Optical constants

Refractive index of MoS2 (Molybdenum disulfide)

Song et al. 2019: 13-layer (13L) film; n,k 0.193–1.69 µm

Data
tabulated nk
Range
0.193–1.69 µm
Points
1084
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.193–1.69 µm
Refractive index n
4.53756
Extinction coefficient k
0.976479
Permittivity ε1
19.6359
Permittivity ε2
8.86167
Absorption coefficient α
208829 cm⁻¹
Penetration depth δ = λ/(2πk)
95.7721 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-2.335 µm⁻¹
Group index ng
5.90961
Group velocity dispersion
— fs²/mm
Dispersion parameter D
— ps/(nm·km)
Photon energy
2.11001 eV

ε = (n + ik)², α = 4πk/λ, ng = 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): Song et al. 2019: 13-layer (13L) film; n,k 0.193–1.69 µm
mos2 = ls.fetch_refractiveindex("main", "MoS2", "Song-13L", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(mos2.range_nm)  # (193, 1690) nm
eps = mos2.eps([633])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

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

13-layer, 13L

Conditions

film thickness
13L
substrate
c-sapphire

References

B. Song, H. Gu, M. Fang, X. Chen, H. Jiang, R. Wang, T. Zhai, Y.-T. Ho, S. Liu. Layer-dependent dielectric function of wafer-scale 2D MoS2. Adv. Optical Mater. 7, 1801250 (2019) (Numerical data kindly provided by Baokun Song)
  • doi:10.1002/adom.201801250 Layer‐Dependent Dielectric Function of Wafer‐Scale 2D MoS <sub>2</sub>, Advanced Optical Materials (2018)

Cite

Baokun Song et al.. Layer‐Dependent Dielectric Function of Wafer‐Scale 2D MoS <sub>2</sub>. Advanced Optical Materials, 7, 1801250 (2018), doi:10.1002/adom.201801250; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

