Optical constants

Refractive index of MoS₂ (Molybdenum disulfide)

Munkhbat et al. 2022: multilayer flakes; n(o),k 0.30–1.69 µm

Data: tabulated nk
Range: 0.3–1.69 µm
Points: 977
Optical axis: o
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: 4.71244
Extinction coefficient k: 0.961723

Permittivity ε₁: 21.2822
Permittivity ε₂: 9.06412

Absorption coefficient α: 205673 cm⁻¹
Penetration depth δ = λ/(2πk): 97.2415 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -5.526 µm⁻¹

Group index n_g: 7.95952
Group velocity dispersion: — fs²/mm

Dispersion parameter D: — 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

# MoS2 (Molybdenum disulfide): Munkhbat et al. 2022: multilayer flakes; n(o),k 0.30–1.69 µm
mos2 = ls.fetch_refractiveindex("main", "MoS2", "Munkhbat-o", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(mos2.range_nm)  # (300, 1690) nm
eps = mos2.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_e57bf6308725/lightsmith"
mos2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(mos2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (mos2/munkhbat-2022-o).

# ... load mos2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=mos2)],
    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.

Comments and conditions

Multilayer flakes. In-plane (ordinary ray, o). Room temperature.

Conditions

direction: o

References

B. Munkhbat, P. Wrobel, T. J. Antosiewicz, T. O. Shegai. Optical constants of several multilayer transition metal dichalcogenides spectroscopic ellipsometry in the 300–1700 nm range: high index, anisotropy, and hyperbolicity. ACS Photonics 9, 2398–2407 (2022) (Numerical data kindly provided by Tomasz Antosiewicz)

doi:10.1021/acsphotonics.2c00433 Optical Constants of Several Multilayer Transition Metal Dichalcogenides Measured by Spectroscopic Ellipsometry in the 300–1700 nm Range: High Index, Anisotropy, and Hyperbolicity, ACS Photonics (2022)

Cite

Battulga Munkhbat, Piotr Wróbel, Tomasz J. Antosiewicz and Timur O. Shegai. Optical Constants of Several Multilayer Transition Metal Dichalcogenides Measured by Spectroscopic Ellipsometry in the 300–1700 nm Range: High Index, Anisotropy, and Hyperbolicity. ACS Photonics, 9, 2398-2407 (2022), doi:10.1021/acsphotonics.2c00433; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

