Optical constants

Refractive index of MoS₂ (Molybdenum disulfide)

Ullberg et al. 2025: monolayer (1L) film; n,k 0.24–1.5 µm

Data: tabulated nk
Range: 0.24–1.5 µm
Points: 1261
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 4.15695
Extinction coefficient k: 1.16766

Permittivity ε₁: 15.9168
Permittivity ε₂: 9.70781

Absorption coefficient α: 249715 cm⁻¹
Penetration depth δ = λ/(2πk): 80.0913 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -7.79007 µm⁻¹

Group index n_g: 8.73439
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): Ullberg et al. 2025: monolayer (1L) film; n,k 0.24–1.5 µm
mos2 = ls.fetch_refractiveindex("main", "MoS2", "Ullberg", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(mos2.range_nm)  # (239.968, 1499.78) 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_cfd93284777a/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/ullberg-2025).

# ... 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

Monolayer (2D) MoS2 (n,k) measured via spectroscopic ellipsometry, at room temperature in ambient atmosphere, on single-polished sapphire substrate.

Conditions

film thickness: 1L
substrate: sapphire

References

N. Ullberg, E. Peci, M. Magnozzi, V. Derycke. Achieving high visibility of monolayer MoS₂ using backside-illuminated thin films. Langmuir 41, 11893-11902 (2025)

doi:10.1021/acs.langmuir.4c05229 Achieving High Visibility of Monolayer MoS<sub>2</sub> Using Backside-Illuminated Thin Films, Langmuir (2025)

Cite

Nathan Ullberg, Ermes Peci, Michele Magnozzi and Vincent Derycke. Achieving High Visibility of Monolayer MoS<sub>2</sub> Using Backside-Illuminated Thin Films. Langmuir, 41, 11893-11902 (2025), doi:10.1021/acs.langmuir.4c05229; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

