Optical constants

Refractive index of MoS₂ (Molybdenum disulfide)

Ermolaev et al. 2020: monolayer (1L) film; n,k 0.290–3.30 µm

Data: tabulated nk
Range: 0.29–3.3 µm
Points: 3011
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 4.83232
Extinction coefficient k: 1.14113

Permittivity ε₁: 22.0491
Permittivity ε₂: 11.0286

Absorption coefficient α: 244042 cm⁻¹
Penetration depth δ = λ/(2πk): 81.9531 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -3.94 µm⁻¹

Group index n_g: 7.14746
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): Ermolaev et al. 2020: monolayer (1L) film; n,k 0.290–3.30 µm
mos2 = ls.fetch_refractiveindex("main", "MoS2", "Ermolaev-1L", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(mos2.range_nm)  # (290, 3300) 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_bdd7d48398a9/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/ermolaev-2020-1l).

# ... 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=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

Broadband optical constants of monolayer MoS₂ on SiO₂/Si substrate were measured by spectroscopic ellipsometry in the spectral range 290–3300 nm. Tauc-Lorentz oscillators were used in ellipsometry model to describe the optical response of excitons.

Conditions

film thickness: 1L
substrate: SiO2/Si

References

G. A. Ermolaev, Yu. V. Stebunov, A. A. Vyshnevyy, D. E. Tatarkin, D. I. Yakubovsky, S. M. Novikov, D. G. Baranov, T. Shegai, A. Y. Nikitin, A. V. Arsenin, V. S. Volkov. Broadband optical properties of monolayer and bulk MoS₂. NPJ 2D Mater. Appl., 4, 21 (2020) (Numerical data kindly provided by Georgy Ermolaev)

doi:10.1038/s41699-020-0155-x Broadband optical properties of monolayer and bulk MoS2, npj 2D Materials and Applications (2020)

Cite

Georgy A. Ermolaev et al.. Broadband optical properties of monolayer and bulk MoS2. npj 2D Materials and Applications, 4, 21 (2020), doi:10.1038/s41699-020-0155-x; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