977 rows as published

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

MoS2 (Molybdenum disulfide), Munkhbat et al. 2022: multilayer flakes; n(o),k 0.30–1.69 µm: n and k versus wavelength
λ (µm)	n	k
0.3	3.126059	2.491241
0.301	3.132675	2.476525
0.302	3.138445	2.461892
0.303	3.143375	2.447387
0.304	3.147473	2.433051
0.305	3.150745	2.418926
0.306	3.153204	2.405054
0.307	3.15486	2.391474
0.308	3.155727	2.378229
0.309	3.155822	2.365357
0.31	3.15516	2.352899
0.311	3.15376	2.340895
0.312	3.151642	2.329381
0.313	3.148823	2.318399
0.314	3.145328	2.30799
0.315	3.141179	2.298196
0.316	3.136402	2.289058
0.317	3.131027	2.280621
0.318	3.125083	2.272932
0.319	3.118605	2.266039
0.32	3.111631	2.259994
0.321	3.104204	2.254853
0.322	3.096377	2.250679
0.323	3.088211	2.247538
0.324	3.079779	2.245507
0.325	3.071175	2.244667
0.326	3.062519	2.245113
0.327	3.053968	2.246941
0.328	3.045732	2.250254
0.329	3.038093	2.255144
0.33	3.031437	2.261675
0.331	3.026286	2.269827
0.332	3.023324	2.279416
0.333	3.023398	2.289943
0.334	3.027405	2.30036
0.335	3.035956	2.30883
0.336	3.04868	2.312694
0.337	3.063329	2.30914
0.338	3.075549	2.296869
0.339	3.080447	2.277789
0.34	3.075353	2.256669
0.341	3.061122	2.238515
0.342	3.040835	2.226275
0.343	3.017734	2.220584
0.344	2.994136	2.220724
0.345	2.971348	2.225562
0.346	2.949964	2.234036
0.347	2.930179	2.245313
0.348	2.911991	2.258787
0.349	2.89532	2.274036
0.35	2.880068	2.290769
0.351	2.86614	2.308784
0.352	2.853457	2.32794
0.353	2.841959	2.348137
0.354	2.831605	2.369298
0.355	2.822368	2.391368
0.356	2.814232	2.414298
0.357	2.807195	2.438049
0.358	2.801264	2.462583
0.359	2.79645	2.487864
0.36	2.792773	2.513856
0.361	2.790257	2.540522
0.362	2.78893	2.567821
0.363	2.78883	2.595708
0.364	2.789984	2.624108
0.365	2.792382	2.652973
0.366	2.796045	2.682273
0.367	2.800998	2.711966
0.368	2.807268	2.742006
0.369	2.814883	2.772347
0.37	2.823871	2.802933
0.371	2.83426	2.83371
0.372	2.846077	2.864614
0.373	2.859339	2.895579
0.374	2.874069	2.926543
0.375	2.890285	2.957437
0.376	2.908006	2.988188
0.377	2.927247	3.018719
0.378	2.948019	3.048947
0.379	2.970328	3.078789
0.38	2.994176	3.108155
0.381	3.019561	3.136952
0.382	3.046472	3.165086
0.383	3.074892	3.192458
0.384	3.104798	3.218966
0.385	3.136158	3.244508
0.386	3.16893	3.268979
0.387	3.203064	3.292275
0.388	3.238499	3.314291
0.389	3.275164	3.334925
0.39	3.312977	3.354076
0.391	3.351843	3.371649
0.392	3.391657	3.387554
0.393	3.432304	3.401707
0.394	3.473654	3.414033
0.395	3.51557	3.42447
0.396	3.557904	3.432966
0.397	3.6005	3.439483
0.398	3.643194	3.444
0.399	3.685817	3.446511
0.4	3.728197	3.447029
0.401	3.770162	3.445587
0.402	3.81154	3.442235
0.403	3.852164	3.437046
0.404	3.891873	3.430111
0.405	3.930518	3.421538
0.406	3.967958	3.411457
0.407	4.004072	3.400009
0.408	4.038751	3.387353
0.409	4.071908	3.373659
0.41	4.103476	3.359106
0.411	4.133407	3.343881
0.412	4.161679	3.328172
0.413	4.188289	3.31217
0.414	4.213258	3.296065
0.415	4.236629	3.280041
0.416	4.258464	3.264274
0.417	4.278847	3.248932
0.418	4.297877	3.23417
0.419	4.315671	3.22013
0.42	4.332361	3.206938
0.421	4.348088	3.194705
0.422	4.363008	3.183523
0.423	4.377281	3.173467
0.424	4.391076	3.164593
0.425	4.404564	3.156938
0.426	4.41792	3.150519
0.427	4.431316	3.145336
0.428	4.444926	3.141369