1084 rows as published
MoS2 (Molybdenum disulfide), Song et al. 2019: 13-layer (13L) film; n,k 0.193–1.69 µm: n and k versus wavelength
λ (µm)nk
0.1931.4470252.179305
0.1941.4638542.203692
0.1951.4819362.225151
0.1961.5009532.244093
0.1971.5206532.260834
0.1981.5408352.27562
0.1991.5613322.288653
0.21.5820032.300098
0.2011.6027272.310097
0.2021.6233982.318771
0.2031.6439222.326231
0.2041.6642162.332579
0.2051.6842092.337907
0.2061.7038332.342304
0.2071.7230342.345856
0.2081.741762.348645
0.2091.759972.35075
0.211.7776272.352252
0.2111.7947032.353226
0.2121.8111752.353748
0.2131.8270262.353892
0.2141.8422482.353729
0.2151.8568352.353332
0.2161.870792.352766
0.2171.884122.352097
0.2181.8968372.351388
0.2191.9089582.350698
0.221.9205062.350084
0.2211.9315072.349598
0.2221.941992.349289
0.2231.9519892.349203
0.2241.961542.349379
0.2251.9706832.349854
0.2261.9794592.350662
0.2271.9879112.35183
0.2281.9960842.353381
0.2292.0040232.355335
0.232.0117752.357708
0.2312.0193882.360509
0.2322.0269072.363746
0.2332.0343792.367421
0.2342.0418522.371532
0.2352.0493692.376075
0.2362.0569752.381041
0.2372.0647132.386417
0.2382.0726232.392187
0.2392.0807472.398333
0.242.0891192.404834
0.2412.0977772.411664
0.2422.1067532.418797
0.2432.1160762.426203
0.2442.1257772.433851
0.2452.1358792.441709
0.2462.1464062.44974
0.2472.1573762.457909
0.2482.1688082.466178
0.2492.1807142.474507
0.252.1931062.482858
0.2512.2059922.49119
0.2522.2193762.499461
0.2532.2332612.507632
0.2542.2476452.515661
0.2552.2625242.523508
0.2562.2778912.531131
0.2572.2937352.53849
0.2582.3100452.545547
0.2592.3268022.552263
0.262.3439912.558602
0.2612.3615872.564526
0.2622.3795682.570003
0.2632.3979072.574999
0.2642.4165742.579484
0.2652.435542.58343
0.2662.454772.58681
0.2672.4742292.589599
0.2682.493882.591778
0.2692.5136842.593326
0.272.5336022.594229
0.2712.5535912.594472
0.2722.5736112.594047
0.2732.5936182.592945
0.2742.6135692.591164
0.2752.6334212.588702
0.2762.6531292.585561
0.2772.6726522.581748
0.2782.6919442.577271
0.2792.7109662.572141
0.282.7296762.566372
0.2812.7480352.559983
0.2822.7660032.552993
0.2832.7835452.545425
0.2842.8006252.537303
0.2852.8172112.528655
0.2862.8332722.519509
0.2872.8487792.509898
0.2882.8637072.499853
0.2892.8780312.489408
0.292.8917312.478599
0.2912.9047872.467461
0.2922.9171832.456032
0.2932.9289072.444348
0.2942.9399462.432448
0.2952.9502932.420369
0.2962.959942.408148
0.2972.9688842.395824
0.2982.9771242.383434
0.2992.9846592.371014
0.32.9914932.3586
0.3012.997632.346228
0.3023.0030752.333931
0.3033.0078382.321744
0.3043.0119272.309698
0.3053.0153542.297824
0.3063.018132.286154
0.3073.020272.274716
0.3083.0217872.263537
0.3093.0226982.252645
0.313.0230192.242064
0.3113.0227672.23182
0.3123.0219592.221935
0.3133.0206142.212431
0.3143.0187522.203329
0.3153.0163912.194649
0.3163.0135512.186409
0.3173.0102532.178627
0.3183.0065162.171321
0.3193.002362.164506
0.322.9978082.158197
0.3212.9928782.152409
0.3222.9875932.147154
0.3232.9819742.142445
0.3242.976042.138295
0.3252.9698142.134716
0.3262.9633172.131716
0.3272.956572.129308
0.3282.9495952.127501
0.3292.9424132.126303
0.332.9350452.125725
0.3312.9275132.125773
0.3322.919842.126456
0.3332.9120472.127781
0.3342.9041572.129756
0.3352.8961922.132388
0.3362.8881742.135682
0.3372.8801272.139644
0.3382.8720752.144281
0.3392.8640392.149598
0.342.8560462.155598
0.3412.8481192.162288