3011 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), Ermolaev et al. 2020: monolayer (1L) film; n,k 0.290–3.30 µm: n and k versus wavelength
λ (µm)	n	k
0.29	2.29091	3.21676
0.291	2.32147	3.23025
0.292	2.35315	3.24353
0.293	2.38601	3.25656
0.294	2.42015	3.2693
0.295	2.45566	3.28167
0.296	2.49261	3.2936
0.297	2.53112	3.30501
0.298	2.57129	3.31579
0.299	2.61323	3.32582
0.3	2.65674	3.33491
0.301	2.70257	3.34302
0.302	2.75054	3.34988
0.303	2.8004	3.35524
0.304	2.85263	3.35889
0.305	2.90774	3.36054
0.306	2.96505	3.3598
0.307	3.02503	3.35628
0.308	3.08776	3.34951
0.309	3.15273	3.33903
0.31	3.2209	3.32407
0.311	3.2911	3.30414
0.312	3.36418	3.27816
0.313	3.43862	3.24569
0.314	3.51381	3.20598
0.315	3.59015	3.1575
0.316	3.66601	3.09958
0.317	3.73942	3.03204
0.318	3.80934	2.95379
0.319	3.87331	2.86526
0.32	3.93017	2.76508
0.321	3.97659	2.65541
0.322	4.01071	2.53668
0.323	4.03029	2.41069
0.324	4.03346	2.2799
0.325	4.01916	2.14837
0.326	3.9869	2.01823
0.327	3.93742	1.89384
0.328	3.8709	1.77619
0.329	3.7901	1.67004
0.33	3.69665	1.57662
0.331	3.59399	1.49821
0.332	3.48392	1.43504
0.333	3.36904	1.38766
0.334	3.25188	1.35618
0.335	3.13589	1.34037
0.336	3.02223	1.33926
0.337	2.91388	1.35173
0.338	2.81159	1.37655
0.339	2.71691	1.41227
0.34	2.63119	1.45727
0.341	2.55616	1.50917
0.342	2.49244	1.56576
0.343	2.43997	1.62493
0.344	2.39674	1.6815
0.345	2.35979	1.73597
0.346	2.32768	1.78919
0.347	2.29975	1.84135
0.348	2.2757	1.89207
0.349	2.2549	1.94194
0.35	2.23702	1.99102
0.351	2.22196	2.0389
0.352	2.20943	2.08564
0.353	2.19911	2.13177
0.354	2.19083	2.17733
0.355	2.18449	2.22234
0.356	2.18004	2.26596
0.357	2.17722	2.30956
0.358	2.17602	2.3523
0.359	2.17632	2.39422
0.36	2.17805	2.43576
0.361	2.18115	2.47698
0.362	2.18553	2.51746
0.363	2.1912	2.55767
0.364	2.19803	2.59719
0.365	2.20608	2.63647
0.366	2.21521	2.67513
0.367	2.22538	2.71317
0.368	2.2368	2.75145
0.369	2.24909	2.78874
0.37	2.26263	2.82628
0.371	2.27697	2.86287
0.372	2.29241	2.89932
0.373	2.30895	2.93566
0.374	2.3264	2.97147
0.375	2.34497	3.00717
0.376	2.36444	3.04235
0.377	2.3848	3.07703
0.378	2.40629	3.1116
0.379	2.42893	3.14606
0.38	2.45248	3.18
0.381	2.47692	3.21342
0.382	2.50255	3.2467
0.383	2.52909	3.27945
0.384	2.55687	3.31203
0.385	2.58557	3.34406
0.386	2.61519	3.3755
0.387	2.6461	3.40673
0.388	2.67835	3.43771
0.389	2.71156	3.46805
0.39	2.74574	3.49771
0.391	2.78132	3.52704
0.392	2.81789	3.55564
0.393	2.85544	3.58347
0.394	2.89445	3.61085
0.395	2.93447	3.63738
0.396	2.97601	3.66336
0.397	3.01857	3.6884
0.398	3.0627	3.71276
0.399	3.10785	3.73608
0.4	3.15401	3.7583
0.401	3.20177	3.77963
0.402	3.25054	3.79975
0.403	3.30028	3.81859
0.404	3.35164	3.83631
0.405	3.40395	3.85261
0.406	3.45786	3.8676
0.407	3.51266	3.881
0.408	3.5683	3.89276
0.409	3.62548	3.90292
0.41	3.68341	3.91126
0.411	3.742	3.91771
0.412	3.802	3.92227
0.413	3.86253	3.92476
0.414	3.92434	3.92514
0.415	3.9865	3.92329
0.416	4.0489	3.91917
0.417	4.11143	3.91274
0.418	4.17483	3.90382
0.419	4.2381	3.89247
0.42	4.30201	3.87845
0.421	4.3655	3.8619
0.422	4.42843	3.84283
0.423	4.49064	3.82125
0.424	4.55287	3.79683
0.425	4.61405	3.7699
0.426	4.67489	3.74008
0.427	4.73435	3.70781
0.428	4.79227	3.67318
0.429	4.8485	3.63629
0.43	4.9037	3.59666
0.431	4.95689	3.55495
0.432	5.00871	3.51064
0.433	5.05752	3.46517
0.434	5.10467	3.41737
0.435	5.15003	3.36728
