Optical constants

Refractive index of WS₂ (Tungsten disulfide)

Hsu et al. 2019: 2-layer (2L) film; n,k 0.40–0.85 µm

Data: tabulated nk
Range: 0.397–0.8502 µm
Points: 1973
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 4.37507
Extinction coefficient k: 0.52814

Permittivity ε₁: 18.8623
Permittivity ε₂: 4.62129

Absorption coefficient α: 112948 cm⁻¹
Penetration depth δ = λ/(2πk): 177.073 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -14.7826 µm⁻¹

Group index n_g: 13.0613
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

# WS2 (Tungsten disulfide): Hsu et al. 2019: 2-layer (2L) film; n,k 0.40–0.85 µm
ws2 = ls.fetch_refractiveindex("main", "WS2", "Hsu-2L", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ws2.range_nm)  # (396.97, 850.23) nm
eps = ws2.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_e9421150b16c/lightsmith"
ws2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(ws2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (ws2/hsu-2019-2l).

# ... load ws2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=ws2)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=850, 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

2-layer (2L)

Conditions

film thickness: 2L

References

C. Hsu, R. Frisenda, R. Schmidt, A. Arora, S. M. de Vasconcellos, R. Bratschitsch, H. S. J. van der Zant, A. Castellanos-Gomez. Thickness-dependent refractive index of 1L, 2L, and 3L MoS₂, MoSe₂, WS₂, and WSe₂. Adv. Optical Mater. 7, 1900239 (2019) (Numerical data kindly provided by Andres Castellanos-Gomez)

doi:10.1002/adom.201900239 Thickness‐Dependent Refractive Index of 1L, 2L, and 3L MoS 2 , MoSe 2 , WS 2 , and WSe 2, Advanced Optical Materials (2019)

Cite

Chunwei Hsu et al.. Thickness‐Dependent Refractive Index of 1L, 2L, and 3L MoS 2 , MoSe 2 , WS 2 , and WSe 2. Advanced Optical Materials, 7, 1900239 (2019), doi:10.1002/adom.201900239; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