0.3422.8402832.169671
0.3432.8325642.177751
0.3442.8249872.186531
0.3452.817582.196014
0.3462.8103682.206202
0.3472.8033822.217096
0.3482.7966482.228698
0.3492.7901962.241009
0.352.7840572.254028
0.3512.7782612.267754
0.3522.772842.282185
0.3532.7678272.297318
0.3542.7632572.31315
0.3552.7591632.329675
0.3562.7555822.346887
0.3572.7525512.364778
0.3582.7501082.383339
0.3592.7482932.402559
0.362.7471472.422424
0.3612.7467112.44292
0.3622.7470292.464029
0.3632.7481452.48573
0.3642.7501042.508
0.3652.7529552.530812
0.3662.7567442.554134
0.3672.7615192.577933
0.3682.7673312.602168
0.3692.7742272.626794
0.372.7822572.65176
0.3712.7914692.67701
0.3722.801912.702478
0.3732.8136222.728096
0.3742.8266482.753782
0.3752.8410212.77945
0.3762.8567732.805006
0.3772.8739232.830345
0.3782.8924852.855357
0.3792.9124582.879924
0.382.9338282.903923
0.3812.9565672.927225
0.3822.9806282.949702
0.3833.0059442.971224
0.3843.032432.991669
0.3853.0599793.010921
0.3863.0884673.028878
0.3873.1177473.045456
0.3883.147663.060591
0.3893.1780363.074245
0.393.2086953.086409
0.3913.239463.097103
0.3923.2701563.10638
0.3933.3006243.114318
0.3943.3307193.121026
0.3953.3603223.126632
0.3963.3893413.131282
0.3973.4177143.135131
0.3983.4454083.138339
0.3993.4724223.141063
0.43.4987833.14345
0.4013.5245413.145636
0.4023.5497663.147736
0.4033.5745473.14985
0.4043.5989793.152053
0.4053.6231683.154399
0.4063.6472183.156923
0.4073.6712353.159639
0.4083.6953193.162544
0.4093.7195643.165618
0.413.7440563.16883
0.4113.7688683.172137
0.4123.7940683.175486
0.4133.819713.17882
0.4143.8458383.182074
0.4153.8724863.185183
0.4163.899683.188078
0.4173.9274333.190691
0.4183.9557533.192952
0.4193.9846373.194795
0.424.0140773.196156
0.4214.0440573.19697
0.4224.0745553.197179
0.4234.1055443.196727
0.4244.1369913.195561
0.4254.1688613.193632
0.4264.2011123.190896
0.4274.2337023.187312
0.4284.2665823.182844
0.4294.2997053.17746
0.434.3330193.171132
0.4314.366473.163838
0.4324.4000053.155557
0.4334.4335683.146277
0.4344.4671043.135987
0.4354.5005563.12468
0.4364.5338683.112356
0.4374.5669843.099017
0.4384.5998493.084668
0.4394.632413.069322
0.444.6646123.052991
0.4414.6964043.035693
0.4424.7277383.01745
0.4434.7585642.998285
0.4444.7888382.978226
0.4454.8185162.957303
0.4464.8475582.935548
0.4474.8759242.912996
0.4484.903582.889684
0.4494.9304932.865651
0.454.9566352.840937
0.4514.9819772.815583
0.4525.0064982.789632
0.4535.0301762.763127
0.4545.0529952.736112
0.4555.0749392.708631
0.4565.0959982.680728
0.4575.1161632.652447
0.4585.1354282.623832
0.4595.1537912.594925
0.465.171252.565769
0.4615.1878072.536406
0.4625.2034672.506874
0.4635.2182362.477215
0.4645.2321232.447465
0.4655.2451382.417662
0.4665.2572912.387839
0.4675.2685982.358031
0.4685.2790732.32827
0.4695.2887322.298586
0.475.2975912.269008
0.4715.305672.239562
0.4725.3129882.210275
0.4735.3195632.18117
0.4745.3254172.152269
0.4755.330572.123592
0.4765.3350422.09516
0.4775.3388562.066988
0.4785.3420322.039094
0.4795.3445932.011492
0.485.3465581.984196
0.4815.347951.957216
0.4825.348791.930564
0.4835.3490991.90425
0.4845.3488971.878281
0.4855.3482041.852665
0.4865.3470411.827408
0.4875.3454271.802516
0.4885.343381.777993
0.4895.340921.753842
0.495.3380651.730066
0.4915.3348311.706668
0.4925.3312371.683648
0.4935.3272991.661008
0.4945.3230311.638747
0.4955.3184511.616866
0.4965.3135741.595363
0.4975.3084121.574238
0.4985.3029811.553488