0.436	5.19214	3.31661
0.437	5.23226	3.26398
0.438	5.27022	3.20952
0.439	5.30489	3.15505
0.44	5.33732	3.09909
0.441	5.36696	3.04267
0.442	5.39384	2.98596
0.443	5.41839	2.92824
0.444	5.44019	2.87056
0.445	5.45934	2.8131
0.446	5.47615	2.75508
0.447	5.49018	2.69848
0.448	5.50217	2.64071
0.449	5.51159	2.58461
0.45	5.51886	2.52848
0.451	5.52386	2.47422
0.452	5.52692	2.41927
0.453	5.52796	2.36634
0.454	5.52713	2.31377
0.455	5.52453	2.2625
0.456	5.52029	2.21256
0.457	5.51452	2.164
0.458	5.5072	2.11604
0.459	5.49854	2.06954
0.46	5.48848	2.02374
0.461	5.47745	1.98017
0.462	5.46517	1.93734
0.463	5.45195	1.89601
0.464	5.43786	1.85615
0.465	5.42273	1.8171
0.466	5.40717	1.78015
0.467	5.3907	1.744
0.468	5.37338	1.70868
0.469	5.35586	1.67537
0.47	5.33759	1.64285
0.471	5.31895	1.61171
0.472	5.3	1.5819
0.473	5.28044	1.55288
0.474	5.26101	1.52564
0.475	5.24105	1.49916
0.476	5.22096	1.47391
0.477	5.20042	1.44941
0.478	5.18019	1.4265
0.479	5.15958	1.40432
0.48	5.13896	1.38324
0.481	5.11801	1.36287
0.482	5.0975	1.34393
0.483	5.07671	1.32566
0.484	5.05603	1.30839
0.485	5.03548	1.29209
0.486	5.01508	1.27673
0.487	4.99448	1.262
0.488	4.97407	1.24819
0.489	4.95387	1.23525
0.49	4.93389	1.22315
0.491	4.91376	1.21167
0.492	4.89426	1.2012
0.493	4.87464	1.19131
0.494	4.8553	1.18219
0.495	4.83587	1.17366
0.496	4.81709	1.16601
0.497	4.79826	1.15894
0.498	4.77973	1.15256
0.499	4.76153	1.14686
0.5	4.74366	1.14182
0.501	4.72613	1.13742
0.502	4.70859	1.13356
0.503	4.6914	1.13033
0.504	4.67458	1.1277
0.505	4.65813	1.12567
0.506	4.64173	1.12417
0.507	4.62573	1.12326
0.508	4.61044	1.1229
0.509	4.59523	1.12308
0.51	4.58013	1.1238
0.511	4.56577	1.12503
0.512	4.55154	1.12679
0.513	4.53775	1.12906
0.514	4.52443	1.13181
0.515	4.51156	1.13504
0.516	4.49916	1.13872
0.517	4.487	1.14294
0.518	4.47558	1.14751
0.519	4.46442	1.15259
0.52	4.45378	1.15809
0.521	4.44368	1.16399
0.522	4.43391	1.17041
0.523	4.42491	1.17707
0.524	4.41629	1.18423
0.525	4.40826	1.19173
0.526	4.40083	1.19956
0.527	4.39403	1.20769
0.528	4.38771	1.2163
0.529	4.38218	1.22498
0.53	4.37718	1.23411
0.531	4.37288	1.24346
0.532	4.36926	1.25301
0.533	4.3663	1.26296
0.534	4.36412	1.27283
0.535	4.36264	1.28305
0.536	4.36192	1.29312
0.537	4.36196	1.30348
0.538	4.36277	1.31385
0.539	4.3644	1.32445
0.54	4.36679	1.33475
0.541	4.37004	1.34519
0.542	4.37401	1.35525
0.543	4.37888	1.36536
0.544	4.38456	1.37525
0.545	4.39103	1.38485
0.546	4.39848	1.39435
0.547	4.40654	1.40325
0.548	4.41556	1.41192
0.549	4.42536	1.4201
0.55	4.43563	1.42757
0.551	4.44713	1.43479
0.552	4.45904	1.4412
0.553	4.47158	1.44693
0.554	4.48503	1.45203
0.555	4.4987	1.45622
0.556	4.51321	1.45968
0.557	4.52817	1.46224
0.558	4.5435	1.46388
0.559	4.55915	1.46456
0.56	4.57543	1.46424
0.561	4.59148	1.46291
0.562	4.60802	1.46051
0.563	4.62456	1.45704
0.564	4.64102	1.4525
0.565	4.65731	1.44691
0.566	4.67333	1.44028
0.567	4.68902	1.43264
0.568	4.70466	1.42379
0.569	4.71976	1.41394
0.57	4.73389	1.40346
0.571	4.74769	1.39183
0.572	4.76073	1.37939
0.573	4.77292	1.36622
0.574	4.78451	1.35203
0.575	4.79484	1.33762
0.576	4.8044	1.32232
0.577	4.81266	1.30704
0.578	4.82004	1.29104
0.579	4.82628	1.27484
0.58	4.83136	1.25854
0.581	4.83537	1.24182
0.582	4.83809	1.22565
0.583	4.83967	1.20971
0.584	4.84011	1.19369
0.585	4.83939	1.17814
0.586	4.8376	1.16355
0.587	4.83468	1.14924
0.588	4.83074	1.13573