1973 rows as published

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

WS2 (Tungsten disulfide), Hsu et al. 2019: 2-layer (2L) film; n,k 0.40–0.85 µm: n and k versus wavelength
λ (µm)	n	k
0.39697	4.3175	3.0079
0.39719	4.2407	2.6984
0.39741	4.2063	2.6428
0.39762	4.1735	2.6054
0.39784	4.1338	2.5295
0.39806	4.0986	2.517
0.39827	4.0658	2.4977
0.39849	4.0873	2.517
0.39871	4.0431	2.4864
0.39893	4.0374	2.483
0.39914	4.0317	2.4773
0.39936	4.0873	2.5011
0.39958	4.2268	2.5794
0.3998	4.4342	2.7188
0.40001	4.6122	2.8333
0.40023	4.8107	2.9614
0.40045	5.0113	3.0941
0.40066	5.2143	3.2358
0.40088	5.3673	3.3526
0.4011	5.4569	3.4331
0.40132	5.4785	3.4501
0.40153	5.5204	3.4875
0.40175	5.5714	3.534
0.40197	5.6247	3.5828
0.40219	5.6712	3.627
0.4024	5.72	3.6757
0.40262	5.7596	3.7109
0.40284	5.7971	3.7483
0.40306	5.8118	3.763
0.40327	5.8016	3.7506
0.40349	5.7823	3.7267
0.40371	5.7721	3.7097
0.40393	5.7574	3.6859
0.40414	5.7449	3.6667
0.40436	5.7279	3.6383
0.40458	5.72	3.6213
0.4048	5.7143	3.6088
0.40501	5.72	3.61
0.40523	5.7166	3.5998
0.40545	5.7109	3.585
0.40567	5.7143	3.5771
0.40589	5.72	3.5714
0.4061	5.7324	3.5703
0.40632	5.7608	3.5828
0.40654	5.7982	3.6088
0.40676	5.8356	3.6349
0.40697	5.8776	3.6701
0.40719	5.9104	3.6961
0.40741	5.9478	3.7313
0.40763	5.983	3.7664
0.40785	6.0113	3.7925
0.40806	6.0306	3.805
0.40828	6.0431	3.8129
0.4085	6.0533	3.814
0.40872	6.0658	3.822
0.40894	6.0737	3.8186
0.40915	6.0839	3.8197
0.40937	6.0941	3.8231
0.40959	6.0998	3.822
0.40981	6.1032	3.814
0.41002	6.1066	3.8084
0.41024	6.1077	3.7959
0.41046	6.1111	3.7902
0.41068	6.11	3.7755
0.4109	6.1088	3.7608
0.41111	6.1077	3.746
0.41133	6.1134	3.7449
0.41155	6.119	3.7438
0.41177	6.127	3.7472
0.41199	6.1304	3.7415
0.41221	6.1315	3.7358
0.41242	6.1281	3.7256
0.41264	6.1247	3.7177
0.41286	6.1145	3.6984
0.41308	6.1134	3.6927
0.4133	6.1077	3.678
0.41351	6.1043	3.6701
0.41373	6.0986	3.6576
0.41395	6.0975	3.6519
0.41417	6.0964	3.644
0.41439	6.0975	3.6406
0.41461	6.0896	3.6213
0.41482	6.0839	3.6088
0.41504	6.085	3.6032
0.41526	6.0907	3.6066
0.41548	6.0964	3.6122
0.4157	6.0975	3.6111
0.41592	6.1032	3.6168
0.41613	6.1111	3.627
0.41635	6.1168	3.6372
0.41657	6.1179	3.6428
0.41679	6.119	3.644
0.41701	6.1202	3.6428
0.41723	6.1236	3.6462
0.41745	6.1224	3.6406
0.41766	6.1213	3.6372
0.41788	6.1224	3.6338
0.4181	6.1259	3.6349
0.41832	6.1224	3.627
0.41854	6.119	3.6213
0.41876	6.1179	3.6179
0.41897	6.1213	3.6213
0.41919	6.1224	3.6202
0.41941	6.119	3.61
0.41963	6.1156	3.5998
0.41985	6.1168	3.5986
0.42007	6.1179	3.5952
0.42029	6.1213	3.5986
0.42051	6.1224	3.5998
0.42072	6.1259	3.6054
0.42094	6.1361	3.6247
0.42116	6.1417	3.6372
0.42138	6.1497	3.6519
0.4216	6.1576	3.6689
0.42182	6.1655	3.6814
0.42204	6.1735	3.6961
0.42226	6.1814	3.7109
0.42247	6.1893	3.7256
0.42269	6.2018	3.7494
0.42291	6.2143	3.7732
0.42313	6.2245	3.7948
0.42335	6.2324	3.814
0.42357	6.2404	3.8333