0.4995.2972931.533112
0.55.2913611.513108
0.5015.2851981.493472
0.5025.2788151.474202
0.5035.2722241.455296
0.5045.2654351.436749
0.5055.2584581.418558
0.5065.2513041.40072
0.5075.2439811.383231
0.5085.23651.366087
0.5095.2288671.349285
0.515.2210921.332821
0.5115.2131811.31669
0.5125.2051431.30089
0.5135.1969851.285415
0.5145.1887121.270263
0.5155.1803311.255429
0.5165.1718491.240909
0.5175.163271.2267
0.5185.15461.212798
0.5195.1458441.1992
0.525.1370061.185902
0.5215.1280921.1729
0.5225.1191051.160192
0.5235.1100491.147774
0.5245.1009281.135643
0.5255.0917461.123796
0.5265.0825061.11223
0.5275.0732111.100943
0.5285.0638631.089932
0.5295.0544671.079196
0.535.0450231.068731
0.5315.0355361.058536
0.5325.0260061.048609
0.5335.0164371.038948
0.5345.0068291.029553
0.5354.9971861.020422
0.5364.9875091.011553
0.5374.9777991.002947
0.5384.968060.994602
0.5394.9582910.986518
0.544.9484950.978696
0.5414.9386730.971135
0.5424.9288280.963836
0.5434.918960.9568
0.5444.909070.950027
0.5454.8991620.943519
0.5464.8892360.937277
0.5474.8792930.931304
0.5484.8693370.925601
0.5494.8593690.92017
0.554.849390.915015
0.5514.8394040.910139
0.5524.8294120.905546
0.5534.8194170.901238
0.5544.8094220.89722
0.5554.7994310.893497
0.5564.7894460.890074
0.5574.7794730.886956
0.5584.7695150.884148
0.5594.7595760.881657
0.564.7496630.87949
0.5614.7397810.877652
0.5624.7299370.876151
0.5634.7201380.874995
0.5644.7103920.874192
0.5654.7007080.87375
0.5664.6910970.873676
0.5674.6815680.873981
0.5684.6721340.874672
0.5694.6628090.87576
0.574.6536070.877253
0.5714.6445440.87916
0.5724.6356380.88149
0.5734.6269090.884252
0.5744.6183770.887454
0.5754.6100650.891105
0.5764.6020.89521
0.5774.5942080.899777
0.5784.5867180.90481
0.5794.5795640.910312
0.584.5727770.916285
0.5814.5663970.922728
0.5824.5604610.929637
0.5834.555010.937006
0.5844.5500880.944825
0.5854.5457410.953081
0.5864.5420160.961754
0.5874.5389610.97082
0.5884.5366260.980252
0.5894.5350620.990013
0.594.5343171.000061
0.5914.5344391.010348
0.5924.5354771.020816
0.5934.5374721.031402
0.5944.5404641.042034
0.5954.5444871.052633
0.5964.5495651.063111
0.5974.5557191.073376
0.5984.5629561.083327
0.5994.5712731.09286
0.64.5806561.101867
0.6014.5910741.110239
0.6024.6024881.117866
0.6034.6148381.12464
0.6044.6280541.130459
0.6054.6420481.135227
0.6064.6567231.138858
0.6074.6719651.141276
0.6084.6876521.142421
0.6094.7036541.142246
0.614.7198331.140722
0.6114.7360491.137838
0.6124.7521611.133601
0.6134.7680291.128034
0.6144.7835211.12118
0.6154.798511.113095
0.6164.8128791.103853
0.6174.8265211.093536
0.6184.8393461.08224
0.6194.8512741.070068
0.624.8622411.057129
0.6214.8721961.043535
0.6224.8811041.029399
0.6234.8889411.014834
0.6244.8956980.999952
0.6254.9013750.984859
0.6264.9059830.969659
0.6274.9095420.954449
0.6284.912080.939321
0.6294.9136290.924359
0.634.9142280.909644
0.6314.9139210.89525
0.6324.9127520.881244
0.6334.910770.86769
0.6344.9080240.854646
0.6354.9045650.842168
0.6364.9004470.830308
0.6374.8957230.819115
0.6384.8904480.808639
0.6394.884680.798926
0.644.8784790.790026
0.6414.8719070.781985
0.6424.8650350.774853
0.6434.8579360.768681
0.6444.8506950.76352
0.6454.8434050.759421
0.6464.8361750.756435
0.6474.829130.754612
0.6484.8224120.753994
0.6494.816190.754613
0.654.8106550.756486
0.6514.8060280.759605
0.6524.8025580.763925
0.6534.8005190.769354
0.6544.8002010.775737
0.6554.8018990.78284
