Optical constants

Refractive index of WS2 (Tungsten disulfide)

Ermolaev et al. 2020: monolayer film; n,k 0.365–1.70 µm

Data
tabulated nk
Range
0.365–1.7 µm
Points
1336
State
gas
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.365–1.7 µm
Refractive index n
2.6302
Extinction coefficient k
0.48896
Permittivity ε1
6.67887
Permittivity ε2
2.57213
Absorption coefficient α
104569 cm⁻¹
Penetration depth δ = λ/(2πk)
191.262 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-33 µm⁻¹
Group index ng
22.021
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

# WS2 (Tungsten disulfide): Ermolaev et al. 2020: monolayer film; n,k 0.365–1.70 µm
ws2 = ls.fetch_refractiveindex("main", "WS2", "Ermolaev", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ws2.range_nm)  # (365, 1700) nm
eps = ws2.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

Optical constants of monolayer WS2 were measured by spectroscopic ellipsometry in the spectral range 365–1700 nm. WS2 samples were grown on sapphire by atmospheric pressure chemical vapor deposition and then transferred on silicon wafers covered by 295 nm SiO2. 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, D. I. Yakubovsky, Yu. V. Stebunov, A. V. Arsenin, V. S. Volkov. Spectral ellipsometry of monolayer transition metal dichalcogenides: Analysis of excitonic peaks in dispersion. J. Vac. Sci. Technol. B 38, 014002 (2020) (Numerical data kindly provided by Georgy Ermolaev)
  • doi:10.1116/1.5122683 Spectral ellipsometry of monolayer transition metal dichalcogenides: Analysis of excitonic peaks in dispersion, Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena (2019)

Cite

Georgy A. Ermolaev, Dmitry I. Yakubovsky, Yury V. Stebunov, Aleksey V. Arsenin and Valentyn S. Volkov. Spectral ellipsometry of monolayer transition metal dichalcogenides: Analysis of excitonic peaks in dispersion. Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena, 38, 014002 (2019), doi:10.1116/1.5122683; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