0.429	4.458919	3.138579
0.43	4.473459	3.136912
0.431	4.488702	3.136295
0.432	4.504797	3.136639
0.433	4.521883	3.13784
0.434	4.540088	3.139778
0.435	4.559527	3.142323
0.436	4.580302	3.14533
0.437	4.602497	3.148645
0.438	4.626185	3.152102
0.439	4.651417	3.15553
0.44	4.678229	3.158751
0.441	4.706638	3.161581
0.442	4.736641	3.163836
0.443	4.768215	3.165329
0.444	4.801318	3.165876
0.445	4.835887	3.165296
0.446	4.871841	3.163414
0.447	4.909079	3.160062
0.448	4.947479	3.155084
0.449	4.986906	3.148336
0.45	5.027206	3.139688
0.451	5.068211	3.129026
0.452	5.109741	3.116255
0.453	5.151606	3.101302
0.454	5.193606	3.08411
0.455	5.235539	3.06465
0.456	5.277197	3.04291
0.457	5.318377	3.018906
0.458	5.358874	2.992672
0.459	5.398493	2.964266
0.46	5.437046	2.933766
0.461	5.474358	2.90127
0.462	5.510264	2.866894
0.463	5.544618	2.830766
0.464	5.577289	2.793029
0.465	5.608164	2.753838
0.466	5.637151	2.713353
0.467	5.664173	2.671741
0.468	5.689175	2.62917
0.469	5.71212	2.585811
0.47	5.732988	2.54183
0.471	5.751777	2.497392
0.472	5.768499	2.452654
0.473	5.783182	2.407766
0.474	5.795864	2.362872
0.475	5.806598	2.318104
0.476	5.815442	2.273586
0.477	5.822465	2.229429
0.478	5.82774	2.185736
0.479	5.831348	2.142599
0.48	5.83337	2.100098
0.481	5.833893	2.058304
0.482	5.833001	2.017278
0.483	5.830782	1.977071
0.484	5.827321	1.937727
0.485	5.822704	1.89928
0.486	5.817012	1.861759
0.487	5.810328	1.825183
0.488	5.802727	1.789567
0.489	5.794285	1.75492
0.49	5.785073	1.721246
0.491	5.775158	1.688545
0.492	5.764606	1.656813
0.493	5.753478	1.626041
0.494	5.741829	1.59622
0.495	5.729715	1.567336
0.496	5.717185	1.539375
0.497	5.704288	1.51232
0.498	5.691065	1.486152
0.499	5.67756	1.460854
0.5	5.663808	1.436404
0.501	5.649845	1.412782
0.502	5.635705	1.389967
0.503	5.621415	1.367938
0.504	5.607005	1.346672
0.505	5.5925	1.326149
0.506	5.577922	1.306346
0.507	5.563292	1.287243
0.508	5.548632	1.268819
0.509	5.533957	1.251053
0.51	5.519285	1.233924
0.511	5.504631	1.217414
0.512	5.490007	1.201502
0.513	5.475426	1.18617
0.514	5.460898	1.1714
0.515	5.446435	1.157173
0.516	5.432044	1.143473
0.517	5.417735	1.130283
0.518	5.403513	1.117587
0.519	5.389386	1.105368
0.52	5.375359	1.093614
0.521	5.361437	1.082308
0.522	5.347625	1.071436
0.523	5.333927	1.060987
0.524	5.320346	1.050946
0.525	5.306885	1.041301
0.526	5.293547	1.032041
0.527	5.280334	1.023154
0.528	5.267248	1.014629
0.529	5.25429	1.006456
0.53	5.241462	0.9986243
0.531	5.228764	0.9911251
0.532	5.216197	0.9839489
0.533	5.203762	0.9770872
0.534	5.191459	0.9705315
0.535	5.179288	0.9642739
0.536	5.167249	0.9583069
0.537	5.155342	0.9526232
0.538	5.143567	0.9472161
0.539	5.131923	0.942079
0.54	5.12041	0.9372058
0.541	5.109027	0.9325906
0.542	5.097774	0.928228
0.543	5.086649	0.9241126
0.544	5.075653	0.9202397
0.545	5.064783	0.9166046
0.546	5.05404	0.913203
0.547	5.043423	0.9100308
0.548	5.03293	0.9070842
0.549	5.02256	0.9043599
0.55	5.012313	0.9018545
0.551	5.002188	0.8995651
0.552	4.992184	0.897489
0.553	4.9823	0.8956237
0.554	4.972534	0.893967
0.555	4.962887	0.8925171
0.556	4.953357	0.8912722
0.557	4.943944	0.8902309
0.558	4.934646	0.889392
0.559	4.925463	0.8887546
0.56	4.916395	0.888318
0.561	4.90744	0.8880819
0.562	4.898599	0.888046
0.563	4.889871	0.8882105
0.564	4.881255	0.8885757
