 1218-1223 (2021)

doi:10.1364/ome.417670 Optical characterization of Y3Al5O12 and Lu3Al5O12 single crystals, Optical Materials Express (2021)

Cite

J. Hrabovský, M. Kučera, L. Paloušová, L. Bi and M. Veis. Optical characterization of Y3Al5O12 and Lu3Al5O12 single crystals. Optical Materials Express, 11, 1218 (2021), doi:10.1364/ome.417670; 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

Lu3Al5O12 (Lutetium aluminium garnet, LuAG), Hrabovský et al. 2021: n 0.193–1.69 µm: n and k versus wavelength
λ (µm)	n
0.193	2.142986
0.194052	2.136483
0.195111	2.130173
0.196174	2.124045
0.197244	2.118093
0.19832	2.11231
0.199401	2.106688
0.200488	2.101222
0.201582	2.095905
0.202681	2.090731
0.203786	2.085696
0.204897	2.080793
0.206015	2.076018
0.207138	2.071366
0.208267	2.066832
0.209403	2.062413
0.210545	2.058104
0.211693	2.053902
0.212847	2.049803
0.214008	2.045802
0.215175	2.041898
0.216348	2.038086
0.217528	2.034364
0.218714	2.030729
0.219907	2.027177
0.221106	2.023707
0.222312	2.020315
0.223524	2.017
0.224743	2.013758
0.225968	2.010588
0.2272	2.007487
0.228439	2.004454
0.229685	2.001485
0.230937	1.99858
0.232197	1.995737
0.233463	1.992953
0.234736	1.990227
0.236016	1.987558
0.237303	1.984943
0.238597	1.982382
0.239898	1.979872
0.241206	1.977413
0.242521	1.975003
0.243844	1.97264
0.245173	1.970324
0.24651	1.968053
0.247854	1.965825
0.249206	1.963641
0.250565	1.961499
0.251931	1.959397
0.253305	1.957334
0.254686	1.955311
0.256075	1.953325
0.257471	1.951376
0.258875	1.949462
0.260287	1.947584
0.261706	1.945739
0.263133	1.943928
0.264568	1.94215
0.266011	1.940403
0.267461	1.938687
0.26892	1.937002
0.270386	1.935346
0.271861	1.933718
0.273343	1.93212
0.274833	1.930548
0.276332	1.929004
0.277839	1.927486
0.279354	1.925994
0.280877	1.924527
0.282409	1.923084
0.283949	1.921666
0.285497	1.920271
0.287054	1.918899
0.288619	1.91755
0.290193	1.916224
0.291775	1.914918
0.293366	1.913634
0.294966	1.912371
0.296574	1.911128
0.298192	1.909905
0.299818	1.908701
0.301453	1.907517
0.303096	1.906351
0.304749	1.905203
0.306411	1.904074
0.308082	1.902962
0.309762	1.901867
0.311451	1.900789
0.313149	1.899728
0.314857	1.898683
0.316573	1.897655
0.3183	1.896641
0.320035	1.895643
0.321781	1.894661
0.323535	1.893692
0.325299	1.892739
0.327073	1.8918
0.328857	1.890874
0.33065	1.889962
0.332453	1.889064
0.334266	1.888179
0.336088	1.887307
0.337921	1.886448
0.339764	1.885601
0.341616	1.884766
0.343479	1.883944
0.345352	1.883133
0.347235	1.882334
0.349129	1.881546
0.351033	1.88077
0.352947	1.880004
0.354871	1.87925
0.356806	1.878506
0.358752	1.877772
0.360708	1.877049
0.362675	1.876336
0.364653	1.875632
0.366641	1.874939
0.36864	1.874255
0.370651	1.873581
0.372672	1.872915
0.374704	1.872259
0.376747	1.871612
0.378801	1.870974
0.380867	1.870344
0.382944	1.869723
0.385032	1.86911
0.387131	1.868506
0.389242	1.867909
0.391365	1.867321