1336 rows as published
WS2 (Tungsten disulfide), Ermolaev et al. 2020: monolayer film; n,k 0.365–1.70 µm: n and k versus wavelength
λ (µm)nk
0.3652.4022.775
0.3662.4232.779
0.3672.4442.782
0.3682.4662.786
0.3692.4882.789
0.372.512.791
0.3712.5322.794
0.3722.5552.796
0.3732.5772.798
0.3742.62.8
0.3752.6232.801
0.3762.6462.802
0.3772.6692.803
0.3782.6922.803
0.3792.7152.803
0.382.7392.803
0.3812.7622.803
0.3822.7862.802
0.3832.812.8
0.3842.8342.799
0.3852.8582.797
0.3862.8822.794
0.3872.9062.792
0.3882.932.789
0.3892.9542.785
0.392.9782.782
0.3913.0022.778
0.3923.0262.773
0.3933.052.768
0.3943.0742.763
0.3953.0982.758
0.3963.1222.752
0.3973.1462.746
0.3983.172.74
0.3993.1932.733
0.43.2172.726
0.4013.242.719
0.4023.2642.712
0.4033.2872.704
0.4043.312.696
0.4053.3342.688
0.4063.3572.68
0.4073.382.672
0.4083.4032.664
0.4093.4262.656
0.413.4492.648
0.4113.4722.639
0.4123.4952.631
0.4133.5182.623
0.4143.5422.615
0.4153.5662.607
0.4163.592.599
0.4173.6152.592
0.4183.6412.584
0.4193.6672.577
0.423.6952.569
0.4213.7232.561
0.4223.7532.553
0.4233.7852.544
0.4243.8172.535
0.4253.8522.524
0.4263.8882.513
0.4273.9262.499
0.4283.9652.483
0.4294.0062.465
0.434.0482.444
0.4314.0922.419
0.4324.1352.39
0.4334.1782.357
0.4344.2212.32
0.4354.2612.279
0.4364.32.233
0.4374.3352.184
0.4384.3662.131
0.4394.3932.076
0.444.4162.019
0.4414.4331.96
0.4424.4461.902
0.4434.4551.843
0.4444.4591.785
0.4454.4591.729
0.4464.4551.674
0.4474.4481.622
0.4484.4381.571
0.4494.4261.523
0.454.4121.477
0.4514.3971.434
0.4524.381.393
0.4534.3621.354
0.4544.3431.318
0.4554.3231.283
0.4564.3031.251
0.4574.2821.22
0.4584.2611.191
0.4594.241.164
0.464.2191.139
0.4614.1971.115
0.4624.1761.092
0.4634.1551.071
0.4644.1331.051
0.4654.1121.033
0.4664.0911.015
0.4674.070.9991
0.4684.0490.984
0.4694.0280.9701
0.474.0080.9573
0.4713.9880.9455
0.4723.9670.9348
0.4733.9480.925
0.4743.9280.9163
0.4753.9090.9086
0.4763.890.9018
0.4773.8710.896
0.4783.8530.8912
0.4793.8350.8873
0.483.8180.8844
0.4813.8010.8824
0.4823.7840.8814
0.4833.7680.8813
0.4843.7530.8821
0.4853.7380.8838
0.4863.7250.8864
0.4873.7110.8899
0.4883.6990.8943
0.4893.6870.8995
0.493.6770.9056
0.4913.6670.9124
0.4923.6590.92
0.4933.6520.9282
0.4943.6460.9371
0.4953.6420.9466
0.4963.6380.9565
0.4973.6370.9668
0.4983.6370.9774
0.4993.6390.9881
0.53.6420.9988
0.5013.6481.009
0.5023.6551.019
0.5033.6651.029
0.5043.6761.038
0.5053.6891.046
0.5063.7041.052
0.5073.7211.058
0.5083.7391.061
0.5093.7591.062
0.513.781.062
0.5113.8031.059
0.5123.8261.053
0.5133.851.045
0.5143.8741.033
0.5153.8981.019
0.5163.9211.002
0.5173.9430.9819
0.5183.9650.9591
0.5193.9840.9338
0.524.0020.9062
0.5214.0170.8764
0.5224.030.8449
0.5234.040.812
0.5244.0470.778
0.5254.0520.7432
0.5264.0540.7081
0.5274.0530.673
0.5284.050.638
0.5294.0440.6036
0.534.0350.57
0.5314.0250.5373
0.5324.0120.5058
0.5333.9980.4755
0.5343.9820.4466
0.5353.9640.4191
0.5363.9450.3931
0.5373.9250.3685
0.5383.9050.3455
0.5393.8830.3239
0.543.8610.3038
0.5413.8390.2852
0.5423.8160.2679
0.5433.7920.2519
0.5443.7690.2372
0.5453.7450.2237
0.5463.7220.2113
0.5473.6980.1999
0.5483.6740.1895