1261 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), Ullberg et al. 2025: monolayer (1L) film; n,k 0.24–1.5 µm: n and k versus wavelength
λ (µm)	n	k
0.23996787	0.91950058	3.20184637
0.24097061	0.96003688	3.22424579
0.2419676	1.00165871	3.24450965
0.24296811	1.04416626	3.26256132
0.24396733	1.08735855	3.27832768
0.24496996	1.13095045	3.29165965
0.24596623	1.17455487	3.30237804
0.24697063	1.21813178	3.31075808
0.24796839	1.26147618	3.31685286
0.24896925	1.30402127	3.32037195
0.24996814	1.3458054	3.32173041
0.25097	1.38664135	3.32101957
0.25196967	1.42604374	3.31814005
0.25296702	1.46444399	3.31373796
0.2539671	1.50055639	3.30725965
0.25496462	1.53524597	3.29955831
0.25596473	1.56804458	3.29060117
0.25696739	1.59885859	3.28066228
0.2579672	1.6276477	3.26996265
0.25896401	1.65439584	3.2587934
0.25996854	1.67897041	3.24734184
0.26096442	1.70171686	3.23594693
0.26196796	1.72215371	3.2247353
0.2629681	1.74096284	3.21404516
0.26396465	1.75783344	3.20405792
0.26496313	1.77301603	3.19498245
0.26596348	1.78691339	3.18701381
0.26696567	1.79931256	3.18033361
0.26796386	1.81060153	3.17507597
0.2689637	1.82114745	3.17135189
0.26996516	1.83104925	3.16928618
0.27096225	1.84036131	3.16895417
0.27196674	1.849613	3.17034267
0.27296668	1.85904053	3.17348376
0.2739619	1.86888469	3.17835674
0.2749644	1.87925121	3.18497571
0.27596198	1.89049085	3.19324234
0.27696682	1.90292955	3.20301656
0.27796654	1.91682631	3.21413789
0.27896096	1.93240631	3.22644695
0.27996251	1.94990621	3.23969385
0.28096491	1.96951089	3.25364186
0.2819617	1.99139283	3.26798075
0.28296558	2.01566999	3.28237886
0.28396362	2.04242778	3.29646761
0.28496219	2.07170207	3.30986333
0.2859612	2.10347378	3.32213565
0.2869606	2.13762839	3.33290272
0.28796032	2.17400073	3.34178127
0.2889603	2.21236595	3.34840556
0.28996047	2.25242789	3.35246638
0.29096076	2.2938513	3.35369091
0.29196109	2.33623977	3.35188125
0.29296141	2.37922095	3.34685877
0.29396163	2.42236048	3.33854946
0.29496169	2.46525007	3.32691017
0.29596151	2.50746828	3.31199024
0.29696102	2.54862797	3.29387891
0.29796015	2.58835552	3.27273136
0.29895881	2.62631617	3.2487471
0.29995693	2.66218731	3.22219018
0.30096174	2.6957121	3.19333357
0.30195859	2.72672337	3.16242125
0.30296207	2.7550656	3.12974615
0.30395734	2.78061684	3.09561733
0.30495916	2.8032708	3.06036715
0.30596007	2.82298781	3.02428789
0.30695996	2.83980601	2.98761755
0.30795876	2.85375547	2.95061178
0.30895639	2.86484574	2.91355384
0.30996049	2.87313309	2.87667569
0.31095555	2.87875429	2.84012673
0.31195702	2.88180992	2.80408113
0.31295706	2.88229313	2.76880074
0.31395558	2.88041554	2.73432312
0.31496049	2.87627282	2.70078748
0.31595575	2.86987141	2.66839182
0.31695733	2.86140584	2.63715843
0.31795712	2.85096021	2.60719011
0.31895503	2.83855149	2.57865089
0.31995922	2.82436819	2.55153547
0.32096145	2.80842679	2.52599197
0.32195325	2.79083595	2.50209016
0.32295962	2.77172594	2.47988241
0.32395537	2.75108829	2.45954086
0.32495727	2.72914323	2.44104911
0.32595682	2.70587426	2.42459689
0.32695392	2.68149328	2.41018951
0.32795714	2.65606147	2.39796603
0.32895781	2.62974332	2.38798001
0.32995582	2.6026699	2.38032134
0.3309599	2.57500041	2.37505371
0.33195234	2.54690496	2.37222932
0.33295968	2.51857376	2.37187787
0.33395517	2.49017667	2.3740402
0.33495663	2.46192801	2.3786952
0.33595501	2.43398647	2.38585999
0.33695936	2.40660107	2.39544497
0.33795131	2.37989982	2.40744875
0.33895838	2.3541455	2.42170512
0.33995283	2.32941574	2.43820443
0.34095313	2.30595127	2.45673361
0.34194991	2.28384134	2.47720347
0.34295253	2.26320664	2.49945825
0.3439515	2.24418056	2.5232953
0.34495631	2.22676288	2.54863105
0.34595736	2.21107839	2.57521653
0.34695452	2.19712212	2.60292761
0.34795745	2.18488076	2.63163604
0.34895637	2.17441004	2.66111548
0.34995116	2.16563351	2.69129824
0.35095165	2.15852019	2.72205045
0.35195787	2.15306741	2.75321051
0.35294978	2.14917724	2.7847412
0.3539574	2.14680386	2.81654091
0.35495047	2.14591381	2.84850708
0.35594912	2.14643012	2.8806021
0.35695341	2.14827961	2.91280373
0.35795305	2.15144106	2.9450221
0.35894791	2.15586238	2.97723123
0.35994832	2.16145026	3.00947389
0.36095431	2.16820305	3.04167318