0.393499	1.866741
0.395645	1.866168
0.397802	1.865603
0.399971	1.865045
0.402152	1.864494
0.404345	1.863951
0.40655	1.863415
0.408767	1.862886
0.410996	1.862364
0.413237	1.861849
0.41549	1.86134
0.417756	1.860838
0.420034	1.860343
0.422324	1.859854
0.424627	1.859371
0.426943	1.858894
0.429271	1.858423
0.431612	1.857959
0.433965	1.8575
0.436331	1.857047
0.438711	1.8566
0.441103	1.856159
0.443508	1.855723
0.445927	1.855292
0.448358	1.854867
0.450803	1.854447
0.453261	1.854033
0.455733	1.853623
0.458218	1.853219
0.460716	1.85282
0.463229	1.852425
0.465755	1.852036
0.468294	1.851651
0.470848	1.851271
0.473415	1.850895
0.475997	1.850524
0.478592	1.850158
0.481202	1.849796
0.483826	1.849438
0.486464	1.849085
0.489117	1.848736
0.491784	1.848391
0.494466	1.848051
0.497162	1.847714
0.499873	1.847381
0.502599	1.847053
0.505339	1.846728
0.508095	1.846407
0.510866	1.84609
0.513651	1.845776
0.516452	1.845466
0.519268	1.84516
0.5221	1.844858
0.524947	1.844559
0.527809	1.844263
0.530687	1.843971
0.533581	1.843682
0.536491	1.843396
0.539416	1.843114
0.542357	1.842835
0.545315	1.842559
0.548288	1.842286
0.551278	1.842017
0.554284	1.84175
0.557307	1.841487
0.560346	1.841226
0.563401	1.840968
0.566473	1.840714
0.569562	1.840462
0.572668	1.840212
0.575791	1.839966
0.57893	1.839722
0.582087	1.839481
0.585261	1.839243
0.588453	1.839007
0.591661	1.838774
0.594888	1.838543
0.598132	1.838315
0.601393	1.83809
0.604672	1.837866
0.60797	1.837645
0.611285	1.837427
0.614618	1.837211
0.61797	1.836997
0.621339	1.836785
0.624727	1.836576
0.628134	1.836369
0.631559	1.836164
0.635003	1.835961
0.638465	1.83576
0.641947	1.835561
0.645447	1.835365
0.648967	1.83517
0.652506	1.834977
0.656064	1.834787
0.659641	1.834598
0.663238	1.834411
0.666855	1.834226
0.670491	1.834043
0.674147	1.833862
0.677823	1.833682
0.681519	1.833504
0.685236	1.833328
0.688972	1.833154
0.692729	1.832981
0.696506	1.832811
0.700304	1.832641
0.704123	1.832474
0.707963	1.832308
0.711823	1.832143
0.715704	1.83198
0.719607	1.831819
0.723531	1.831659
0.727476	1.8315
0.731443	1.831343
0.735432	1.831188
0.739442	1.831034
0.743474	1.830881
0.747528	1.83073
0.751604	1.83058
0.755703	1.830431
0.759823	1.830284
0.763967	1.830138
0.768133	1.829993
0.772321	1.82985
0.776532	1.829707
0.780767	1.829566
0.785024	1.829426
0.789305	1.829288
0.793609	1.82915
0.797936	1.829014
0.802287	1.828878
0.806662	1.828744
0.811061	1.828611
0.815484	1.828479
0.81993	1.828348
0.824401	1.828218
0.828897	1.828089
0.833416	1.827961
0.837961	1.827834
0.84253	1.827708
0.847125	1.827583
0.851744	1.827458
0.856388	1.827335
0.861058	1.827213
0.865753	1.827091
0.870474	1.826971
0.875221	1.826851
0.879993	1.826732
0.884792	1.826614
0.889616	1.826496
0.894467	1.82638
0.899345	1.826264
0.904249	1.826149
0.90918	1.826034
0.914137	1.825921
0.919122	1.825808
0.924134	1.825696
0.929173	1.825584
0.93424	1.825473