0.5493.650.18
0.553.6270.1715
0.5513.6030.1638
0.5523.5790.157
0.5533.5560.1509
0.5543.5320.1456
0.5553.5090.141
0.5563.4850.1371
0.5573.4620.1339
0.5583.4390.1314
0.5593.4150.1295
0.563.3920.1282
0.5613.3680.1275
0.5623.3450.1275
0.5633.3210.1281
0.5643.2970.1293
0.5653.2740.1312
0.5663.250.1337
0.5673.2250.1369
0.5683.2010.1408
0.5693.1760.1454
0.573.1510.1508
0.5713.1260.157
0.5723.10.164
0.5733.0740.1721
0.5743.0480.1811
0.5753.0210.1913
0.5762.9930.2026
0.5772.9650.2153
0.5782.9360.2295
0.5792.9070.2454
0.582.8770.2631
0.5812.8460.2828
0.5822.8140.3049
0.5832.7820.3297
0.5842.750.3574
0.5852.7170.3884
0.5862.6830.4233
0.5872.650.4625
0.5882.6170.5066
0.5892.5850.556
0.592.5540.6115
0.5912.5250.6736
0.5922.50.7428
0.5932.480.8196
0.5942.4660.9042
0.5952.4610.9962
0.5962.4671.095
0.5972.4851.199
0.5982.5171.308
0.5992.5671.417
0.62.6341.526
0.6012.7191.629
0.6022.8241.724
0.6032.9461.805
0.6043.0851.869
0.6053.2361.911
0.6063.3961.928
0.6073.5581.918
0.6083.7151.881
0.6093.8621.817
0.613.9921.732
0.6114.1011.631
0.6124.1881.52
0.6134.2531.405
0.6144.2981.29
0.6154.3241.179
0.6164.3371.075
0.6174.3370.9782
0.6184.3290.8904
0.6194.3140.8109
0.624.2940.7395
0.6214.2710.6755
0.6224.2450.6183
0.6234.2190.5672
0.6244.1910.5216
0.6254.1640.4808
0.6264.1370.4442
0.6274.110.4113
0.6284.0830.3818
0.6294.0580.3552
0.634.0330.3312
0.6314.0090.3094
0.6323.9850.2896
0.6333.9630.2717
0.6343.9410.2553
0.6353.920.2403
0.6363.90.2266
0.6373.8810.214
0.6383.8620.2024
0.6393.8440.1917
0.643.8270.1819
0.6413.810.1728
0.6423.7940.1643
0.6433.7780.1565
0.6443.7630.1492
0.6453.7480.1424
0.6463.7340.136
0.6473.7210.1301
0.6483.7080.1246
0.6493.6950.1194
0.653.6820.1145
0.6513.670.1099
0.6523.6590.1056
0.6533.6480.1016
0.6543.6370.09777
0.6553.6260.09417
0.6563.6160.09076
0.6573.6060.08754
0.6583.5960.08449
0.6593.5860.0816
0.663.5770.07886
0.6613.5680.07626
0.6623.5590.07378
0.6633.550.07143
0.6643.5420.06919
0.6653.5340.06705
0.6663.5260.06502
0.6673.5180.06308
0.6683.510.06122
0.6693.5030.05945
0.673.4950.05776
0.6713.4880.05613
0.6723.4810.05458
0.6733.4740.0531
0.6743.4680.05167
0.6753.4610.0503
0.6763.4550.04899
0.6773.4480.04773
0.6783.4420.04652
0.6793.4360.04535
0.683.430.04423
0.6813.4240.04315
0.6823.4180.04211
0.6833.4130.04111
0.6843.4070.04015
0.6853.4020.03922
0.6863.3960.03832
0.6873.3910.03746
0.6883.3860.03662
0.6893.3810.03581
0.693.3760.03503
0.6913.3710.03428
0.6923.3660.03355
0.6933.3610.03284
0.6943.3560.03216
0.6953.3520.03149
0.6963.3470.03085
0.6973.3430.03023
0.6983.3380.02963
0.6993.3340.02905
0.73.330.02848
0.7013.3250.02793
0.7023.3210.0274
0.7033.3170.02688
0.7043.3130.02637
0.7053.3090.02589
0.7063.3050.02541
0.7073.3010.02495
0.7083.2970.0245
0.7093.2940.02406
0.713.290.02364
0.7113.2860.02323
0.7123.2820.02282
0.7133.2790.02243
0.7143.2750.02205
0.7153.2720.02168
0.7163.2680.02132
0.7173.2650.02096
0.7183.2620.02062
0.7193.2580.02028
0.723.2550.01996
0.7213.2520.01964
0.7223.2480.01933
0.7233.2450.01902
0.7243.2420.01873
0.7253.2390.01844
0.7263.2360.01815
0.7273.2330.01788
0.7283.230.01761
0.7293.2270.01734
