Optical constants

Refractive index of MoS₂ (Molybdenum disulfide)

Hsu et al. 2019: monolayer (1L) film; n,k 0.40–0.86 µm

Data: tabulated nk
Range: 0.397–0.857 µm
Points: 2001
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 4.41307
Extinction coefficient k: 1.231

Permittivity ε₁: 17.9598
Permittivity ε₂: 10.865

Absorption coefficient α: 263262 cm⁻¹
Penetration depth δ = λ/(2πk): 75.97 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -2.6087 µm⁻¹

Group index n_g: 5.94593
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): Hsu et al. 2019: monolayer (1L) film; n,k 0.40–0.86 µm
mos2 = ls.fetch_refractiveindex("main", "MoS2", "Hsu-1L", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(mos2.range_nm)  # (396.97, 856.97) 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_a153c7ee4149/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/hsu-2019-1l).

# ... 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=856, 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

Monolayer (1-layer, 1L)

Conditions

film thickness: 1L

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

2001 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), Hsu et al. 2019: monolayer (1L) film; n,k 0.40–0.86 µm: n and k versus wavelength
λ (µm)	n	k
0.39697	2.8095	3.0444
0.39719	2.781	3.0253
0.39741	2.8057	2.9911
0.39762	2.8245	2.9709
0.39784	2.8349	2.9555
0.39806	2.8537	2.9353
0.39827	2.8696	2.9184
0.39849	2.8838	2.9034
0.39871	2.8959	2.8869
0.39893	2.9105	2.873
0.39914	2.9263	2.8573
0.39936	2.9397	2.8484
0.39958	2.9517	2.837
0.3998	2.9625	2.8272
0.40001	2.9746	2.8175
0.40023	2.9879	2.8086
0.40045	3.0	2.7997
0.40066	3.0095	2.7934
0.40088	3.019	2.7879
0.4011	3.0286	2.7815
0.40132	3.0381	2.7769
0.40153	3.0476	2.7731
0.40175	3.0571	2.7701
0.40197	3.0679	2.7671
0.40219	3.08	2.7642
0.4024	3.0908	2.7612
0.40262	3.1003	2.7582
0.40284	3.1086	2.7561
0.40306	3.1168	2.754
0.40327	3.1263	2.7519
0.40349	3.1346	2.7498
0.40371	3.1429	2.7494
0.40393	3.1511	2.7498
0.40414	3.1594	2.7494
0.40436	3.1676	2.7506
0.40458	3.1759	2.7511
0.4048	3.1841	2.7523
0.40501	3.1924	2.7527
0.40523	3.1994	2.754
0.40545	3.2063	2.7544
0.40567	3.2133	2.7557
0.40589	3.2203	2.757
0.4061	3.2286	2.7574
0.40632	3.2381	2.7587
0.40654	3.2463	2.7608
0.40676	3.2559	2.7629
0.40697	3.2654	2.7642
0.40719	3.2749	2.7654
0.40741	3.2844	2.7676
0.40763	3.294	2.7697
0.40785	3.3035	2.7726
0.40806	3.313	2.7739
0.40828	3.3225	2.776
0.4085	3.3321	2.7781
0.40872	3.3403	2.7811
0.40894	3.3486	2.7841
0.40915	3.3581	2.787
0.40937	3.3663	2.7908
0.40959	3.3746	2.7947
0.40981	3.3829	2.7985
0.41002	3.3911	2.8031
0.41024	3.4006	2.8078
0.41046	3.4102	2.8124
0.41068	3.4197	2.8171
0.4109	3.4292	2.8217
0.41111	3.4387	2.8264
0.41133	3.4495	2.8319
0.41155	3.4603	2.8366