0.939334	1.825363
0.944456	1.825253
0.949606	1.825144
0.954784	1.825036
0.959991	1.824928
0.965225	1.824821
0.970489	1.824714
0.975781	1.824608
0.981101	1.824503
0.986451	1.824398
0.99183	1.824293
0.997239	1.824189
1.00268	1.824085
1.00814	1.823982
1.01364	1.82388
1.01917	1.823778
1.02473	1.823676
1.03031	1.823574
1.03593	1.823474
1.04158	1.823373
1.04726	1.823273
1.05297	1.823173
1.05871	1.823074
1.06449	1.822975
1.07029	1.822876
1.07613	1.822777
1.08199	1.822679
1.08789	1.822581
1.09383	1.822484
1.09979	1.822386
1.10579	1.822289
1.11182	1.822193
1.11788	1.822096
1.12398	1.822
1.13011	1.821904
1.13627	1.821808
1.14246	1.821712
1.14869	1.821616
1.15496	1.821521
1.16125	1.821426
1.16759	1.82133
1.17395	1.821235
1.18036	1.82114
1.18679	1.821046
1.19326	1.820951
1.19977	1.820856
1.20631	1.820762
1.21289	1.820667
1.2195	1.820573
1.22615	1.820478
1.23284	1.820384
1.23956	1.820289
1.24632	1.820195
1.25312	1.820101
1.25995	1.820006
1.26682	1.819912
1.27373	1.819817
1.28067	1.819722
1.28766	1.819628
1.29468	1.819533
1.30174	1.819438
1.30884	1.819343
1.31597	1.819248
1.32315	1.819153
1.33036	1.819057
1.33762	1.818962
1.34491	1.818866
1.35225	1.81877
1.35962	1.818674
1.36703	1.818578
1.37449	1.818481
1.38198	1.818385
1.38952	1.818288
1.3971	1.818191
1.40471	1.818093
1.41237	1.817996
1.42008	1.817898
1.42782	1.817799
1.4356	1.817701
1.44343	1.817602
1.4513	1.817502
1.45922	1.817403
1.46717	1.817303
1.47517	1.817203
1.48322	1.817102
1.49131	1.817001
1.49944	1.816899
1.50761	1.816797
1.51584	1.816695
1.5241	1.816592
1.53241	1.816489
1.54077	1.816385
1.54917	1.816281
1.55762	1.816177
1.56611	1.816071
1.57465	1.815966
1.58324	1.815859
1.59187	1.815753
1.60055	1.815645
1.60928	1.815538
1.61805	1.815429
1.62688	1.81532
1.63575	1.81521
1.64467	1.8151
1.65364	1.814989
1.66265	1.814878
1.67172	1.814765
1.68083	1.814653
1.69	1.814539

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: —

Lu₃Al₅O₁₂ (Lutetium aluminium garnet, LuAG): all datasets

Hrabovský et al. 2021: n 0.193–1.69 µm n 0.193–1.69 µm default

About Lu3Al5O12 (Lutetium aluminium garnet, LuAG)

Lutetium aluminium garnet (Lu₃Al₅O₁₂, or LuAG) is a synthetic garnet crystal. Owing to its outstanding properties, such as high density, high thermal conductivity, and good transparency in the visible and near-infrared regions, it's widely used in scintillator applications for high-energy photon detection. Additionally, LuAG has been studied as a potential host material for solid-state lasers, particularly when doped with rare-earth ions. Its transparency and luminescent characteristics make it valuable in various optical and photonic devices.

Lutetium aluminium garnet - Wikipedia

More about Lu3Al5O12 (Lutetium aluminium garnet, LuAG) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Lu3Al5O12/nk/Hrabovsky.yml
ID: ds_5cac97d6ae04
API: /v1/datasets/ds_5cac97d6ae04

Plot