0.565	4.872751	0.8891424
0.566	4.86436	0.8899114
0.567	4.85608	0.890884
0.568	4.847913	0.8920618
0.569	4.839859	0.8934464
0.57	4.831917	0.8950402
0.571	4.824089	0.8968455
0.572	4.816375	0.8988652
0.573	4.808776	0.9011024
0.574	4.801293	0.9035607
0.575	4.793929	0.9062439
0.576	4.786684	0.9091563
0.577	4.779561	0.9123028
0.578	4.772562	0.9156883
0.579	4.765689	0.9193187
0.58	4.758947	0.9231998
0.581	4.752337	0.9273385
0.582	4.745866	0.9317417
0.583	4.739536	0.9364173
0.584	4.733354	0.9413735
0.585	4.727325	0.9466193
0.586	4.721456	0.9521641
0.587	4.715755	0.9580184
0.588	4.710229	0.9641931
0.589	4.704889	0.9706999
0.59	4.699745	0.9775516
0.591	4.69481	0.9847613
0.592	4.690097	0.9923436
0.593	4.68562	1.000314
0.594	4.681398	1.008687
0.595	4.67745	1.017482
0.596	4.673798	1.026716
0.597	4.670465	1.036407
0.598	4.66748	1.046577
0.599	4.664873	1.057246
0.6	4.662681	1.068436
0.601	4.660942	1.08017
0.602	4.659702	1.092471
0.603	4.659012	1.105362
0.604	4.658929	1.118867
0.605	4.659518	1.133011
0.606	4.660854	1.147815
0.607	4.663021	1.163301
0.608	4.666114	1.179486
0.609	4.67024	1.196386
0.61	4.675523	1.214009
0.611	4.682101	1.232356
0.612	4.690132	1.251419
0.613	4.699793	1.271174
0.614	4.711283	1.291578
0.615	4.724826	1.312564
0.616	4.740671	1.334034
0.617	4.759092	1.355848
0.618	4.780389	1.377813
0.619	4.804882	1.399669
0.62	4.832908	1.421075
0.621	4.864805	1.441587
0.622	4.900897	1.460636
0.623	4.941463	1.47751
0.624	4.986696	1.491331
0.625	5.036647	1.501044
0.626	5.091148	1.505418
0.627	5.149721	1.503073
0.628	5.211473	1.492551
0.629	5.274999	1.472435
0.63	5.33831	1.441535
0.631	5.398844	1.399144
0.632	5.453578	1.345315
0.633	5.499301	1.281123
0.634	5.533027	1.208807
0.635	5.552501	1.131719
0.636	5.556671	1.054029
0.637	5.546021	0.9802145
0.638	5.522667	0.9144343
0.639	5.490201	0.8598766
0.64	5.453294	0.8181636
0.641	5.41703	0.7888572
0.642	5.385916	0.7692089
0.643	5.362595	0.7544832
0.644	5.346742	0.7392108
0.645	5.334987	0.7191963
0.646	5.322387	0.693191
0.647	5.304667	0.6630267
0.648	5.279744	0.6322262
0.649	5.247816	0.604287
0.65	5.210548	0.5816666
0.651	5.170372	0.5655481
0.652	5.129282	0.5548867
0.653	5.08732	0.5492719
0.654	5.044993	0.5487133
0.655	5.002742	0.5530914
0.656	4.960879	0.5622945
0.657	4.919621	0.5762855
0.658	4.879141	0.5951343
0.659	4.839617	0.6190323
0.66	4.801273	0.6482996
0.661	4.764434	0.6833871
0.662	4.729578	0.7248746
0.663	4.697405	0.7734597
0.664	4.668926	0.8299311
0.665	4.645569	0.8951117
0.666	4.629303	0.9697525
0.667	4.622777	1.054348
0.668	4.629425	1.148838
0.669	4.653484	1.252172
0.67	4.699812	1.361724
0.671	4.773368	1.472635
0.672	4.878188	1.577275
0.673	5.01582	1.66517
0.674	5.183424	1.723898
0.675	5.372199	1.741366
0.676	5.567305	1.709362
0.677	5.750339	1.627103
0.678	5.904121	1.502654
0.679	6.017552	1.350765
0.68	6.087813	1.188129
0.681	6.119081	1.028865
0.682	6.11934	0.8822693
0.683	6.097345	0.7528806
0.684	6.060787	0.6417578
0.685	6.015623	0.5479084
0.686	5.966098	0.4693842
0.687	5.915061	0.4039613
0.688	5.864328	0.3494994
0.689	5.815001	0.3040987
0.69	5.767696	0.2661444
0.691	5.722723	0.2342977
0.692	5.68019	0.2074635
0.693	5.640088	0.1847523
0.694	5.602336	0.1654436
0.695	5.566813	0.1489538
0.696	5.533381	0.1348095
0.697	5.501895	0.1226256
0.698	5.472211	0.1120874