0.42379	6.2506	3.8549
0.42401	6.2608	3.8764
0.42423	6.2687	3.8934
0.42444	6.2766	3.9127
0.42466	6.2868	3.9365
0.42488	6.2971	3.9603
0.4251	6.3073	3.9841
0.42532	6.3152	4.0102
0.42554	6.3231	4.034
0.42576	6.3265	4.0533
0.42598	6.3322	4.0726
0.4262	6.3379	4.0896
0.42642	6.3435	4.1088
0.42663	6.3492	4.1281
0.42685	6.3549	4.1428
0.42707	6.3583	4.1576
0.42729	6.3639	4.1746
0.42751	6.3673	4.1916
0.42773	6.3685	4.2063
0.42795	6.3673	4.2188
0.42817	6.3662	4.2313
0.42839	6.3673	4.2438
0.42861	6.3662	4.254
0.42883	6.3673	4.2642
0.42905	6.3685	4.2766
0.42927	6.3696	4.2914
0.42948	6.3707	4.3061
0.4297	6.3719	4.3163
0.42992	6.3707	4.3288
0.43014	6.3696	4.3435
0.43036	6.3685	4.3537
0.43058	6.3651	4.3617
0.4308	6.3639	4.3651
0.43102	6.3628	4.3685
0.43124	6.3594	4.3719
0.43146	6.356	4.3753
0.43168	6.3526	4.3741
0.4319	6.3492	4.3753
0.43212	6.3458	4.3719
0.43234	6.3401	4.3685
0.43256	6.3345	4.3651
0.43278	6.3288	4.3617
0.433	6.3231	4.356
0.43321	6.3175	4.3481
0.43343	6.3095	4.3424
0.43365	6.3016	4.3367
0.43387	6.2937	4.3288
0.43409	6.2857	4.3186
0.43431	6.2778	4.3106
0.43453	6.2698	4.305
0.43475	6.2619	4.2993
0.43497	6.254	4.2914
0.43519	6.246	4.2857
0.43541	6.2381	4.2823
0.43563	6.2302	4.2789
0.43585	6.2222	4.2732
0.43607	6.2143	4.263
0.43629	6.2063	4.2574
0.43651	6.2007	4.2494
0.43673	6.195	4.2415
0.43695	6.1893	4.2313
0.43717	6.1814	4.2211
0.43739	6.1757	4.2109
0.43761	6.1701	4.2029
0.43783	6.1644	4.1927
0.43805	6.1587	4.1848
0.43827	6.1531	4.1746
0.43849	6.1474	4.1621
0.43871	6.144	4.1496
0.43893	6.1383	4.1372
0.43915	6.1327	4.1247
0.43937	6.1293	4.1122
0.43959	6.1236	4.0998
0.43981	6.1179	4.085
0.44003	6.1122	4.0726
0.44025	6.1088	4.0601
0.44047	6.1077	4.0499
0.44069	6.1066	4.0374
0.44091	6.1032	4.0249
0.44113	6.0998	4.0079
0.44135	6.0964	3.9932
0.44157	6.093	3.9784
0.44179	6.0896	3.9637
0.44201	6.0839	3.9467
0.44223	6.0782	3.9297
0.44245	6.0748	3.9104
0.44267	6.0714	3.8934
0.44289	6.068	3.8741
0.44311	6.0646	3.8549
0.44333	6.059	3.8356
0.44355	6.0556	3.814
0.44377	6.0522	3.7925
0.44399	6.0488	3.7732
0.44421	6.0454	3.7517
0.44443	6.0442	3.7324
0.44465	6.0431	3.7131
0.44487	6.0442	3.6916
0.44509	6.0431	3.6701
0.44531	6.042	3.6462
0.44553	6.0408	3.6224
0.44575	6.0397	3.5986
0.44597	6.0363	3.5703
0.44619	6.0351	3.5442
0.44641	6.0317	3.5159
0.44663	6.0283	3.4875
0.44685	6.0272	3.4637
0.44707	6.0238	3.4354
0.44729	6.0204	3.407
0.44751	6.0193	3.3832
0.44774	6.0159	3.3549
0.44796	6.0147	3.3311
0.44818	6.0136	3.305
0.4484	6.0125	3.2789
0.44862	6.0136	3.2551
0.44884	6.0147	3.2313
0.44906	6.0159	3.2075
0.44928	6.0193	3.1882
0.4495	6.0204	3.1644
0.44972	6.0238	3.1451
0.44994	6.0249	3.1213
0.45016	6.0261	3.0975
0.45038	6.0295	3.0782
0.4506	6.0283	3.0499
0.45082	6.0272	3.0215
0.45104	6.0283	2.9977
0.45127	6.0272	2.9694
0.45149	6.0283	2.9456
0.45171	6.0272	2.9195
0.45193	6.0261	2.8934
0.45215	6.0272	2.8696
0.45237	6.0283	2.8458