0.41177	3.4711	2.8421
0.41199	3.4844	2.8467
0.41221	3.4978	2.8522
0.41242	3.5111	2.8586
0.41264	3.5244	2.8649
0.41286	3.5378	2.8704
0.41308	3.5511	2.8759
0.4133	3.5644	2.8806
0.41351	3.5765	2.8861
0.41373	3.5886	2.8924
0.41395	3.6006	2.8988
0.41417	3.6127	2.9051
0.41439	3.6248	2.9115
0.41461	3.6368	2.9178
0.41482	3.6489	2.925
0.41504	3.661	2.9322
0.41526	3.6717	2.9394
0.41548	3.6838	2.9466
0.4157	3.6959	2.9538
0.41592	3.7079	2.961
0.41613	3.7213	2.9682
0.41635	3.7346	2.9754
0.41657	3.7479	2.9826
0.41679	3.7625	2.9898
0.41701	3.7771	2.9961
0.41723	3.7917	3.0025
0.41745	3.8063	3.008
0.41766	3.821	3.0143
0.41788	3.8356	3.0198
0.4181	3.8502	3.0253
0.41832	3.8648	3.0308
0.41854	3.8794	3.0363
0.41876	3.894	3.0418
0.41897	3.9086	3.0465
0.41919	3.9244	3.0512
0.41941	3.939	3.0567
0.41963	3.9549	3.0613
0.41985	3.9708	3.066
0.42007	3.9854	3.0706
0.42029	4.0	3.0753
0.42051	4.0159	3.0791
0.42072	4.0317	3.0838
0.42094	4.0476	3.0876
0.42116	4.0622	3.0922
0.42138	4.0768	3.096
0.4216	4.0927	3.099
0.42182	4.1098	3.102
0.42204	4.1257	3.1049
0.42226	4.1429	3.107
0.42247	4.1587	3.1091
0.42269	4.1759	3.1113
0.42291	4.1917	3.1134
0.42313	4.2076	3.1155
0.42335	4.2248	3.1176
0.42357	4.2432	3.1189
0.42379	4.2603	3.121
0.42401	4.2787	3.1223
0.42423	4.2971	3.1235
0.42444	4.3156	3.124
0.42466	4.3352	3.1252
0.42488	4.3537	3.1257
0.4251	4.3708	3.1261
0.42532	4.3892	3.1265
0.42554	4.4076	3.1269
0.42576	4.426	3.1273
0.42598	4.4444	3.1269
0.4262	4.4629	3.1273
0.42642	4.4813	3.1278
0.42663	4.4997	3.1273
0.42685	4.5168	3.1269
0.42707	4.5352	3.1257
0.42729	4.5537	3.1244
0.42751	4.5721	3.1231
0.42773	4.5917	3.1218
0.42795	4.6114	3.1197
0.42817	4.6311	3.1176
0.42839	4.6521	3.1155
0.42861	4.6717	3.1134
0.42883	4.6902	3.1113
0.42905	4.7098	3.1075
0.42927	4.7283	3.1045
0.42948	4.7467	3.1007
0.4297	4.7663	3.096
0.42992	4.786	3.0914
0.43014	4.8057	3.0867
0.43036	4.8254	3.0821
0.43058	4.8438	3.0774
0.4308	4.8635	3.0719
0.43102	4.8819	3.0664
0.43124	4.9003	3.0609
0.43146	4.9187	3.0554
0.43168	4.9371	3.0499
0.4319	4.9556	3.0435
0.43212	4.9752	3.0372
0.43234	4.9937	3.0317
0.43256	5.0133	3.0245
0.43278	5.033	3.0173
0.433	5.0514	3.0093
0.43321	5.0698	3.0012
0.43343	5.0883	2.9923
0.43365	5.1067	2.9834
0.43387	5.1251	2.9737
0.43409	5.1422	2.964
0.43431	5.1594	2.9542
0.43453	5.1765	2.9436
0.43475	5.1937	2.9331
0.43497	5.2108	2.9216
0.43519	5.2279	2.9094
0.43541	5.2438	2.8971
0.43563	5.261	2.8848
0.43585	5.2768	2.8734
0.43607	5.2927	2.8611
0.43629	5.3098	2.8488
0.43651	5.3257	2.8366
0.43673	5.3416	2.8243
0.43695	5.3562	2.812
0.43717	5.3721	2.7997
0.43739	5.3879	2.7875
0.43761	5.4038	2.7743
0.43783	5.4184	2.7612
0.43805	5.4343	2.7481
0.43827	5.4489	2.735
0.43849	5.4635	2.7218
0.43871	5.4781	2.7087
0.43893	5.4914	2.6956
0.43915	5.506	2.6816