0.36195538	2.17608659	3.07381978
0.3629514	2.18506724	3.10590252
0.36395291	2.19508816	3.13796224
0.36494922	2.2061633	3.16995446
0.365951	2.21827579	3.20186651
0.36694743	2.23141133	3.23370269
0.3679493	2.24554149	3.26549541
0.36894569	2.26067902	3.29722124
0.36994748	2.2768331	3.32885478
0.37095472	2.29400723	3.36039338
0.37194515	2.31220598	3.39183516
0.3729521	2.33141412	3.42319414
0.37395324	2.35166651	3.45443123
0.37494843	2.37296915	3.4855318
0.37594893	2.39534346	3.51647575
0.37695478	2.41879797	3.54723079
0.37795451	2.44334841	3.5777914
0.37894797	2.46899256	3.60813731
0.37994667	2.49575846	3.63823189
0.38095065	2.52366348	3.66803455
0.38194818	2.55271744	3.69751165
0.38295094	2.58293617	3.72661658
0.3839471	2.61432402	3.75532565
0.38494845	2.64689642	3.78358585
0.38594303	2.68065637	3.81136222
0.38694275	2.71559895	3.83862725
0.38794768	2.75173766	3.86531002
0.38894563	2.789081	3.89135459
0.38994873	2.82761848	3.91670898
0.39094469	2.86735506	3.94132099
0.39194574	2.90827711	3.96513508
0.39295194	2.95036948	3.98811544
0.39395081	2.99362549	4.01018168
0.39494218	3.03803393	4.03127563
0.39595119	3.08356579	4.0513302
0.39693996	3.13020038	4.0703156
0.39794645	3.17790238	4.08816004
0.39894523	3.2266557	4.10479375
0.39994902	3.27641168	4.12015042
0.40094492	3.32714139	4.13420006
0.40194579	3.37878952	4.14688066
0.40295166	3.43132043	4.15811117
0.40394943	3.48467954	4.16784365
0.40493892	3.53881624	4.17606667
0.40594656	3.59366211	4.18268408
0.40694587	3.64916248	4.18764084
0.40795011	3.70525281	4.19095434
0.40894583	3.76186336	4.19252926
0.40994643	3.81892315	4.192315
0.41093831	3.8763531	4.19034961
0.41194869	3.93408528	4.18652873
0.4129503	3.99202634	4.18084544
0.41394297	4.05011548	4.17331212
0.41494042	4.10824341	4.16385322
0.41594269	4.16634611	4.15250351
0.41694982	4.224323	4.1392336
0.41794774	4.28208443	4.12401989
0.4189363	4.3395634	4.10691791
0.41994377	4.39663753	4.08786601
0.4209418	4.4532521	4.06693687
0.42194459	4.50928912	4.04410111
0.42293774	4.56468316	4.01939752
0.42393557	4.61933338	3.99285777
0.42493813	4.67315166	3.96449029
0.42594544	4.7260785	3.9343625
0.42694283	4.77797967	3.90248197
0.4279449	4.82883138	3.86893557
0.42893685	4.87851714	3.83370751
0.42994832	4.92699454	3.79692594
0.43093461	4.97414768	3.75857836
0.43194049	5.01996334	3.71878547
0.43293595	5.06432248	3.67755402
0.43393601	5.10721555	3.63500164
0.43494071	5.14852663	3.59116563
0.43593473	5.18824244	3.54614909
0.43693331	5.22628933	3.50000404
0.43793648	5.26263376	3.45281939
0.43894427	5.29724373	3.40467139
0.43994109	5.33004436	3.3556149
0.44094245	5.36101721	3.30576257
0.44193262	5.39021461	3.25525612
0.44294308	5.41750668	3.2040999
0.44394227	5.44288694	3.15239068
0.44494598	5.46636208	3.10022331
0.4459382	5.48792821	3.04769061
0.44693485	5.5075349	2.99485968
0.44793597	5.52522901	2.94185614
0.44894158	5.54094894	2.88872726
0.4499354	5.55471293	2.8355743
0.45093362	5.5665555	2.78248953
0.45193627	5.57642266	2.72954412
0.4529434	5.58433611	2.67682941
0.45393841	5.59028002	2.62444256
0.4549378	5.59421815	2.57247888
0.45594159	5.5961623	2.52108511
0.45693299	5.59609482	2.47041595
0.45794562	5.59400051	2.42066756
0.45892877	5.58998921	2.37211086
0.45993322	5.58425361	2.32496066
0.46094207	5.57703472	2.27939593
0.46193814	5.56866662	2.23547094
0.46293853	5.55946755	2.19315484
0.46394326	5.54964075	2.15228279
0.46493493	5.53931149	2.11264041
0.46593084	5.52855251	2.07409024
0.46693103	5.51728427	2.03650607
0.46793553	5.50545912	1.99983701
0.46894435	5.49306848	1.96407747
0.46993972	5.48011953	1.92924375
0.47093933	5.46658347	1.89535792
0.4719432	5.45248638	1.86244955
0.47293331	5.43788004	1.83054141
0.47392759	5.42284117	1.79964617
0.47492606	5.40735645	1.76977408
0.47592875	5.39149286	1.74093558
0.47693567	5.37531504	1.7131244
0.47792845	5.35888332	1.68633405
0.47892536	5.34222421	1.66056847
0.47992644	5.32538964	1.63581339
0.48093172	5.30843865	1.61204679
0.48194122	5.2914062	1.58926073
0.48293615	5.27435475	1.56743134
0.4839352	5.25732184	1.54652493
0.48493839	5.24033792	1.52653237
0.4859267	5.22343099	1.50741631
0.48693817	5.20665618	1.48915036
0.48793466	5.19005983	1.47169687