0.733.2240.01709
0.7313.2210.01684
0.7323.2180.01659
0.7333.2150.01635
0.7343.2120.01611
0.7353.210.01588
0.7363.2070.01566
0.7373.2040.01544
0.7383.2010.01522
0.7393.1990.01501
0.743.1960.0148
0.7413.1930.0146
0.7423.1910.0144
0.7433.1880.01421
0.7443.1860.01402
0.7453.1830.01383
0.7463.1810.01365
0.7473.1780.01347
0.7483.1760.01329
0.7493.1730.01312
0.753.1710.01295
0.7513.1690.01279
0.7523.1660.01262
0.7533.1640.01247
0.7543.1620.01231
0.7553.1590.01216
0.7563.1570.01201
0.7573.1550.01186
0.7583.1520.01171
0.7593.150.01157
0.763.1480.01143
0.7613.1460.01129
0.7623.1440.01116
0.7633.1420.01103
0.7643.1390.0109
0.7653.1370.01077
0.7663.1350.01064
0.7673.1330.01052
0.7683.1310.0104
0.7693.1290.01028
0.773.1270.01016
0.7713.1250.01005
0.7723.1230.009936
0.7733.1210.009825
0.7743.1190.009715
0.7753.1170.009608
0.7763.1150.009502
0.7773.1130.009398
0.7783.1120.009296
0.7793.110.009195
0.783.1080.009096
0.7813.1060.008998
0.7823.1040.008902
0.7833.1020.008808
0.7843.1010.008715
0.7853.0990.008623
0.7863.0970.008533
0.7873.0950.008444
0.7883.0930.008357
0.7893.0920.008271
0.793.090.008186
0.7913.0880.008103
0.7923.0870.008021
0.7933.0850.00794
0.7943.0830.00786
0.7953.0820.007781
0.7963.080.007704
0.7973.0780.007627
0.7983.0770.007552
0.7993.0750.007478
0.83.0740.007405
0.8013.0720.007333
0.8023.070.007262
0.8033.0690.007192
0.8043.0670.007123
0.8053.0660.007055
0.8063.0640.006988
0.8073.0630.006921
0.8083.0610.006856
0.8093.060.006792
0.813.0580.006728
0.8113.0570.006665
0.8123.0550.006604
0.8133.0540.006543
0.8143.0520.006482
0.8153.0510.006423
0.8163.0490.006364
0.8173.0480.006307
0.8183.0470.006249
0.8193.0450.006193
0.823.0440.006137
0.8213.0420.006083
0.8223.0410.006028
0.8233.040.005975
0.8243.0380.005922
0.8253.0370.00587
0.8263.0360.005818
0.8273.0340.005768
0.8283.0330.005717
0.8293.0320.005668
0.833.030.005619
0.8313.0290.00557
0.8323.0280.005523
0.8333.0260.005475
0.8343.0250.005429
0.8353.0240.005383
0.8363.0230.005337
0.8373.0210.005292
0.8383.020.005248
0.8393.0190.005204
0.843.0180.00516
0.8413.0170.005117
0.8423.0150.005075
0.8433.0140.005033
0.8443.0130.004992
0.8453.0120.004951
0.8463.0110.00491
0.8473.0090.00487
0.8483.0080.004831
0.8493.0070.004792
0.853.0060.004753
0.8513.0050.004715
0.8523.0040.004677
0.8533.0020.00464
0.8543.0010.004603
0.8553.00.004566
0.8562.9990.00453
0.8572.9980.004494
0.8582.9970.004459
0.8592.9960.004424
0.862.9950.004389
0.8612.9940.004355
0.8622.9930.004321
0.8632.9910.004288
0.8642.990.004255
0.8652.9890.004222
0.8662.9880.004189
0.8672.9870.004157
0.8682.9860.004125
0.8692.9850.004094
0.872.9840.004063
0.8712.9830.004032
0.8722.9820.004002
0.8732.9810.003972
0.8742.980.003942
0.8752.9790.003912
0.8762.9780.003883
0.8772.9770.003854
0.8782.9760.003825
0.8792.9750.003797
0.882.9740.003769
0.8812.9730.003741
0.8822.9720.003714
0.8832.9710.003686
0.8842.970.003659
0.8852.9690.003633
0.8862.9680.003606
0.8872.9670.00358
0.8882.9670.003554
0.8892.9660.003528
0.892.9650.003503
0.8912.9640.003478
0.8922.9630.003453
0.8932.9620.003428
0.8942.9610.003404
0.8952.960.003379
0.8962.9590.003355