0.6564.8058920.790337
0.6574.8124070.797802
0.6584.8215920.804712
0.6594.8334620.810463
0.664.847870.814411
0.6614.8644790.815922
0.6624.8827590.814449
0.6634.9020160.809594
0.6644.9214520.801173
0.6654.9402460.789241
0.6664.9576390.774084
0.6674.9730070.756176
0.6684.9859110.736112
0.6694.9961090.71454
0.675.0035410.692086
0.6715.0082970.669313
0.6725.0105750.646689
0.6735.010640.62458
0.6745.0087840.603247
0.6755.0053030.582866
0.6765.0004790.56354
0.6774.9945660.545313
0.6784.9877910.528189
0.6794.9803450.512142
0.684.972390.497126
0.6814.9640620.483085
0.6824.955470.469955
0.6834.9467030.457672
0.6844.9378330.446171
0.6854.9289180.435389
0.6864.9200020.425267
0.6874.9111210.415752
0.6884.90230.406791
0.6894.8935610.398339
0.694.884920.390352
0.6914.8763870.382793
0.6924.867970.375626
0.6934.8596750.36882
0.6944.8515060.362345
0.6954.8434630.356177
0.6964.8355470.350291
0.6974.8277580.344667
0.6984.8200950.339284
0.6994.8125540.334127
0.74.8051350.329179
0.7014.7978340.324425
0.7024.7906480.319854
0.7034.7835750.315452
0.7044.776610.311209
0.7054.7697520.307116
0.7064.7629970.303163
0.7074.7563410.299341
0.7084.7497810.295645
0.7094.7433150.292065
0.714.7369390.288597
0.7114.730650.285233
0.7124.7244440.28197
0.7134.718320.278801
0.7144.7122750.275722
0.7154.7063040.272729
0.7164.7004060.269818
0.7174.6945780.266984
0.7184.6888160.264225
0.7194.6831180.261538
0.724.6774820.258918
0.7214.6719040.256365
0.7224.666380.253874
0.7234.660910.251444
0.7244.6554880.249072
0.7254.650110.246756
0.7264.6447740.244494
0.7274.6394730.242285
0.7284.6342020.240127
0.7294.6289530.238018
0.734.6237130.235957
0.7314.6184650.233944
0.7324.613170.231979
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0.9354.1724430.145229
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0.9414.1660940.144228
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0.9434.1640140.143901
0.9444.1629810.143739
0.9454.1619520.143577
0.9464.1609270.143417
0.9474.1599060.143257
0.9484.158890.143097
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0.954.156870.142781
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0.9534.1538720.142312
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0.9554.1518940.142004
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0.9664.1412950.140355
0.9674.1403540.140209
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0.9694.1384840.139919
0.974.1375540.139775
0.9714.1366280.139632
0.9724.1357060.139489
0.9734.1347870.139347
0.9744.1338720.139206
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0.9984.1129040.135988
0.9994.1120690.135861
1.04.1112380.135734
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1.313.937190.111823
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1.333.9291730.110933
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1.353.9213580.110093
1.35253.9203940.109991
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1.363.9175210.10969
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1.373.9137280.109299
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1.683.809720.101521
1.68253.8089430.101485
1.6853.8081660.101449
1.68753.8073890.101414
1.693.8066130.101379

Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
—
Reflectance R
—

Fresnel reflection calculator

Direction
Rp
—
Rs
—
R = (Rp+Rs)/2
—
Phase φp
—
Phase φs
—
Brewster angle θB
—
Critical angle θC
—