0.43937	5.5206	2.6685
0.43959	5.534	2.6554
0.43981	5.5473	2.6423
0.44003	5.5606	2.6291
0.44025	5.5752	2.616
0.44047	5.5886	2.6038
0.44069	5.6019	2.5906
0.44091	5.6152	2.5784
0.44113	5.6286	2.5661
0.44135	5.6406	2.553
0.44157	5.6527	2.5407
0.44179	5.6648	2.5284
0.44201	5.6768	2.5161
0.44223	5.6889	2.503
0.44245	5.6997	2.4907
0.44267	5.7092	2.4776
0.44289	5.7187	2.4653
0.44311	5.7283	2.4522
0.44333	5.7378	2.4399
0.44355	5.746	2.4268
0.44377	5.7543	2.4137
0.44399	5.7625	2.4006
0.44421	5.7695	2.3866
0.44443	5.7765	2.3735
0.44465	5.7835	2.3612
0.44487	5.7905	2.3481
0.44509	5.7975	2.3358
0.44531	5.8044	2.3235
0.44553	5.8114	2.3113
0.44575	5.8171	2.2981
0.44597	5.8241	2.2859
0.44619	5.8311	2.2736
0.44641	5.8381	2.2622
0.44663	5.8438	2.2499
0.44685	5.8495	2.2385
0.44707	5.8552	2.2262
0.44729	5.861	2.2148
0.44751	5.8667	2.2042
0.44774	5.8724	2.1936
0.44796	5.8781	2.1822
0.44818	5.8838	2.1716
0.4484	5.8895	2.161
0.44862	5.8952	2.1504
0.44884	5.8997	2.1398
0.44906	5.9054	2.1301
0.44928	5.9111	2.1195
0.4495	5.9168	2.1089
0.44972	5.9225	2.0984
0.44994	5.9283	2.0886
0.45016	5.934	2.078
0.45038	5.9397	2.0683
0.4506	5.9441	2.0586
0.45082	5.9498	2.0488
0.45104	5.9556	2.0382
0.45127	5.9613	2.0285
0.45149	5.9657	2.0188
0.45171	5.9702	2.009
0.45193	5.9733	1.9993
0.45215	5.9778	1.9896
0.45237	5.9822	1.9798
0.45259	5.9854	1.9709
0.45281	5.9886	1.9612
0.45303	5.9917	1.9515
0.45325	5.9949	1.9417
0.45347	5.9981	1.9329
0.45369	6.0	1.9231
0.45391	6.0032	1.9134
0.45414	6.0051	1.9036
0.45436	6.007	1.8939
0.45458	6.0089	1.8842
0.4548	6.0108	1.8744
0.45502	6.0127	1.8647
0.45524	6.0146	1.855
0.45546	6.0165	1.8461
0.45568	6.0171	1.8372
0.4559	6.019	1.8283
0.45612	6.021	1.8194
0.45635	6.0216	1.8105
0.45657	6.0235	1.8016
0.45679	6.0241	1.7927
0.45701	6.026	1.7847
0.45723	6.0267	1.7767
0.45745	6.0286	1.7686
0.45767	6.0292	1.7614
0.45789	6.0298	1.7534
0.45811	6.0305	1.7453
0.45834	6.0311	1.7373
0.45856	6.0317	1.7293
0.45878	6.0324	1.7212
0.459	6.033	1.7132
0.45922	6.0337	1.7051
0.45944	6.0343	1.6979
0.45966	6.0349	1.6899
0.45988	6.0356	1.6818
0.46011	6.0362	1.6738
0.46033	6.0356	1.6658
0.46055	6.0362	1.6577
0.46077	6.0356	1.6497
0.46099	6.0362	1.6416
0.46121	6.0356	1.6344
0.46143	6.0362	1.6272
0.46165	6.0356	1.6192
0.46188	6.0362	1.6112
0.4621	6.0356	1.6031
0.46232	6.0362	1.5951
0.46254	6.0356	1.587
0.46276	6.0337	1.579
0.46298	6.033	1.5718
0.4632	6.0311	1.5646
0.46343	6.0292	1.5574
0.46365	6.0286	1.5502
0.46387	6.0267	1.543
0.46409	6.026	1.5358
0.46431	6.0241	1.5286
0.46453	6.0235	1.5214
0.46475	6.0216	1.5142
0.46498	6.0197	1.5079
0.4652	6.0178	1.5015
0.46542	6.0159	1.4952
0.46564	6.014	1.4888
0.46586	6.0121	1.4825
0.46608	6.0102	1.4761
0.46631	6.0083	1.4698
0.46653	6.0063	1.4634
0.46675	6.0044	1.4571
0.46697	6.0025	1.4507