0.8972.9580.003332
0.8982.9570.003308
0.8992.9570.003285
0.92.9560.003262
0.9012.9550.003239
0.9022.9540.003216
0.9032.9530.003193
0.9042.9520.003171
0.9052.9510.003149
0.9062.9510.003127
0.9072.950.003106
0.9082.9490.003084
0.9092.9480.003063
0.912.9470.003042
0.9112.9460.003021
0.9122.9460.003
0.9132.9450.00298
0.9142.9440.002959
0.9152.9430.002939
0.9162.9420.002919
0.9172.9410.002899
0.9182.9410.00288
0.9192.940.00286
0.922.9390.002841
0.9212.9380.002822
0.9222.9370.002803
0.9232.9370.002784
0.9242.9360.002765
0.9252.9350.002747
0.9262.9340.002729
0.9272.9340.00271
0.9282.9330.002692
0.9292.9320.002674
0.932.9310.002657
0.9312.9310.002639
0.9322.930.002622
0.9332.9290.002605
0.9342.9280.002587
0.9352.9280.00257
0.9362.9270.002554
0.9372.9260.002537
0.9382.9250.00252
0.9392.9250.002504
0.942.9240.002488
0.9412.9230.002472
0.9422.9230.002455
0.9432.9220.00244
0.9442.9210.002424
0.9452.920.002408
0.9462.920.002393
0.9472.9190.002377
0.9482.9180.002362
0.9492.9180.002347
0.952.9170.002332
0.9512.9160.002317
0.9522.9160.002302
0.9532.9150.002288
0.9542.9140.002273
0.9552.9140.002259
0.9562.9130.002244
0.9572.9120.00223
0.9582.9110.002216
0.9592.9110.002202
0.962.910.002188
0.9612.910.002174
0.9622.9090.002161
0.9632.9080.002147
0.9642.9080.002134
0.9652.9070.00212
0.9662.9060.002107
0.9672.9060.002094
0.9682.9050.002081
0.9692.9040.002068
0.972.9040.002055
0.9712.9030.002042
0.9722.9020.00203
0.9732.9020.002017
0.9742.9010.002005
0.9752.9010.001992
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1.6242.7376.801e-06
1.6252.7376.614e-06
1.6262.7376.429e-06
1.6272.7376.247e-06
1.6282.7376.068e-06
1.6292.7375.891e-06
1.632.7375.718e-06
1.6312.7365.547e-06
1.6322.7365.379e-06
1.6332.7365.214e-06
1.6342.7365.051e-06
1.6352.7364.891e-06
1.6362.7364.734e-06
1.6372.7364.58e-06
1.6382.7364.428e-06
1.6392.7364.279e-06
1.642.7364.133e-06
1.6412.7363.989e-06
1.6422.7353.848e-06
1.6432.7353.71e-06
1.6442.7353.574e-06
1.6452.7353.441e-06
1.6462.7353.311e-06
1.6472.7353.183e-06
1.6482.7353.058e-06
1.6492.7352.936e-06
1.652.7352.816e-06
1.6512.7352.699e-06
1.6522.7342.584e-06
1.6532.7342.472e-06
1.6542.7342.363e-06
1.6552.7342.256e-06
1.6562.7342.152e-06
1.6572.7342.05e-06
1.6582.7341.951e-06
1.6592.7341.854e-06
1.662.7341.76e-06
1.6612.7341.669e-06
1.6622.7341.58e-06
1.6632.7331.493e-06
1.6642.7331.409e-06
1.6652.7331.328e-06
1.6662.7331.249e-06
1.6672.7331.172e-06
1.6682.7331.098e-06
1.6692.7331.027e-06
1.672.7339.578e-07
1.6712.7338.912e-07
1.6722.7338.271e-07
1.6732.7337.655e-07
1.6742.7327.062e-07
1.6752.7326.494e-07
1.6762.7325.951e-07
1.6772.7325.432e-07
1.6782.7324.936e-07
1.6792.7324.465e-07
1.682.7324.018e-07
1.6812.7323.595e-07
1.6822.7323.196e-07
1.6832.7322.821e-07
1.6842.7322.469e-07
1.6852.7322.141e-07
1.6862.7311.837e-07
1.6872.7311.556e-07
1.6882.7311.299e-07
1.6892.7311.065e-07
1.692.7318.544e-08
1.6912.7316.672e-08
1.6922.7315.033e-08
1.6932.7313.626e-08
1.6942.7312.45e-08
1.6952.7311.505e-08
1.6962.7317.892e-09
1.6972.7313.029e-09
1.6982.734.522e-10
1.6992.730.0
1.72.730.0

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
—