0.45259	6.0272	2.8197
0.45281	6.0261	2.7936
0.45303	6.0227	2.763
0.45325	6.0238	2.7392
0.45347	6.0227	2.7109
0.45369	6.0238	2.6893
0.45391	6.0249	2.6678
0.45414	6.0261	2.644
0.45436	6.0295	2.6247
0.45458	6.0351	2.6077
0.4548	6.0385	2.5884
0.45502	6.0442	2.5737
0.45524	6.0499	2.5589
0.45546	6.0556	2.5442
0.45568	6.059	2.5272
0.4559	6.0624	2.5102
0.45612	6.0635	2.4932
0.45635	6.0669	2.4784
0.45657	6.0658	2.4569
0.45679	6.0646	2.4354
0.45701	6.0635	2.4138
0.45723	6.0646	2.3968
0.45745	6.0658	2.3798
0.45767	6.0669	2.3628
0.45789	6.0658	2.3435
0.45811	6.0646	2.3265
0.45834	6.0612	2.3072
0.45856	6.0533	2.2834
0.45878	6.0454	2.2596
0.459	6.042	2.2426
0.45922	6.0385	2.2256
0.45944	6.0374	2.2109
0.45966	6.0363	2.1961
0.45988	6.0374	2.1837
0.46011	6.0431	2.1757
0.46033	6.0533	2.1746
0.46055	6.0567	2.1621
0.46077	6.0601	2.1519
0.46099	6.059	2.1372
0.46121	6.0646	2.1315
0.46143	6.0703	2.1258
0.46165	6.0805	2.1247
0.46188	6.0884	2.119
0.4621	6.0986	2.1179
0.46232	6.1088	2.1145
0.46254	6.1236	2.1156
0.46276	6.1383	2.1168
0.46298	6.1531	2.1179
0.4632	6.1633	2.1145
0.46343	6.1712	2.1088
0.46365	6.1814	2.1077
0.46387	6.1893	2.1043
0.46409	6.1973	2.1009
0.46431	6.2052	2.0975
0.46453	6.2132	2.0941
0.46475	6.2211	2.0907
0.46498	6.2313	2.0918
0.4652	6.2415	2.0907
0.46542	6.2562	2.0964
0.46564	6.2687	2.0998
0.46586	6.2812	2.1032
0.46608	6.2891	2.102
0.46631	6.3016	2.1077
0.46653	6.3118	2.1088
0.46675	6.322	2.1122
0.46697	6.3299	2.1111
0.46719	6.3401	2.1145
0.46741	6.3481	2.1134
0.46764	6.3628	2.1213
0.46786	6.373	2.1224
0.46808	6.3878	2.1304
0.4683	6.4002	2.136
0.46852	6.4127	2.1417
0.46875	6.4229	2.1451
0.46897	6.4354	2.1531
0.46919	6.4433	2.1542
0.46941	6.4535	2.1599
0.46963	6.4615	2.161
0.46985	6.4694	2.1621
0.47008	6.4819	2.1701
0.4703	6.4966	2.1803
0.47052	6.5068	2.1837
0.47074	6.5215	2.1939
0.47096	6.534	2.2018
0.47119	6.5465	2.212
0.47141	6.5612	2.2245
0.47163	6.576	2.237
0.47185	6.5884	2.2472
0.47207	6.6009	2.2574
0.4723	6.6088	2.2608
0.47252	6.5578	2.1916
0.47274	6.4342	2.0703
0.47296	6.3061	1.9444
0.47318	6.1735	1.814
0.47341	6.0385	1.6814
0.47363	5.9036	1.551
0.47385	5.7642	1.4206
0.47407	5.6814	1.3605
0.4743	5.6689	1.3503
0.47452	5.6587	1.3401
0.47474	5.6463	1.3299
0.47496	5.6338	1.3197
0.47518	5.619	1.3072
0.47541	5.6088	1.297
0.47563	5.5986	1.2868
0.47585	5.5884	1.2766
0.47607	5.5714	1.2642
0.4763	5.5544	1.2517
0.47652	5.5374	1.2392
0.47674	5.5227	1.229
0.47696	5.5079	1.2188
0.47718	5.4932	1.2086
0.47741	5.4762	1.1984
0.47763	5.4637	1.1905
0.47785	5.458	1.1848
0.47807	5.4524	1.1791
0.4783	5.4444	1.1735
0.47852	5.4365	1.1678
0.47874	5.4286	1.1621
0.47896	5.4229	1.1565
0.47919	5.415	1.1508
0.47941	5.407	1.1451
0.47963	5.3968	1.1394
0.47985	5.3889	1.1338
0.48008	5.3787	1.1281
0.4803	5.3685	1.1224
0.48052	5.3583	1.1168
0.48074	5.3503	1.1111
0.48097	5.3356	1.1032
0.48119	5.3209	1.0952
0.48141	5.3061	1.0873
0.48163	5.2937	1.0794