0.589	4.82566	1.12279
0.59	4.81979	1.11124
0.591	4.81309	1.10084
0.592	4.80542	1.09146
0.593	4.79706	1.08353
0.594	4.78838	1.07733
0.595	4.77903	1.07266
0.596	4.7694	1.06984
0.597	4.75941	1.06902
0.598	4.74982	1.07038
0.599	4.74063	1.07403
0.6	4.73192	1.08029
0.601	4.72454	1.08893
0.602	4.71854	1.10052
0.603	4.71472	1.11489
0.604	4.71373	1.13195
0.605	4.7163	1.15149
0.606	4.72324	1.17313
0.607	4.73542	1.19623
0.608	4.75425	1.22054
0.609	4.77933	1.24334
0.61	4.81253	1.26428
0.611	4.85311	1.28056
0.612	4.89875	1.28985
0.613	4.95064	1.29071
0.614	5.00514	1.28122
0.615	5.06094	1.25995
0.616	5.11176	1.22849
0.617	5.15644	1.18781
0.618	5.19404	1.13856
0.619	5.22125	1.08631
0.62	5.23963	1.03056
0.621	5.24881	0.97521
0.622	5.25	0.92209
0.623	5.24462	0.87243
0.624	5.23408	0.8269
0.625	5.21969	0.78578
0.626	5.20255	0.74907
0.627	5.18296	0.71558
0.628	5.16286	0.68708
0.629	5.14155	0.66138
0.63	5.12009	0.63909
0.631	5.09948	0.62037
0.632	5.07862	0.60371
0.633	5.05834	0.58944
0.634	5.03876	0.57729
0.635	5.01937	0.56674
0.636	5.00139	0.55821
0.637	4.98429	0.5512
0.638	4.96756	0.54537
0.639	4.95225	0.54097
0.64	4.93738	0.53757
0.641	4.92347	0.53526
0.642	4.91051	0.53394
0.643	4.89852	0.53353
0.644	4.88752	0.53398
0.645	4.87751	0.53521
0.646	4.86853	0.5372
0.647	4.86062	0.53988
0.648	4.85359	0.54335
0.649	4.84797	0.54732
0.65	4.84342	0.55203
0.651	4.84026	0.55729
0.652	4.83861	0.56284
0.653	4.83845	0.56899
0.654	4.84001	0.57546
0.655	4.84342	0.58213
0.656	4.84884	0.58886
0.657	4.85674	0.59566
0.658	4.86678	0.60184
0.659	4.87937	0.60731
0.66	4.89522	0.61179
0.661	4.91341	0.61448
0.662	4.93521	0.61494
0.663	4.96001	0.61226
0.664	4.98749	0.60554
0.665	5.01711	0.59385
0.666	5.04798	0.5763
0.667	5.07884	0.55211
0.668	5.10808	0.52086
0.669	5.13378	0.48258
0.67	5.15398	0.43799
0.671	5.16732	0.38668
0.672	5.17153	0.33426
0.673	5.16652	0.27948
0.674	5.15229	0.22678
0.675	5.13104	0.17996
0.676	5.10291	0.13706
0.677	5.07048	0.10072
0.678	5.03563	0.07109
0.679	4.99996	0.04786
0.68	4.96473	0.03038
0.681	4.92969	0.01752
0.682	4.8979	0.00931
0.683	4.86857	0.00449
0.684	4.84111	0.00236
0.685	4.81812	0.00195
0.686	4.79698	0.00164
0.687	4.77841	0.00137
0.688	4.76059	0.00113
0.689	4.74395	0.000925752
0.69	4.72833	0.000750977
0.691	4.71359	0.000607353
0.692	4.69963	0.000493591
0.693	4.68635	0.00040844
0.694	4.6737	0.000343058
0.695	4.66115	0.000282634
0.696	4.64958	0.000231106
0.697	4.63804	0.000184078
0.698	4.62735	0.00014465
0.699	4.61665	0.000109453
0.7	4.60672	8.07724e-05
0.701	4.59674	5.60388e-05
0.702	4.58708	3.62073e-05
0.703	4.57773	2.09684e-05
0.704	4.56867	1.00524e-05
0.705	4.55988	3.20743e-06
0.706	4.55133	1.96301e-07
0.707	4.54303	0.0
0.708	4.53495	0.0
0.709	4.52709	0.0
0.71	4.51913	0.0
0.711	4.51167	0.0
0.712	4.50409	0.0
0.713	4.49698	0.0
0.714	4.48977	0.0
0.715	4.48271	0.0
0.716	4.47609	0.0
0.717	4.46935	0.0
0.718	4.46275	0.0
0.719	4.45629	0.0
0.72	4.44997	0.0
0.721	4.44378	0.0
0.722	4.43745	0.0
0.723	4.43151	0.0
0.724	4.42568	0.0
0.725	4.41996	0.0
0.726	4.41412	0.0
0.727	4.40861	0.0
0.728	4.40298	0.0
0.729	4.39745	0.0
0.73	4.39224	0.0
0.731	4.38691	0.0
0.732	4.38166	0.0
0.733	4.37651	0.0
0.734	4.37144	0.0
0.735	4.36646	0.0
0.736	4.36157	0.0
0.737	4.35675	0.0
0.738	4.35201	0.0
0.739	4.34734	0.0
0.74	4.34256	0.0
0.741	4.33804	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