0.46719	6.0006	1.4444
0.46741	5.9987	1.438
0.46764	5.9968	1.4317
0.46786	5.9937	1.4253
0.46808	5.9917	1.419
0.4683	5.9898	1.4126
0.46852	5.9867	1.4063
0.46875	5.9848	1.3999
0.46897	5.9816	1.3936
0.46919	5.9797	1.3872
0.46941	5.9778	1.3809
0.46963	5.9746	1.3745
0.46985	5.9727	1.3682
0.47008	5.9708	1.3618
0.4703	5.9676	1.3555
0.47052	5.9657	1.3491
0.47074	5.9625	1.3428
0.47096	5.9594	1.3373
0.47119	5.9575	1.3318
0.47141	5.9543	1.3263
0.47163	5.9511	1.3208
0.47185	5.9492	1.3153
0.47207	5.946	1.3098
0.4723	5.9441	1.3043
0.47252	5.941	1.2988
0.47274	5.9378	1.2933
0.47296	5.9359	1.2878
0.47318	5.9327	1.2831
0.47341	5.9295	1.2785
0.47363	5.9263	1.2738
0.47385	5.9232	1.2691
0.47407	5.92	1.2645
0.4743	5.9181	1.259
0.47452	5.9149	1.2535
0.47474	5.9117	1.2488
0.47496	5.9098	1.2442
0.47518	5.9067	1.2395
0.47541	5.9035	1.2349
0.47563	5.9003	1.2302
0.47585	5.8971	1.2256
0.47607	5.894	1.2217
0.4763	5.8895	1.2179
0.47652	5.8863	1.2133
0.47674	5.8832	1.2086
0.47696	5.8813	1.204
0.47718	5.8781	1.1993
0.47741	5.8749	1.1955
0.47763	5.8705	1.1917
0.47785	5.8673	1.1879
0.47807	5.8641	1.1832
0.4783	5.8597	1.1786
0.47852	5.8565	1.1739
0.47874	5.8533	1.1693
0.47896	5.8489	1.1654
0.47919	5.8457	1.1616
0.47941	5.8425	1.157
0.47963	5.8394	1.1523
0.47985	5.8362	1.1477
0.48008	5.833	1.1439
0.4803	5.8286	1.14
0.48052	5.8254	1.1362
0.48074	5.8222	1.1316
0.48097	5.819	1.1278
0.48119	5.8159	1.124
0.48141	5.8127	1.1202
0.48163	5.8095	1.1163
0.48186	5.8063	1.1125
0.48208	5.8032	1.1096
0.4823	5.8	1.1058
0.48253	5.7968	1.102
0.48275	5.7937	1.0981
0.48297	5.7905	1.0943
0.48319	5.7873	1.0914
0.48342	5.7841	1.0876
0.48364	5.781	1.0838
0.48386	5.7778	1.0799
0.48408	5.7746	1.077
0.48431	5.7714	1.0732
0.48453	5.7683	1.0694
0.48475	5.7651	1.0664
0.48498	5.7619	1.0634
0.4852	5.7575	1.0605
0.48542	5.7543	1.0575
0.48564	5.7511	1.0545
0.48587	5.7479	1.0516
0.48609	5.7448	1.0486
0.48631	5.7416	1.0465
0.48654	5.7384	1.0435
0.48676	5.7352	1.0406
0.48698	5.7321	1.0376
0.4872	5.7276	1.0355
0.48743	5.7244	1.0325
0.48765	5.7213	1.0296
0.48787	5.7168	1.0275
0.4881	5.7137	1.0245
0.48832	5.7105	1.0215
0.48854	5.7073	1.0194
0.48877	5.7041	1.0164
0.48899	5.701	1.0135
0.48921	5.6965	1.0114
0.48943	5.6933	1.0093
0.48966	5.6902	1.0063
0.48988	5.6857	1.0042
0.4901	5.6825	1.0021
0.49033	5.6794	0.99994
0.49055	5.6762	0.99783
0.49077	5.673	0.99571
0.491	5.6698	0.99359
0.49122	5.6667	0.99148
0.49144	5.6622	0.98936
0.49167	5.659	0.98724
0.49189	5.6559	0.98428
0.49211	5.6527	0.98216
0.49234	5.6495	0.98005
0.49256	5.6463	0.97708
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0.85601	5.0741	0.0
0.85625	5.1238	0.0
0.85649	5.1714	0.0
0.85673	5.2698	0.0

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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