0.699	5.444191	0.1029373
0.7	5.417705	0.09496299
0.701	5.392632	0.08798894
0.702	5.368862	0.0818694
0.703	5.346293	0.07648279
0.704	5.324832	0.07172724
0.705	5.304394	0.06751705
0.706	5.284902	0.06377982
0.707	5.266287	0.06045416
0.708	5.248486	0.0574878
0.709	5.231439	0.05483608
0.71	5.215095	0.05246071
0.711	5.199407	0.05032874
0.712	5.18433	0.04841175
0.713	5.169824	0.04668511
0.714	5.155854	0.04512744
0.715	5.142387	0.04372012
0.716	5.129391	0.04244689
0.717	5.116839	0.04129352
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1.455	4.093796	0.0001477706
1.4575	4.093251	0.0001472695
1.46	4.092709	0.000146772
1.4625	4.09217	0.0001462779
1.465	4.091635	0.0001457872
1.4675	4.091102	0.0001452999
1.47	4.090573	0.0001448159
1.4725	4.090047	0.0001443352
1.475	4.089524	0.0001438578
1.4775	4.089004	0.0001433836
1.48	4.088487	0.0001429126
1.4825	4.087973	0.0001424448
1.485	4.087462	0.0001419801
1.4875	4.086954	0.0001415186
1.49	4.086449	0.0001410601
1.4925	4.085947	0.0001406046
1.495	4.085448	0.0001401522
1.4975	4.084952	0.0001397027
1.5	4.084458	0.0001392562
1.5025	4.083967	0.0001388126
1.505	4.08348	0.0001383719
1.5075	4.082994	0.0001379341
1.51	4.082512	0.0001374991
1.5125	4.082032	0.000137067
1.515	4.081556	0.0001366376
1.5175	4.081081	0.0001362109
1.52	4.08061	0.000135787
1.5225	4.080141	0.0001353658
1.525	4.079675	0.0001349473
1.5275	4.079211	0.0001345314
1.53	4.07875	0.0001341182
1.5325	4.078292	0.0001337075
1.535	4.077836	0.0001332994
1.5375	4.077382	0.0001328939
1.54	4.076931	0.0001324909
1.5425	4.076483	0.0001320904
1.545	4.076037	0.0001316924
1.5475	4.075594	0.0001312968
1.55	4.075153	0.0001309037
1.5525	4.074714	0.000130513
1.555	4.074278	0.0001301247
1.5575	4.073844	0.0001297387
1.56	4.073413	0.0001293551
1.5625	4.072984	0.0001289737
1.565	4.072557	0.0001285947
1.5675	4.072132	0.000128218
1.57	4.07171	0.0001278436
1.5725	4.07129	0.0001274713
1.575	4.070873	0.0001271013
1.5775	4.070457	0.0001267335
1.58	4.070044	0.0001263679
1.5825	4.069633	0.0001260044
1.585	4.069224	0.0001256431
1.5875	4.068818	0.0001252839
1.59	4.068413	0.0001249268
1.5925	4.068011	0.0001245717
1.595	4.067611	0.0001242188
1.5975	4.067213	0.0001238678
1.6	4.066817	0.0001235189
1.6025	4.066423	0.0001231721
1.605	4.066031	0.0001228272
1.6075	4.065642	0.0001224842
1.61	4.065254	0.0001221433
1.6125	4.064868	0.0001218043
1.615	4.064485	0.0001214672
1.6175	4.064103	0.000121132
1.62	4.063723	0.0001207987
1.6225	4.063346	0.0001204673
1.625	4.06297	0.0001201377
1.6275	4.062596	0.00011981
1.63	4.062224	0.0001194841
1.6325	4.061854	0.00011916
1.635	4.061486	0.0001188377
1.6375	4.06112	0.0001185172
1.64	4.060756	0.0001181984
1.6425	4.060393	0.0001178814
1.645	4.060033	0.0001175662
1.6475	4.059674	0.0001172526
1.65	4.059317	0.0001169408
1.6525	4.058962	0.0001166307
1.655	4.058608	0.0001163222
1.6575	4.058257	0.0001160154
1.66	4.057907	0.0001157103
1.6625	4.057559	0.0001154068
1.665	4.057213	0.0001151049
1.6675	4.056868	0.0001148046
1.67	4.056525	0.0001145059
1.6725	4.056184	0.0001142089
1.675	4.055845	0.0001139133
1.6775	4.055507	0.0001136194
1.68	4.055171	0.000113327
1.6825	4.054836	0.0001130361
1.685	4.054504	0.0001127468
1.6875	4.054173	0.0001124589
1.69	4.053843	0.0001121726

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: —

Plot