0.48893524	5.17363867	1.45502694
0.48993993	5.15744375	1.43910658
0.49092931	5.14150175	1.42389659
0.4919227	5.12581042	1.40936631
0.49293972	5.11040606	1.39547612
0.49394127	5.09530644	1.38218594
0.49492714	5.08051422	1.36946509
0.49593679	5.06605301	1.35727372
0.49693065	5.05192927	1.34557292
0.4979285	5.03812865	1.3343303
0.49893037	5.02466391	1.32351333
0.49993628	5.01154815	1.31307824
0.50092601	4.99875369	1.30300837
0.50193999	4.98629622	1.29325242
0.50293768	4.97417807	1.28379593
0.50393935	4.96236367	1.27459964
0.50492444	4.95086133	1.26564463
0.50593405	4.93966706	1.25690078
0.50692697	4.92873422	1.24834722
0.50792379	4.91807845	1.23996639
0.50892454	4.90768313	1.23172201
0.50992925	4.89750965	1.22361746
0.51093793	4.88756622	1.21562374
0.51192947	4.87782693	1.2077295
0.51292486	4.86826392	1.19992929
0.51392413	4.8588871	1.19219338
0.51492731	4.84964434	1.18453615
0.51593441	4.84054001	1.17693817
0.5169239	4.8315617	1.16938988
0.51793883	4.82266852	1.1619029
0.51893603	4.81387435	1.15446093
0.51993709	4.80513684	1.1470654
0.52092012	4.79645666	1.13972468
0.52192885	4.78782445	1.13242967
0.52291943	4.77919333	1.12519202
0.52393593	4.77058711	1.11801298
0.52493415	4.76197344	1.11089496
0.52593619	4.75334244	1.10384627
0.52691967	4.74469694	1.09687523
0.52792931	4.73599754	1.08999039
0.52892026	4.72726755	1.08319089
0.52993759	4.71847831	1.07649706
0.5309361	4.7096308	1.06991613
0.53191556	4.70072115	1.06344778
0.53292155	4.6917356	1.05712579
0.53393134	4.68268847	1.05092336
0.5349219	4.67354358	1.04487667
0.53591613	4.66432873	1.03898928
0.53693732	4.65503313	1.03327914
0.53791573	4.64565754	1.02775394
0.53892114	4.63620937	1.02241727
0.53993031	4.62666936	1.01728628
0.54091967	4.61707381	1.01236459
0.54193635	4.60738411	1.00767451
0.54293308	4.59763728	1.00321384
0.54393348	4.58781085	0.9989956
0.54491363	4.57793011	0.9950311
0.54592135	4.56799776	0.99132716
0.5469328	4.5580109	0.98789337
0.5479238	4.54798448	0.98473016
0.54891839	4.53791275	0.98185491
0.5499166	4.52782717	0.97926673
0.55091845	4.51770295	0.97697964
0.55192396	4.50758939	0.97498991
0.55293314	4.49745252	0.97330775
0.55392127	4.48732565	0.97193725
0.55491294	4.4772038	0.97088458
0.55593309	4.46710434	0.97015142
0.55693198	4.4570324	0.96974198
0.55793447	4.44698979	0.96965856
0.55891537	4.43698978	0.96990164
0.55992502	4.42703521	0.97047693
0.56091295	4.41715058	0.97138165
0.56192983	4.40732005	0.97262164
0.56292485	4.39757306	0.9741926
0.56392339	4.38788216	0.97610194
0.56492549	4.37827837	0.97834278
0.56593116	4.36874324	0.98092203
0.56691448	4.35930906	0.98383325
0.56792725	4.34993899	0.98708487
0.56891753	4.34067728	0.99066692
0.56991127	4.33147138	0.99459066
0.57090849	4.32236126	0.99884681
0.57190921	4.31328842	1.00344797
0.57291344	4.304285	1.0083847
0.5739212	4.29528813	1.01367252
0.57493252	4.28631488	1.01930733
0.57592065	4.27729002	1.02530931
0.57691218	4.26818723	1.03169221
0.57790714	4.25889915	1.03850319
0.57893256	4.24936886	1.04580312
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1.45978827	3.61595056	0.0
1.46078583	3.61572746	0.0
1.46178475	3.61550589	0.0
1.46278504	3.61528429	0.0
1.4637867	3.61506353	0.0
1.46478973	3.61484346	0.0
1.46579414	3.61462067	0.0
1.46678257	3.61440062	0.0
1.46778972	3.61418329	0.0
1.46878084	3.6139664	0.0
1.46979074	3.61375058	0.0
1.47078457	3.61352756	0.0
1.47179722	3.61330586	0.0
1.47279376	3.61308562	0.0
1.47379166	3.61286739	0.0
1.47479092	3.61265143	0.0
1.47579152	3.61243767	0.0
1.47679349	3.61222562	0.0
1.4777792	3.61201273	0.0
1.47878387	3.61179934	0.0
1.47978991	3.6115843	0.0
1.48077963	3.61137149	0.0
1.48178838	3.61115791	0.0
1.48278078	3.61094865	0.0
1.48379226	3.61073647	0.0
1.48478734	3.61052328	0.0
1.48578376	3.61031075	0.0
1.48678152	3.6100999	0.0
1.48778061	3.60988851	0.0
1.48878105	3.60967832	0.0
1.48978284	3.60946989	0.0
1.49078598	3.60926501	0.0
1.49179047	3.6090602	0.0
1.49277834	3.6088526	0.0
1.49378551	3.60864647	0.0
1.49479405	3.60844016	0.0
1.4957859	3.60823447	0.0
1.49677907	3.60802815	0.0
1.49779165	3.60781871	0.0
1.49878749	3.60761263	0.0
1.49978465	3.60740887	0.0

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