0.48186	5.2789	1.0714
0.48208	5.2619	1.0635
0.4823	5.2472	1.0578
0.48253	5.2347	1.0521
0.48275	5.2222	1.0465
0.48297	5.2098	1.0408
0.48319	5.1973	1.0351
0.48342	5.1893	1.0317
0.48364	5.1837	1.0283
0.48386	5.178	1.0249
0.48408	5.1701	1.0215
0.48431	5.1644	1.0181
0.48453	5.1565	1.0147
0.48475	5.1531	1.0136
0.48498	5.1451	1.0102
0.4852	5.1349	1.0068
0.48542	5.1247	1.0034
0.48564	5.1168	0.99999
0.48587	5.1088	0.99659
0.48609	5.1054	0.99545
0.48631	5.0952	0.99205
0.48654	5.0873	0.98865
0.48676	5.0816	0.98752
0.48698	5.0737	0.98412
0.4872	5.0658	0.98072
0.48743	5.0578	0.97958
0.48765	5.0476	0.97618
0.48787	5.0374	0.97278
0.4881	5.0295	0.97164
0.48832	5.0215	0.96824
0.48854	5.0113	0.96484
0.48877	5.0034	0.96371
0.48899	4.9932	0.96031
0.48921	4.983	0.95691
0.48943	4.9751	0.95577
0.48966	4.9649	0.95237
0.48988	4.9546	0.94897
0.4901	4.9467	0.94784
0.49033	4.9342	0.94443
0.49055	4.924	0.94103
0.49077	4.9138	0.9399
0.491	4.9036	0.9365
0.49122	4.8934	0.9331
0.49144	4.8832	0.93196
0.49167	4.873	0.92856
0.49189	4.8651	0.92743
0.49211	4.8571	0.92629
0.49234	4.8492	0.92289
0.49256	4.8413	0.92176
0.49278	4.8333	0.92062
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0.61182	3.5714	1.0002
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0.6132	3.5261	1.143
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0.84783	3.6689	0.0057229
0.84807	3.6746	0.0068968
0.84831	3.6712	0.0094206
0.84855	3.6633	0.016358
0.84879	3.6576	0.017572
0.84903	3.6497	0.019173
0.84927	3.6395	0.026251
0.84951	3.6383	0.028724
0.84975	3.6281	0.034014
0.84999	3.6247	0.041506
0.85023	3.619	0.04088

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: —

WS₂ (Tungsten disulfide): all datasets

Bulk

2D structures

Multilayer flakes

About WS2 (Tungsten disulfide)

Tungsten disulfide (WS₂) is a layered transition metal dichalcogenide that possesses distinct properties based on its structural morphology. In its three-dimensional bulk form, WS₂ has indirect bandgap semiconducting properties, which contrasts its behavior when isolated to a monolayer or few-layer forms. When exfoliated to these thin layers, WS₂ undergoes a transition to a direct bandgap semiconductor, making it intriguing for potential applications in electronics, optoelectronics, and photonics. This material's unique hexagonal structure gives it excellent lubrication capabilities, often preferred in environments with high pressures and temperatures. Furthermore, research continues into its promise in nanoelectronic devices, spintronic applications, and as a component in heterostructures with other two-dimensional materials.

Tungsten disulfide - Wikipedia

More about WS2 (Tungsten disulfide) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/WS2/nk/Hsu-2L.yml
ID: ds_e9421150b16c
API: /v1/datasets/ds_e9421150b16c

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